SLAC-R-336 - Stanford University

SLAC-R-336
SLAC
CONF
- 336
- 880747
UC-34d
(T/W
PROCEEDINGS
OF
SUMMER
INSTITUTF,
ON PARTICLE
PHYSICS
July 18-29,1988
PROBING THE WEAK INTERACTION:
Cl? VIOLATION
AND RARE DECAYS
Program
Directors
Gary J. Feldman
Frederick
J. Gilman
David W. G. S. Leith
Ed. by Eileen C. Brennan
Sponsored
contmct
by Stanford
University
with the U.S. Department
and Stanford
of Energy.
January
Printed
in the United
mation
Service, U.S. Department
VA 22161.
States of America.
Linear
Contract
Accelerator
Center
under
DE-AC03-76SF00515.
1989
Available
of Commerce,
from National
Technical
Infor-
5285 Port Royal Road, Springfield,
:
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PREFACE
::-’ . . .:
‘.. -,,:. -’
The sixteenth annual SLAC Summer Institute
on Particle Physics was held
from July 18-29, 19S8. The subject of “Probing the Weak Interaction:
CP Violation and Rare Decays” was studied in both its experimental
and theoretical
aspects by a total of 342 participants
from thirteen countries. The school portion
of the Institute featured excellent lectures on this subject by K. Berkelman, I. Bigi,
B. Cabrera, L. Hall, H. Harari, J. Sandweiss, A.J.S. Smith, M. Witherell,
and L.
Wolfenstein.
The afternoon discussion were wry much enhanced and enlivened by
C. Ahn, R. Aleksan, M. Davier, C. Dibb, R. Ezmaizaldeh,
R. Frey, J. Frieman,
RI. Karliner,
R. Kauffman,
I. Klebanov, A. Lankford,
B. Lockman, C. Munger,
J. Ritchie, D. Shroeder, N. Wang, A. Weinstein,
and M. Woods who acted as
were taken
“provocateurs.”
As is tradit’ lonal, the last three days of the Institute
up by a Topical Conference, with invited talks from ongoing experiments
and the
associated theory.
We thank Eileen Brennan for organizing and running the meeting, and with
great persistence, editing these Proceedings.
She and her staff contributed
much
to the success of the meeting both through their hard work and their good humor.
Gary Feldman
Frederick J. Gilman
David W. G. S. Leith
Program Directors
..
TABLE
OF CONTENTS
page
Part I. LECTURES
I. I. BIG1
“Precious Rarities -On
Rare Decays of K, D and B Mesons”
B. CABRERA
“Superconducting Detectors for Monopoles and
Weakly Interacting Particles”
.
.
L. J. HALL
“Cosmic Relics from the Big Bang”
. .
M. S. WITHERELL
“Double Beta Decay”
.
.
. .
. .
.
. 69
.
85
125
.
H. HARARI
“The Bottom Quark: A Key to ‘Beyond Standard’ Physics”
A.J.S. SMITH
“Experimental
Part II.
TOPICAL
Searches for Rare Decays”
. .
. 31
105
L. WOLFENSTEIN
“Neutrino Masses and Mixings”
J. SANDWEISS
“&Physics in Fixed Target Experiments”
1
.
. .
. .
.
. .
.
. 143
145
. . 147
.
. 151
N. KATAYAMA
“Recent Results from CLEO -An Observation of R” - B” Mixing
and a Search for Charmless B Meson Decays, B- -t p@n- and
3
-+ pfhr+lr-” ., . . . .
D. B. MACFARLANE
“B Decay Studies from ARGUS”
CONFERENCE
+ e+X”
.
J. SHIRAI
“Recent Results from TRISTAN”
M. S. WITHERELL
‘LProspects for B Physics”
S. CONETTI
“Hadroproduction
. . . . . . . . .
.
. . . . . . . 167
.
183
209
.
.
.
.
of $ and X States”
217
.
.
241
.
253
.
B. T. MEADOWS
“Recent Results on S = -3 Baryon Spectroscopy from the
LASS Spectrometer”
.
.
255
S. R. SHARPE
“Calculations of Hadronic Weak Matrix Elements:
A Status Report”
.
.
.
271
J. M. LOSECCO
“Recent Results from IMB”
M. KOSHIBA
“The Neutrino Astrophysics:
H. SCHELLMAN
“Neutrino Production
.
289
.
Birth and Future”
of Charm at FNAL E744”
C. N. BROWN
“Twenty Years of Drell-Yan Dileptons”
CONFERENCE
C. YANAGISAWA
“Recent Results from CUSB-II”
TOPICAL
D. PITMAN
“Evidence for ot
K. BERKELMAN
“Results on b-Decay in e+ e- Collisions, with Emphasis on
CP Violation”
. .
.
. .
.
Part II.
R. J. MORRISON
“Recent Results from E691”
V. CHALOUPKA
“Study of K+ -+ a+e+e-,
K+-+x+p+e-atBNL”
.
,
.
.
.
301
.
315
.
327
.
335
and Search for
. . .
W. M. MORSE
“Search for Flavor Changing Neutral Currents. . . .
I(; -+ p*eF, e+e- and s”ete-’
,347
.
.
355
Part II.
TOPICAL
CONFERENCE
page
G. ZECH
“Observation of Direct CP Violation and Status of the
Qoo - Q+- Measurement in the NA-31 Experiment at CERN” .
.
367
B. PEYAUD
“Results from E731 - $ Measurement at FNAL”
.
.
. .
P. R. BURCHAT
“Status of the SLAC Linear Collider and Mark II”
. . .
.
.
399
D. AMIDE1
“Results from the CDF Experiment
.
. . . .
.
415
at Fermilab”
. 389
APPENDIX
.
.
List of Participants
Previous SLAC Summer Institute
.
. . .
. . _ . . .
Titles and Speakers
.
.
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-62-
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-.
Precious
On Rare
Decays
Rarities
-
of K, D and B Mesons
I. 1. Bigi
:
._,:
. .
:
Department of Physics
University of Notre Dame
Notre Dame, IN 46556
Abstract:
A detailed analysis of K decays has been quite instrumental, if not even crucial for
developing the present Standard Model of particle physics. There is no reason to
believe that such a line of research has already exhausted its discovery potential. Quite
on the contrary we can suspectthat further dedicated studies of the rare decays of K, B
and maybe even D mesons will reveal “New Physics.” At the very least they will
provide highly sensitive tests of the Standard Model. A crucial element in any such
analysis is the reliability of the theoretical tools that are employed. I attempt to give a
comprehensive and detailed evaluation of the scope and the Iimitadons of the various
theoretical technologies that are presently available.
:
.
-..,.1.
.-.
@I. Bigi 1988
-31-
‘.:
. . .. .
.
:.
_ ,.. _-’
I believe that “praying” for inspiration coupled with “working” hard to make
1. INTRODUCTION
An event is called m if it occurs with a probability much smaller than unity.
This, however, does not make it automatically an interesting object for study. The case
of elephant-antielephant fluctuations is sometimes used to illustrate this point. While
there exists no first principle forbidding them to contribute to, say, (g-2) for muons it is
measurements and to calculate rates represents the appropriate method for our field;
therefore, I will use this approach as guidance in the subsequent discussion. May I add
in passing that any similarity between the approach sketched under b and an existing
theoretical school is purely accidental.
The question we want to addressthen is:
“Flavours: Whence do they come - where do they go?”
Yet it has to be understood that even a detailed study of flavour decays (“where
do they go”) will not reveal directly and immediately the reason behind the existence of
different flavours (“whence do they come”). What can be achieved or learnt is the
following:
(a) There has to be a dvnamical distinction between the different flavours; the
utterly obvious that those contributions can safely be ignored. In the following I will
call a rare event precious only if there exists a realistic chance for it to be ever ohserved
- even if it takes many years
Since I am the first lecturer at this Summer Institute, I can be forgiven for
making a few general remarks although later speakerswill address these issues in more
detail and with presumably more eloquence as welt.
The theoretical landScapepresents itself today as a combination of strong and
.-.
.
I
._._:
_-
existence of such new forces - i.e., “New Physics”, hereafter referred to as NP
would in general lead to decay processes
(l.lj
M-1;
1;
electroweak forces which are described in terms of a gauge theory based on the group
SU(3), x SU(Z)L x U(1). (For these lectures 1 ignore the existence of gravity and I do
so without feelings of guilt.) Tomorrow’s theoretical landscape will stilt contain QCD
as the theory of strong interactions; yet the question on the underlying electrowcak
theory remains quite unsettled. This is to sdy that QCD is the “only thing” whereas the
Sum x U(1) gauge theory is only the “best thing”; for the latter merely incorporates
many of the fundamental mysteries of particle physics without offering any
explanations: what is the origin of the various flavour degrees of freedom, why do
they exhibit a family structure and family replication, etc. etc.?
M----ml:
(1.2)
1;
where M and m denote mesons and .-!I and 12 different charged leptons.
Examples are
Enlightenment can be sought via two alternative routes:
&
_::
,^
K,--.+
e*p’
K+-
K+,*$
These processes are strictly forbidden in the Standard Model since they would
violate the individual lepton number.
One can adopt the approach pioneered by the “Eastern Monks” --- These sages
living typically by themselves or in very small groups sought enlightenment by pure
thinking and meditating. Their contacts with the rest of society were rather limited:
Processesof the type
M-
pious people from the surrounding villages and towns would come out to see these
venerable monks and would do so in the hope of being addressedby them (though with
1’1.
(1.3)
(1.4)
M-m1
2
on the other hand can be generated in the Standard Model as a l-loop quantum
effect; yet NP can boost their nansition rates very significantly, modify the
kinematical distributions of the decay products or it could even produce CP
asymmetries!
scant hope to understand such teachings).
B_1 One can follow the example set by the “Western Monk Orders” --- Large
collaborations that set out to cut down forests, take virgin land under the plow, baptize
the heathens (with occasional, unfortunate losses) and do all of this under the motto of
“ora et labora”!
I had already stated the obvious: discovery of this kind of New Physics per se
would not resolve the flavour mystery. However it would teach us lessons that
-32-
..
:. !.-,,: ,:
:,
Perturbation Theory; rare D decays are treated in Sect. V and rare B decays in Sect. VI;
the conclusions are presented in Sect. VII.
I had already stated the obvious: discovery of this kind of New Physics per se
would not resolve the flavour mystery. However it would teach us lessons that
are of crucial importance for any such resolution, namely (i) that a dynamical
distinction does indeed exist and (ii) by which mass scale it is characterised.
Measuring the rates of those transitions that within the Standard Model - can
._
001s
proceed only via l-loop effects will allow us to probe fundamental parameters like
-
quark
diagrams
-
;.
ChPT
I/N
QCD SR
.:.
..,:
:,
:..:
:
.’
‘;..
.-.
~_/
lavour
m(top) and the KM parametersV(td), V(ts).
At the very least we will learn important or even crucial lessonson QCD lessons
that are rather unique due to the interplay of weak forces and strong forces that
occurs in flavour decays.
The last item points also to a central problem in this line of research: when one
finds a difference between an expected and a measured decay rate one would like to
claim that such a discrepancy indirectly establishes the existence of New Physics! Yet
one has to be concerned that this merely signals the need for “New, i.e., better
Physicists or Theorists” meaning that our theoretical computations contained hidden
uncertainties. Therefore we have to subject our tools to a very careful evaluation and
re-evaluation.
There exists a naive folklore about the available theoretical technologies, namely
that our calculations become necessarily more reliable for heavier flavours, i.e., when
going from K decays to D decays and then B decays. One usually cites as supporting
evidence for this folklore that the heavier a flavour hadron is, the more short-distance
dominated its dynamics become. This is reflected also in the emergence of a more and
more universal lifetime for flavour hadrons when their mass increases: ‘T(K*) - 600
z(K,) vs. r(D*) - 2.5 r(Do) vs. r (Bi) c 2 1 (Bd).
0
44
4 ??
0
4
t
0
i
Table I
Pattern of reliability that different theoretical tools offer for heavy flavour decays
However I want to urge you not to accept this folklore at face value. For it is
based on rather simplistic considerations read off from quark diagrams. There are other
theoretical technologies that enjoy a much less tenuous relationship with QCD and that
yield quite a different pattern of reliability for their predictions This is sketched in
Table I, where the symbol ” 0 ” means “not applicable”, ” 44 ” “quite reliable
application”
and “4” “order of magnitude estimates.”
Thus we see that the
‘:
trustworthiness of a theoretical computation has to be evaluated almost on a case-bycase level - a central point of these lectures.
These lectures are organized as follows:
;.
-.
in Sect. II, I discuss K, D and B
decays that are strictly forbidden in the Standard Model; in Sect. 111and IV, I treat K
decays that occur due to quantum corrections; in Sect. III it is the process K+ + rt+ +
“unseen” whereas in Sect. IV, I analyse radiative K decays in the framework of Chiral
-33-
:,
..:..,.
.:::
..- . .
.~..
.
II. “A FARMER AND HIS SON VISIT VIENNA” OR
“BREAKING THE FLAVOUR CODE”
Our understanding of the flavour puzzle - why are there families, why are they
so much alike? - can be illustrated by the following story: A farmer from a little town
had to visit the great city of Vienna to take care of some business. He decided to bring
his little son along who had never seenVienna. While they walked through the streets
the little boy was all eyes and looked left and right. He then pointed at a big building
and asked: “Hey, Daddy, what is this.7” His father looked at it, scratched his head,
A very convenient classification of the effective couplings that generate these
reactions has been provided by Buchmiiller and Wyler.(l) Only “low energy” fields
appearexplicitly, namely
matter fields
photons
weak bosons
light Higgs fields
&SW denotes the Lagrangian of the Standard Model and A:
Anticipating that ANP >>A
(2.2)
characterize the mass
- otherwise we would have seen already these
processes - we conclude that ZN~ better be invariant under SLJ(3)ex S(~)L x U(1)
rotations.
Exchanges of such bosons would produce processeslike
e+e- + ep, er, pr
G
describes the coupling of two scalar fields - @or $* - to two fermion fields
fl and f2 as shown in Fig. 1. Since the two fermion fields have to form a scalar (or
pseudoscalar), one of them has to be left-handed and the other one right-handed.
Accordingly they carry the same electroweak quantum numbers as the left-handed field
alone, namely a weak isospin of half a unit and a non-vanishing hypercharge. If the
two scalars that couple to these fermions are the Higgs field $ and its conjugate $’ then
or
ep --t IX, 7X
which can be searchedfor. At low energies they will produce decay processes
.
:_
scale of the new interactions - again in analogy to the Fermi constant GF = lMk
families, i.e. one that goes beyond the mere difference in mass; in particular there could
be a neurral boson Y which connects members of different families
Y-il~2>l*
#I,.
Ltj,
and
tCd=@
NP +
be secured; it only means that we have to be more persistent and maybe have to
rephrase our questions.
In all likelihood there has to be a dynamical distinction between the different
M-m
Y
W,Z
Q
they carry zero hypercharge; such a coupling cannot be SU(Z)L x U(1) invariant and,
following our prescription stated above, is therefore ruled out. If on the other hand the
two scalars are I@$or $*I$’ then they carry weak isospin one. The two fermions would
(2.1)
It is those that we are going to analyze.
have to cany isospin one as well which - as mentioned above - is not possible. There
is one tiny loophole in this last argument: the right-handed fermion field could be the
charge conjugate of a left-handed field and a weak isospin of one unit is thus attainable.
However such a coupling violates fermion number by two units and is thus allowed at
-34-
‘..
generatenon-renormalizable interactions of dimension d > 5:
questions?” whereupon his father replied: “Of course not, my son, how can you learn
something if you don’t ask questions!” The fact that we have not received yet a
satisfactory answer to the flavour puzzle does not imply that no such answer can ever
r,m,
(either leptons or quarks)
All other fields are “integrated out” in the same fashion as W boson fields are
“integrated out” in the effective weak Lagrangian. There this procedure introduced the
non-renormalizable Fermi interaction of dimension six; here more generally it will
looked at it again, shook his head and said: “I don’t know, my son.” This sequence the son asking a question and his father being unable to answer it - repeated itself a few
times, Then the son said: “Daddy, are you getting mad at me for asking all these
M-
f
:.
,-.
.
. ..
best for neutral fermion fields, namely neutrinos, where such couplings produce
Majorana mass terms. Yet the corresponding scale A,“p has to be huge’and a term
+
c”.
NP ts quite academic in the present context.
Aw
Thus one arrives at a result that one would have guessedimmediately and quite
naively, namely that the New Physics can be described by a dimension six term:
(d = 6)
a;
L elf- -c(Wciw +A
(2.3)
i@j2
w
f, f2
v
Zg”
=C
ci l current x current
^_
I
‘-
‘..
(2.4)
I
The c number coefficients cl are determined by the specific dynamical model one has in
mind.
There is no shortage of such dynamical models: there are many GUTS on the
market that contain “horizontal” interactions, i.e., flavour changing neutral currents
(= FCNC) mediated via spin one or spin zero bosom; extended technicolour models
can be accused of many vices, but not of forbidding FCNC; the same holds for
composite models. Such new forces can in particular be mediated by so-called “leptoquarks” (= LQ), i.e., bosons that carry both lepton and quark quantum numbers. They
Fig. I
emerged first in Pati-Salam models based on a gauge group SU(4) where lepton
number is treated as a fourth colour. Yet they appear in many other models as well and
Fig. 1:
represent a rather generic feature of models that are inspired by a superstring ansatz.
Even “ordinary” Supersymmetry enters this arena if sneutrinos develop a nonvanishing vacuum expectation value. In summary, there are many models that will
produce non-vanishing values for the coefficients ci in (2.4); however nothing definite
can be said or predicted concerning their actual values. In addition, the couplings of
FCNC to up-type quarks - u, c. t - could a priori be.completely different from those to
A dimension five coupling of two scalar fields to two fermion fields.
down-type quarks - d, s, b. In that senseone gains independent pieces of information
when searching for K + elt &D + elr decays.
B. The Down Side
So far we have looked at the optimistic side of things; now let us review the
more depressing aspects.
-35-
..
(i)
(ii)
No decay that violates lepton flavour conservation like K + ep, R ep. D -+ ep,
eprr, or B + ep, epK has been observed yet. The bounds on ANY that can be
derived from that will be given below.
Exactly becausethe New Physics contributions are new they cannot interfere with
the Standard Model conuibutions. Therefore one finds for the branching ratios
.,
.. ..
: 21
_
..
-.
(2.5)
where My denotes the mass of the “new” boson Y and gyq[gyl] its couplings to
quarks [leptons]. An increase in experimental sensitivity, as far as branching
ratios are concerned, by a highly impressive factor of 1O‘ttranslates itself into a
much more modest increaseby a factor of 10 in sensitivity for the mass My! This
is not encouraging when one keeps in mind that no theoretical upper limit on My
has been suggested so far that is reasonably reliable. A non-observation of these
decays will therefore not lead to a breakdown of any meaningful theoretical
benchmark. Such searchesare therefore not for the faint-hearted!
==&
Y
----
s
Fig. 2
(iii) However they are not for the reckless either! The decay of a pseudoscalarmeson
PS = (Q 4) + 1t1,
(u)
is represented in Fig. 2 for an s-channel exchange of the Y
boson. Its transition rate is subject to two concurrent suppression mechanisms:
If Y carries spin one then the rate is helicity suppressed, i.e., it vanishes for
Fig. 2:
Diagram for the decay of a pseudoscalarmeson into a lepton pair.
m(It), m (12) + 0. More specifically
(2.6)
If Y is spinless there is no such “kinematical” suppression. Yet scalar
couplings violate chiral invariance; since this symmetry is apparently the only
principle that can keep fermion masseslight one (as a theorist) is very reluctant to
give it up. Accordingly, one susoects that all such scalar or pseudoscalar
couplings depend on the mass of the field they couple to - exactly Eke Higgs
:
.<
bosons. Thus
-36-
.:
‘.
:
:
I believe that x”,
(2.7)
(p)
M --f m ltz2
transitions whereas
without mass
ANY
suppression factors.
The existing bounds are summarized in Table II, where I have underlined the
“most likely” bounds as explained above.
as before, but this time due to genuine dynamical considerations - as perceived
by theorists.
The exchange of these massive Y bosom produces pointlike interactions, i.e.,
forces of zero range. The transition amplitude then depends on the wave function
of the decaying meson at zero separationor the decay constant:
Process
(2.Q
For K + ep we have
l Mtc
rnN--;s
fk-
is the appropriate quantity for M -+R,l,
decays offer a much better chance to probe
BR
ANP
KL-+v
< 10-8
< 35 TeV
K+ -+ tr+ep
Do+ep
B + ep
< 4.8 x 10-q
< 4.1 x 10-5
< 3 x 10-S
< 20 TeV
< 1 TeV
< 3.4 TeV
;.
_.
:
‘.
: :
.:
Aw
< 16TeV
<9TeV
< 0.24 TeV
c 0.5 TeV
Table II
f M,
and these suppression factors are not huge.
For D + el, B --f ep on the other hand, we encounter huge suppression
factors since rn+ C< rnD < mg, fD << mD and fB << mg. Let me list just one telling
For details on the experimental numbers see the lectures by K. Berkelman and
A. J. S. Smith.@*5)
example: the mode Do + e$’ has been searchedfor unsuccessfully leading to(z)
BR @” -+ e’p’ ) < 0.41 x lOA
E691
(2.9)
C. Resume on the forbidden decavs M+(m) Rt&
(i)
Yet this apparently impressive bound loses its luster if compared to the upper limit on
the quite ordinary mode D+ --f @u:(3)
There is an obligation to continue careful and dedicated searchesfor these striking
decay modes.
(ii)
Improved experimental upper bounds just raise the bounds on ANY, the mass
scale characterizing the New Physics that distinguishes between the different
BR(D++D+v,,
)<6x104
MARKIIJ
(2.10)
From this number one extracts fD _<290 MeV; theoretically one estimates fD - 150-200
MeV and therefore
families, and they do it very slowly
A
NP*min-Qii&
2
BR(D+-+~+v~
._”
“.._:
,:
:..
)=1.5x104
&
(2.11)
i
1
Compare (2.9) with (2.11). and I can rest my case.
When extracting bounds on mass scales that characterize New Physics one
Unfortunately, no sound theoretical upper bounds on Arqp have been
established so far. but this might change in the future.
(iii) Searchesfor D + ekt or B + ep are classical examples of “lamp post searches”:
should therefore quote numbers for two quantities, namely ANP as it appears in (2.3)
one looks for something where it can be seen most easily, not where one has the
best chance of finding it. Nevertheless it would be imprudent to discontinue
them.
M,
-2 = r\2
M,
with ci = 1 (see 2.4) and ANP
up x M, ( i.e., ci = M
Ps
As explained above,
-37-
;. ;. .:
._
-
(iv) In any case one m
search for D -r x/p ep and B + K/K’ ekr decays as well,
or even better for the inclusive modes D + ep + X, B + ep + X. They are not
(v)
III. K+ + z@+ “nothine seen” - THE PRECIOUS RARITY PAR EXCELLENCE
affected by helicity suppression and the inclusive rates are also not reduced by
(f&n&
or (‘B/m&* respectively.
Furthermore the different decays are governed by different hadronic matrix
elements; e.g.,
~0 I~fllD>
CJ
D --t ep
The transition
K++
x+vv
(3.1)
requires a FCNC; in the Standard Model it has therefore to proceed via a one-loop
process as shown in Fig. 3. Computing the contributions of these diagrams -- which
amounts to integrating out the heavy fields W, Z, t, c -- one obtains the effective
interaction Z&AS = I).(@ To cakulate a rate one has to form the appropriate matrix
<K IV&t D>
D+rtek
G
D-r pep
t)
<p IA&D>
where S, P, V, Audenote scalar, pseudoscalar, vector and axialvector currents
element
respectively.
(vi) The mixing angles that are contained in the couplings of these FCNC could in
principle be “dialed” in such a way as to greatly suppress, say, K --f ttep, while
not reducing D -+ nep. In that sense studies of rare K and rare D decays are
<n+v?
Ize,(AS=l)
1 K+>=coeff.
jT<x’
IJF IK’>
(3.2)
With this perturbative treatment one can compute the c number coeff., the leptonic
0)
current J tr and one can identify the general transformation properties of the hadronic
(4
current ’ a. Yet one cannot obtain the magnitude of the on-shell matrix element
complementary, not competitive. It is however a different question whether this
can make up for the much smaller branching ratios that can be reached in K
decays vs. D decays.
<I[+IJFIK+>this way since the latter depends on long-distance dynamics.
Fortunately the well-measured decay K -r tt ev depends on a matrix element
< 8’ IJtI K+ >that can be related to < x+ 1J,“I K+> via an isospin rotation of the
hadronic current and that is probed at almost the identical momentum transfer.
There is a small loophole in this line of reasoning which is analyzed in the
Appendix A and then discarded. BR (K+-trr+ w) can thus be expressed mainly in
terms of quark and lepton parameters- masses,KM angles; the impact of long-distance
dynamics is isolated into one hadronic matrix element whose size can be obtained from
the memred decay K -+ xev:
2
BR(K+ -+ IC+v v) z 1.43 x 1O.5c
c
I
V* (qs) V (qd) D(xa, y, )
4
1 = e, p, 7 ; q = u, c, t
-3s
(3.3)
V(ij) denote the corresponding KM matrix elements and the function D(x,+ ya) enter
when one integrates out the internal loop in the diagrams of Fig. 3. They were first
calculated by Inami and Lin(6) and for y,~= 0 they read
,‘i
D(x,O)=$
[I+&
-[$)xlogx+;
- &.
..; : _.: :
(3.4)
With three families there are thus three unknown parameters - mt, V(td) and V(ts) - that
determine the rate:
BR (K+ + x+ v, 5, ) = 1.43 x 1O-51V’ (cs) V (cd) D(x,, 0) I2 x
d
, + v’ (ts) VW)
X
D (x,, 0)
2
v’ (cs) V(cd) --i
D (XC.0)
(3.5)
=BR(K++n+v,O,)
RR (K+ --f n’v,vT ) is slightly smaller (at most 20%) since the T mass that enters in the
loop cannot be.completely ignored.
Using the unitarity of the 3 x 3 Kh4 matrix one obtains
V (ts) =. -V (cb) = AX*
(3.6)
where the last equality refers to the Wolfenstein representation P1)
(cl
h = sin9,
Fig. 3
A= 1.1 kO.2
For V(td) no such definite statementcan be made:
V(td)=Ah3
(I-p-iq)
(3.7)
(3.8)
V fub) - Al3 (P-in)
I
1_1
Bounds on IV (ub) I yield information on d P*+qL only, but not on the sign of p
Fig. 3a, b, c: Quark diagrams that generate the transition operator s + d j C
which is quite relevant for
IV(~)I =a3 JFZT
.
Using I p I 2 0.8 as
inferred from semi-leptonic B decaysone finds
<BR(K+-tx+vv)
x10”
<{i\f}
form, = {i}
GeV
(3.9)
where the upper [lower] bound holds for p = -0.8 [+O.S]. If one ignores the top
contribution completely one gets BR (K+ --f B’V C’)= 3 x IO‘“.
-39-
: :_
1..
-:
.
The strength of B, -Ed mixing is directly and crucially affected by I V (td) I
Physics of which I will sketch just a few typical examples that can produce sizeable
rates for
K+ -+ tt+ + “unseen”
and mt. The signals observed by ARGUS and by CLEO strongly favour p < 0 and
tend to push p towards -0.8 unless top quarks are very massive. For the range
50 GeV < mt < 200 GeV one can use the auuroximate scaling laws
bmg =(mt)‘.75
,-__
1. The least radical extension: a fourth family
Dh, 0) = mt
The predictions in (3.9) have to be taken with a certain grain of salt: they were
5;...-.
study are the mass m(t’) and the KM parameters V (t’s) and V (t’d). (For the quark
contributions act coherently whereas the lepton terms are incoherent due to the absence
of lepton flavour mixing. This is explicitly expressedin (3.3))
Making V(t’d) and V(t’s) as large as still allowed by the unitarity constraints on
mc=1.5GeV.
(3.10)
While this representsa reasonablechoice, it is not a uniquely determined one. A range
m,-- 1.2 - 1.8 CeV
has to be allowed for; this in turn leads to a non-negligible variation in
X’V
:
There could exist a fourth family with two new quarks t’ and b’ and two new
leptons A and VA. The new parameters that are most significant for the process under
obtained using
BR (K+ +
-,
a 4 x 4 KM matrix would allow to push BR (K+ --f tt+vv) up to the present
v) in particular for moderate top masses. Using “reasonable” and
experimental upper limits. On the other hand generalizing a Wolfenstein ansatz to four
families or inferring the t’ and b’ parameters from fixed point solutions to the
renormalization group equations leads typically to
“typical” values for the KM parameters,namely
A = 1.1, p = -0.7, q = 0.25
one finds for example a roughly 50%[35%] variation in the branching ratio for a top
mass of 40[100] GeV.
With these caveats in mind we conclude that the present findings on B, - B, mixing
Br(K++
10-9, 10.’
(3.13)
2. Jhe most e&ant extension: SUSY
Supersymmetry introduces new neunino-like states,namely photinos 7 (which
can contain some admixtures of other neutralinos). The process K+ -+ X+ + “nothing
imply
BR (K+ -+ tt+ v v) - 10”’ - 1O-9
x+@)<fewx
(3.11)
seen” can then be realized by
More accurate information on mt, B,- Bdmixing, etc. when it becomes
K++tt+*Iy
(3.14)
available will enable us to restate (3.11) in a more precise way. To say it differently:
there is an upper limit on BR (K+ -+ tt+ V v) that the Standard Model with three
if the photinos are sufficiently light - a possible, though not very likely scenario.
Flavour mixing among the different down-type squarks fi = (a, ~.b)can
families can accommodate; its present value is given in (3.11):
generate K+ + x+ 7 7 already on the tree level as shown in Fig.4 where the dots point
BR(K++rr+vQ
St-M
3fam, <L
out the odd R-parity of the field involved. One finds that(7)
(3.12)
BR (K+ -+ X+ yy) 2 10-r”. 10.’
L (“now”)’ - 1o-9
(3.15)
represent conceivable cases.
Without such flavour mixing in the squark mass matrix, one has to invoke oneloop reactions as sketched in Fig. 5. They typically yield rather small numbers,
If data were to show a branching ratio in excess of such a limit we would have to
conclude that New Physics were at work. There is a whole host of candidates for New
-4o-
: :
,: :;
.
1.
:.
.-
namely
BR (K+ -+ x+ 77) - 10-t’ - lo-”
(3.16)
3. The most stirring extension: direct FCNC via ETC. LO, ,.,
With direct FCNC mediated by the exchange of a new boson of mass M, one
finds
BR (K+ + x+ v&,
+ n+v,&) - 16”
(3.17)
where I have ignored any helicity suppression.
4. The
Fig. 4:
Adopting a phrase coined by M. K. Gaillard one includes here
K+ + n+ + “funnies”
Tree level diagram for K- + R- yf,
where “funnies” stand for axion. familon, majoron, Higgs and all the other even more
fascinating objects that have not been invented yet. I will list just two examples which
are - relatively speaking - the ones with the most specific phenomenology.
(a) Higgs:
The Standard Model contains just one flavour diagonal neutral Higgs field; its
mass mo is - strictly speaking - undetermined. Theoretical constraints like the
Weinberg-Linde bound can be evaded if there is a sufficiently heavy quark field
Q, i.e.
MqZSOGeV
(3.18)
This has actually become a more likely scenario in the absence of a direct
observation of top quarks. A very light Higgs becomes then conceivable and the
process
K++ A+ cp, ‘p + p+ p-, e+ e- , “unseen”
(3.19)
Fig, 5:
could occur due to higher order processes.@)
One-loop diagrams for K’ --t X- “Jy.
No decay of this type has been observed; unless some delicate cancellations
between different contributions occur one has to conclude that K+ + x+ ‘p is
forbidden kinematically. i.e.
mcpZ36OMeV
(3.20)
Going beyond the Standard Model and extending the Higgs sector will lead to
more flavour diagonal neutral Higgs fields cpi. Their Yukawa couplings are not
-41-
.:
I._
,,
.. .
‘.
...
:
uniquely fixed anymore by the requirement that they give mass to the gauge
bosons and fermions.
Thus
m (Cpi)c 360 MeV
(3.2 1)
(0)
IV. OTHER PRECIOUS RARE K DECAYS -- A FIELD DAY FOR CHIRAL
PERTURBATION THEORY
There is a rich class of rare K decays that involve photons both on-and off-shell:
is still allowed if the Yukawa coupling of this light Higgs boson is roughly an
order of magnitude smaller than prescribed by the Standard Model.
Majoron:
KL~Ks+w,w*
+
Neuuinos can obtain a Majorana mass only if lepton number is violated. If this
1+1-
K-+X?’
global symmetry is broken spontaneously then a Goldstone boson will emerge the (generic) Majoron. It can be accomplished by a scalar partner, and both are
typically rather light objects. Then the decay@)
K+ + A+ + 2 light scalars
(4.1)
(4.2)
4
1+1-
K-+lty(
(4.3)
[K + n y is forbidden by gauge invariance (or alternatively, by angular
would be allowed kinematically. Unfortunately it is unlikely that its branching
ratio would exceed that for K’ -+ x+ v v (with three families).
momentum conservation).]
Unfortunately there exists a certain complication that we have to addressat this
juncture - a complication that is sometimes referred to as the “Problem of the Two
Worlds.”
(i) On the one hand there is the world in which theorists work; it is characterized by
distances d 5 lo-** cm; it is populated by quarks and gluons (and... and ...) and it
is this world where theorists indulge themselves in building models and computing
transition rates.
This tour d’ horizon of Old and New Physics can lead to one conclusion only:
Dedicated searchesfor K+-,+
+ “unseen” are a definite must for seriousresearch!
(ii) On the other hand there is the “Real World” where everybody else works and
everybody (theorists included) lives; it is characterized by much larger distances
d 2 IO-t3 cm and is inhabited by hadrons: pions, p mesons, protons etc. It is in
this world that detectors are built and transition rates measured
Obviously one has to establish communication between these two worlds
which allows to translate results that have been obtained in the Theorists’ World into
those that are testable in the Real World and vice versa. This task is, we all believe,
performed by QCD - in principle. In practice however we have so far fallen short of
realizing this noble goal in a comprehensive way.
To cite but one (relevant) example. The decay KL + ?~yis viewed to proceed
via the diagram in Fig. 6a (and related ones) in the Theorists’ World, whereas it is
represented by Fig.6b in the Real World.
A. Fundamentals
Fortunately there are some favourable circumstancesthat can come to our rescue
-42-
.^
,: .‘.
..,
-. ...
l
if properly exploited:
the only hadrons that appear in K decays are pions and kaons; they double as
@l bound states and as chiral Goldstone bosons, i.e., bosons that emerge due
to the spontaneousrealization of the chiraI (and global) sum.
group:
su (3)L 63 su (3), -3 su (3)L + R + E’S,K: s, q8
l
:, . . ._.~
(4.4)
the massesand momenta that appear are “soft”:
1p 12 _<rnk << (“normal hadronic scale” - 1 GeV)
(4.5)
This vague statementwill be made more precise later on.
Chiral uerturbation theorv (hereafter referred to as ChPT) describes the
theoretical framework that exploits these two facts: it starts from the fundamental
Fig.6a
dogma already mentioned, namely that (approximate) chiral symmeny is realized
spontaneously in nature. This dogma consists actually of two parts:
(i) For massless u, d and s quarks, i.e.
Fig. 6b
m,=md=ma=O
there are eight masslessGoldstone bosons
(4.6)
A= , lf
Fig. 6:
The decay KL + ‘myviewed in the Theorist’s World (6a) and in the Real World
(4.7)
K*, K’, d
(6b).
rl
and one mass scale
47t B = 1.2GeV
(4.8)
where
TX = yy
= 93.3 MeV
(4.9)
.- . .. .. .
: : :I -.
:..
denotes the pion decay constant. The Goldstone nature of these mesons puts severe
consnaints on how they couple to each other and to electromagnetic and weak currents
(ii) When u, d and s quarks obtain non-vanishing masses,chiraIsymmetry is broken
-43-
explicitly and the eight pseudoscalarmesonsceaseto be massless
with the six operators O?4s) expressedas a product of two currents.
Yet
I$, rn$<< 4 << (4n FJ2
(4.10)
-
There are stm&al similarities between (4.12) and (4.14):
(445)
The operators Oi
are expressed solely in terms of the u, d and s quarks,
Q3
i.e., the m
fields. The operators G, also contain only the I.&&l fields,
-
namely the Goldstone bosons rt, K and q.
The coefficients c” represent the effects due to the existence of the heavy
& << rni << (4x TJ2
still holds; thus the real world where pions and kaons do have a mass is not expected to
be so different form one where they are massless. Mom specifically, the real world can
be described as a perturbation around a world where chiral invariance is realized
&l& - the c. b and t quarks and the W bosons - that have been “integrated out”
and do not appear explicitly in the low-energy Lagrangian. Similarly the &ayy
fields - the p and At mesons etc. - do not appear explicitly in (4.12); however
spontaneously. The small quantity which serves as an expansion parameter in this
treatment is given by
they determine the magnitude of the coefficients ci in (4.12, 13).
Yet them are essentialdifferences as well between the expressions (4.12) and (4.14):
There is a fi& number of operators appearing in (4.14). namely six, and their
coefficients ci44 are &&&
through an analysis of renormalization group
(4.11)
equations, at least at sufficiently high momentum scales. In (4.12) on the other
hand an in&t& string of operators Oy appears; furthermore the coefficients ci
(where q = u. d, s; a = IL, K, ?I).
ChF’T thus generates an effective Lagrangian for the strong interactions among
are, as a matter of principle, completely undetetmined by ChPT.
These findings should not come as a surprise: for the chiral Lagrangian describes a
non-renonnalizable interaction as is explained in more detail in Appendix B. Quantum
corrections do therefore force upon us new effective operators at each loop level and
pseudoscalar mesons
(4.12)
i=l
their coefficients are undetermined as a matter of principle. These coefficients will in
general be scaledeuendent since the higher loop contributions will typically contain
‘Ihe Oy denote operators that describe the couplings of Goldstone bosons; 5 am
numerical coefficients that contain the small expansion parametersgiven in (4.11)
--it'E;
=
(4n f
)z
(
divergent momentum integrals.
Details can be found in the literature.(ll) What we should keep in mind for our
subsequentdiscussion is the following:
ChFT is more than just another cute model; it is god based on any assumption
(9
concerning the smallness of the strong coupling as -- instead ChPT is OCD at
(4.13)
‘i
1
where $zP denotes quark masses, meson masses or the momenta carried by the
mesons; in K decays we have for on-shell fields p’ s rnk.
(ij)
--itgo to higher orders in the expansion parameter
(4x2$
new operators with undetermined coefficients Ci (though
structure). Their values can either be extracted from
applied to another; or one can attempt to estimate their
It is instructive to compare the expression (4.12) with the one that is usually
written down to describe the effective weak interactions of u, d and s quarks:
Csff(AS=l)
QO (44s)
ci 0.,
=
(.suffcientlvl low enemies!
Not surprisingly, a certain price has to be paid up-front for this panacea: when we
i=l
-44-
we are forced to include
with a well-defined chiral
one set of data and then
magnitude by employing
: ..
:I
-. ..y:.
: .::::
1: ._._
additional theoretical technologies: phenomenological models like p exchange
dominance, l/N expansions, QCD sum rules and blessed be the day! - lattice
QCD.
This leads typically to a very involved and lengthy analysis and it costs us in
predictive power, but there is nothing ad-hoc about it! And there is still lots of predictive
0
m,
(4.19)
md
0
m,
.
The meaning of the fust term in (4.16) becomesclearer when one expands (4.17) in the
pion fields
power left as can be studied in the literature.
Here we concentrate on the radiative K decays listed in (4.1 4.3) where strong,
electromagnetic and weak forces are intertwined
-2
4f* a(J&JJ,Jl+,
= J,nJ,n+&
Jgt’J,r~~
(4.20)
fn
+
i.e.. it contains the kinetic terms for massless meson fields and their (derivative)
interactions.
The second term which contains the quark mass mahix represents the &
breaking of chiral invariance that yields non-vanishing meson masses
The reader that is interested in results rather than how to obtain them can skio the next
section and go to section C.
B. Construction of the effective Laprannian
-2
f, M;.
The strong Lagrangian can be expressedby three terms:
2(m,+m,)
F2
ZeE =$ u(J&!J,Y+) +vtr@J4111+Y+M)+
+ higher order terms
(4.21)
Finally the last term in (4.16) is produced by loop corrections that generatecouplings of
the meson fields that contain four, six etc. derivatives (or momenta) each of which is
scaled by ‘f,
(4.16)
with
(4.17)
(0
where the matrix I$contains the eight Goldstone boson fields
As usual the elecaomagnetic couplings are obtained by replacing the normal
derivatives with covariant ones:
J,U+D,,Y=J,P-ieA,Q.Ul
where Au denotes the electromagnetic field and Q the quark charge matrix
(4.18)
(4.22)
.(;..
.~
;
. ..
.:
:.
,.
and M denotes the quark mass matrix
-45-
. _.
-..:
‘:
::
.
Otherwise if those discrepancies turned into failures or new ones emerged one
would face a very awkward situation: keeping in mind that ChPT is QCD at low
energies one would have to adapt a dictum by B. Brecht: “I suggest”, says Mr. K.,
“that QCD dissolves Nature and elects a new one.”
(4.23)
There are now additional higher order terms, two of which are of relevance for radiative
K decays(l2)
z:
= -ieL9F,,tr(QD,yD,U+
Ecker, Pith and de Rafael (hereafter referred to as EPR) using the pioneering
work of Donaghue et .l.(t6) have shown in a beautiful series of papers (t4) how to
implement the weak interactions in a china1Lagrangian. One starts from the samequark
level Lagrangian
that was already discussed:
-
+ QD,!.!‘D,U)
+e2 L,,F,,F,,~UJQY’Q)
(4.24)
F &v = J, A, - Jv A,
Z
The two quantities b, Llo are undetermined parametersof the type discussed before.
With the couplings written down so far
(ii)
n”,q
(4)
G
(AS=l)=LV(ud)V
fi
+ h.c.
i=l
SU(3)n. According to the AI = l/2 rule the 8 piece is by far the dominant one. In the
--f -f-r
following we will mostly ignore thea-plet.
mimick in ChPT:
1;:
(AS = 1) = G, @+&&
(c) An intermediate resume
It is this algebraic structure that one has to
+ hc. + non-octet terms
+ higher orders
% V (ud) V’ (us) g,
G, = E
.g+.y
describes the strong and electromagnetic interactions of K’S,
K’s and q’s
- to fl orders in the strong coupling
- for “soft” momenta 1p 1 < 1 GeV
- in terms of a priori undetermined parameters:
L,, L,,
(us)
(4ds)
The operators Oi
which are products of two currents can belong to an 8 or a 27 of
cannot proceed, to implement it one has to include the Wess-ZuminoWitten term
f,
-*
(4.26)
(4.27)
where 4 denotes the man-ix that represents the Noether current for the V-A chiral
rotation:
. ..
It has yielded a successful phenomenology with two possible exceptions, namely an
underestimate of I- (tl --f X+ A-X”) and F (rl + x0 n). One can actually give some
The appropriate numerical size of the parameter gg is obtained from the observed width
forK,+
xx:
rather natural arguments why terms that are of higher order in CbIT are neverthelessof
great numerical importance in those particulaEcases.(t3)
lggl z5.1
(4.29)
For radiative K decays we still need electromagnetic corrections to these weak
-46-
‘:..
:_
-,_:_
--
,-
couplings; as before they are implemented by introducing covariant derivatives, see
(4.22). They also induce terms of higher order in ChpT:
‘W20.Qf,~,.;,L) + ~~%v~,tiQL$u(h~.~,&)
their coupling strength: a priori undetermined parameters are introduced as the
coefficients of the chiral operators. There are three such parameters to the quadratic
order in ChPT
cC2):
i;,(g,[ ’
1 (4.30)
57
1
(4.34)
and six additional ones to the quartic order:
+ he
tC4) : Lg. L,, ; wt. w2>wj, w4
e2f2G
Zc4) (AS = 1, (em)2) = 8 i
(4.35)
These parameterscan be momentum scale dependent, i.e.,
w4 F, F,& (x6. i7 Ql! Q Y+) + kc.
(4.3 1)
Wi = Wi
where
(q2/
A2 )
(4.36)
and this happens when the loop integrals that are generated by quantum corrections
diverge.
and 116_i7 denote the appropriate GelI-Mann matrices acting in Sum
space; wt, wf,
The numerical value of these parameters can be inferred from data: e.g., f,
LL. This, by the way, does not mean that we have
x + Iv andgg from Ks -+
wg and w4 are new a priori unspecified parameters.
from
(e) Summary on the theoretical tools
ChFT describes the suong and elecuoweak interactions of pseudoscalarmesons
by an effective Lagtangian that contains Goldstone boson fields GB, their (covariant)
finally understood the dynamical origin of AI = l/2 rule and its range of validity.
However once the A1 = l/2 rule has been postulated in one reaction, then ChPT allows
us to implement it in a theoretically consistent way and apply it to other processes.
C.$
derivatives, elecuoweak currents and c number coefficients:
ze,= z-
(GB, D, GB, ji”“‘“k,
coeff.)
There are two simple, yet important theorems that apply to radiative K decays:
Theorem I
(4.37)
Ampl(K+xy)=O
(4.32)
It describes the dynamics to all orders in the suong coupling and to the appropriate
perturbative order in the elecuo-weak couplings.
The conflicting requirements of gauge invariance and conservation of orbital
angular momentum enforce the vanishing of this amplitude.
Theorem II
Feynman diagrams can be written down which contain as building blocks
- propagators of Goldstone bosons
- vertices that describe their couplings among themselves
- vertices that in addition contain couplings to elecuo-weak currents.
Amp1 (K + (IL) + y’ s + I’s ) = 0
The expansion parameter is given by
P2
(4n
P2
-------T
(1.3 GeV)
where the final state contains any number of photons and charged lepton pairs and at
most one pion. It is again the conflict between two requirements, this time between
those of gauge invariance and chiral invariance, that leads to a vanishing amplitude to
second, i.e., lowest order in ChFT.
There is a two-fold motivation for studying these decays in a dedicated fashion:
(4.33)
making ChF’T applicable if only soft momenta are present.
There is a price to be paid for including the strong interactions to all orders in
(i)
-47-
They provide stringent tests of our understanding of chiral invariance - a concept
that is deeply rooted in QCD (remember “B. Brecht”).
(ii)
Direct CP violation represents itself as a minute (though highly important)
phenomenon in KL + RX decays. This is partly due to the dominance of the
AI = l/Z over the AI = 3R amplitude in these non-leptonic decays. In radiative K
decays on the other hand one finds, as stated above inTheorem 11that the large
A I = l/2 enhancement is at least partly off-set by the chiral suppression
K,
- P2/(4X Fn )*. This can make AI = 3/2 and 5/2 amplitudes more significant
thus allowing direct CP violation to manifest itself in a less suppressedmanner.
-----
Tz-
+,i-:
I
*. I
‘.I
--f-Y
Ir;K+
Y
KS----
(a) K” .K’-+~Y
CP invariance is assumedfor this discussion. The mass eigenstates KS and KL
have - in this approximation - to be identified with even and odd CP eigenstates
KS
em
respectively.
Y
-c---x:
--__--
T* K
/-. \
,’
’
1\
I
-- ‘.- d’
Y
<
Y
.
Y
Fig. 7a (7b) contains the diagrams of lowest order in ChPT that generate
K, + yy (KL -+ fl). They are not shown to establish bragging rights, but to illustrate
two points of general interest for the serious student of ChpT:
-
Fig. 7a: Diagrams of lowest non-trivial order in ChPT for KS --t -r-r.
some vertices have a decidedly hedgehog-like appearance which will actually
intensify in higher orders. This should not surprise us - after all ChPT is produced
from a non-renormalizable dynamical description.
-
The reactions Ks --3 myand KL --f -r-fthat look so (deceptively) similar on the quark
level are described by very different diagrams in ChpT.
The diagrams of Fig. 7a yield
BR(K,+yy)=2.0x10-6
I&
1’
where we have calibrated gg according to (4.29).
experimental number from NA 32 on it
(4.39)
There exists a preliminary
(4.40)
BR (K, -+ yy) = (2.4 rt 1.2) x lO-6
which agrees with this prediction although the statistical significance is not
Fig. 7b: Same as Fig. 7a, but for KL + w
overwhelming.
So far no reliable number on BR(KL + yy) has been derived within ChPT. For
-4a-
Y
l
The theoretical predictions on r (K, --t y p+p- ) differ by 10% to at most 20%. The
experimental sensitivity level therefore has to reach the few percent level before the
different predictions can be distinguished.
.
.:: ..‘i;.
_::
The ratio I- (KL + y I+& )/r (KL + v) is not sensitive to SU(3)n breaking
and can thus be predicted:
I-(K,+yL+l-)
1
1.59 x 1o-2
rwL-+W)
=
for
4.09 x 10.4
1 dr
-r dZ t
L=e
t =p
(4.41)
K,-
+'YY
peak just above ~0.2 and to drop off rapidly for larger z both in ChlT and in a phase
space descriptionYet in ChfT the peak is even more pronounced and me drop-off is
even steeper than in the phase space ansatz. These differences occur roughly on the
20% level. Details can be found in Ref. 14.
(c) K” , p --r LO“IY
ChPT allows to relate KL -+ x0 yy to K, -+ r( independently of the value of gg:
rq-+ x”YY)=
rcew
(4.42)
5.9 x lo4
which translate into [see (4.39)]:
2
-7 gs
(4.43)
51
I.
I
In describing K, + x0 w one introduces a cut-off in m (n) to avoid the physical x”
BR(Kt,-+rt0~)=6.9x10
Fig. 8:
pure phase spaceansatz (broken line); from Ref. 14.
pole since here one is not interested in studying KL --f rt”rro, R’ + w where both
pions are on-shell. One then finds
-8
BRO(,+rr’yy)
withz=m2(r()/
z5.0.;4x10
The cl-photon mass distribution in KL --t 8’ yy, both for ChPT (solid line) and a
(4.44)
4.
Again ChPT leads to a different distribution in z than, say, a phase space
ansatz. As shown in Fig. 8 this difference is really striking for 5 r (KL -+ K” I’$:
chiral symmetry produces a dramatic suppressionat low values of z.
-49-
which overshoots the observed ratio (4.48) even in the absence of a non-leptonic
enhancement
(d)K’-+rGW
The transition rates for the decays considered so far depended on g8 and ?, ,
but on no other hadronic coupling parameters. This is not uue for K* + K* fl higher
Yet what we have ignored so far is Theorem II, (4.38). which states that we
have to go to the quark order in ChPT. Accordingly, one estimatesroughly
order terms Z(4) that are produced by quantum corrections contribute here; they
acmaby enter via the following combination of their ccefficients
&
‘.:
r(K+-tx+e+e-)
r(K++xOe+v)
32n2
4&,+L,,)-$
(w,+2w2+2wq)
.
(4.45)
1
1
The parameters b + Lto can be extracted from the observed width of x --f e v y. no
That shows that even the dny ratio (4.48) allows for a sizeable non-leptonic
enhancement in K+ + rr+ 1+1- if one takes into account the chiral suppression
such reliable information has so far been obtained on the parameters wt, w2 and ~4.
However we can state a lower limit
BR(K+-trt++~)>4xlO-~
expressed in (4.38).
(4.46)
To turn this qualitative “success” of ChPT into a quantitative one is, however,
quite a different matter: for the counter terms that are produced by the l-loop quantum
corrections contribute to K+ + x+ 1+ 1-. Their impact is represented by the
and a “most likely” value
(4.47)
BR(K++rr+r()-10d
coefficients b , Llo, WI. ~2, WJ, ~4; since the one-loop integrations now yield
divergent results one has to deal with the scale dependent part of these coefficients.
This represents an additional complication relative to me case of K+ + x+~r where
since a QCD treatment suggests ‘t?= 0 (1).
(e) Kk --f rtf ,!+R-
only the scale independent part of these coefficients entered EPR chose the following
procedure to deal with this complication:
At last there exists a measurementof one of thesedecay modes:
r-w++
x+e+e-)
= (5.6 f 1.1) x 10. 6
r(K+-+aOe+v)
- lix, within reason, me parameters such that the absolute width r (K+ + x+ e+e-) is
(4.48)
reproduced.
- Then predict r (K+ -+ K+ p+p-) and the distributions +.-$
The ratio in (4.48) appears surprisingly tiny since naively one might give a different
guesthate:
r(K+-+rr+i+,t+),
z=m2(R+1.)/M:.
IY(K+-+x+e+e-)
r~+47t"e+v)
- 0 (e4) - few x 10e3.
This program can be fulfilled up to a twofold ambiguity; for details consult Ref. 14.
(f) K”,p
+x01+1-
(4.49)
Of course one can do better than this overly naive ansatz: one can describe K++x+e+eas an electromagnetic correction to the non-leptonic (pole) transition K + x with its
The discussion of Ks --f 1~” I+,!- proceeds in complete analogy to
K*+x*L+I.
A completely new element - and one of fundamental importance -
non-leptonic enhancementfactor m:
however enters when one analyzes
KL + x0 R+k
2
r(K+-tx+e+e-)
r(K++xOe+v)
e2% 2gm
_
t
nk
- 1o-5g’,
:
::.
..I...
(4.50)
(4.52)
For the final state in
I
K,-t-+fy’
!, 1+ Irepresents an a
-5o-
eigenstate of CP
(4.53)
.I
,,:
.:.
.-
cpr @” r’ ) I=, 1 = CP [x”] CP [fl(-lf
= (-1) (+1) (-1) = +1
(4.54)
Yet the initial KL is CP odd in the (almost realized) limit of CP invariance; since
The ChPT loyalists of EPR and previously the authors of Ref.16 as well have
arrived at quite different conclusions:
.
KL + IL’ e+e‘ is dominated by the CP violating one-photon process
therefore
Cp [initial1 f Cp [final]
(4.55)
(4.61)
one realizes that the reaction (4.53) can proceed only via a violation of CP invariance!
Accordingly one obtains as an order of magnitude estimate
I 1.5 x lo-r2
BR(KL-+r?Y*+rtoefe-)={
BR(JSt,+rtO~+rcoe+e~)-
~e,~2BR~~~rr~e~e-)-10“2-10~‘1
manifestation of CP violation in KL decays one has to guard against two other
possibilities:
(a) The R+1- pair is produced not from a (virtual) photon, like in (4.53); instead it
comes from a Higgs scalar (that can be on-shell or off-shell for that matter). The
observation of KL + no ,I+,!- --- with presumably BR (KL + rsOp+w ) >>
BR (KL + no e+e- ) --- would in this scenario not represent a CP violation, but
@)
instead the presence of New Physics. This would obviously constitute a highly
desirable interpretation.
Unfortunately there exists a much more mundane process leading to
KL --f x”l+,t-, namely
...::.
-. :
(4.62)
(1.5 x IO’”
(4.56)
Yet before an observation of KL -+ x0 .I+.!- can be listed as another
.‘j.
where the two values listed in (4.62) reflect the two-fold ambiguity in the size of the
higher order parameters wi that was mentioned in our discussion of K+ + is+l+i-.
No direct CP violation has actually been included in obtaining (4.62).
.
Acordingly very little manifest CP violation is expected in the lepton distributions
.
etc.
The two-photon contribution to KL + A’ p+p- is not suppressed leading to a
relatively sizeablebranching ratio
BR(KL4~‘~‘~)-~BROCL-)11’e+e-)
.
(4.63)
CP violation can then manifest itself in a PansverSEpolarizationof the muons in
KL -+ x0 p+p. Rough estimatesfor the degree of hansversepolarization yield
PO1I (Jl) - 0.05 - 0.5
(4.64)
I want to address the conflict between (4.59) and (4.61) with the following two
preconceived notions:
i.e., a process of higher order in QED, yet without CP viotation.
There is no simple way to estimate the relative weight between the two
reactions, namely the CP violating one-photon processes(4.53) and the CP conserving
two-photon process (4.57) since they are characterized by parameters of comparable
size:
(4.58)
A more detailed dynamical treatment is therefore called for. Sehgal has applied an
analysis that is basedon vector meson dominance and found (*n
(i)
(ii)
ChPT when applied carefully and properly cannot be wrong.
It is highly unlikely that this conflict is due to algebraic mistakes.
BPR have examined the most general effective chit-al Lagtangian where vector and axial
vector fields appear explicitly. (In the usual approach these fields are integrated out
and enter only indirectly via the coefficients of the Goldstone boson operators). They
find that the vector coupling employed in Ref. 15 cannot appear directly due to the
constraints imposed by chiraI invariance. Although they can be induced indirectly by
higher order contributions their coefficients in ChPT are so tiny as to render them
totally insignificant. To say it differently: it would constitute an exmemelyheavy blow
to ChPT ifthe dynamical description ofRef.15 were borne out by experiment!
Let me add two more notes on CP violation in radiative K decays before
i
‘-.
..
concluding this section:
rCK’jx+e+e-)-rCK‘jrre+e-)
r(K+-+ a+e+e)+r(K-+
a depressing result and
temptation, at least for a theorist:
prediction that can be made there am typically more reliable man for
Thethemxical
.
.
- 1o-5
7t-e+e- )
r(K+-tn+yf)-r(K-+7r~)
< lo.3
r(K++x+fl)+r(x--t7t-v)
-
(4.65)
K decays;
Finding them or not finding them has very obvious implications for or against the
KM implementation of CP violation;
A very rich suucture exists in their phenomenology.
(4.66)
I subscribe quite strongly to these statements, Nevertheless I would consider it
quite foolish to suspendfurther searchesfor CP violation in K decays:
After all, nobody has really demonstrated yet that sufficient experimental
which does not appear to be beyond our experimental capabilities.
Resumeon Ram K Decays
(1)
sensitivity can be acquired in B decay studies.
It should not be forgotten that theoretical predictions could be contradicted by the
A study of radiative K decays will teach us significant and quite important lessons
on QCD; in particular it will provide us with crucial tests of our understanding of
experimental tindings. If that happened as far as CP violation in B decays is
concerned we would have made progress in a negative way: we would have
learnt that me KM ansatz does not represent the leading source of the observed
CP violation in KL decays. Yet we would not know which force it is that
generatesthis fundamentally important phenomenon.
Dedicated searches for CP asymmetries in K decays and in B decays should
therefore not be viewed as competitors, but as comolementine each other.
chiral symmetry and its breaking.
(2)
A well developed theoretical technology has emerged that provides us with a
quantitative treatment of these K decays: Chital Perturbation Theory.
(3)
As always mere is a prize to be paid: ChFI inuoduces - as a matter of principle a priori unspecified parameters: gg, g27, b, Llo, WI. ... wq. Yet ChPT
produces many highly non-trivial relations between different transition rates:
Therefore one has to measute many decay rates and distributions to fully exploit
the opportunities that are offered by K decays. This makes a K factors a hiehlv
desirable undertaking.
Item (1) - (3) concerned our understanding of QCD.
Yet also our
understanding of the weak forces and of New Physics can be extended by further
experimentation in this field
(4)
:-.
A dedicated searchfor
K+ + rt+ + “unseen”
(5)
is an unequivocal must - as stated before.
Helicity suppression etc. presumably do not affect K -+ ep, xep in a crucial way.
(6)
CP violadoq:
It has been stated with increasing vigour (though not necessarily rigour as well)
that dedicated searchesfor CP violation in B decays present an almost irresistible
-52-
V.
“Waitine for a Miracle” -- Rare D Decavs
According to the Standard Model D decaysrepresent a decidedly dull affair: the
relevant KM parameters -- V(cs) and V(cd) -- are “known” since they can be inferred
from V(ud), V(U) and V(cb); at most tiny Do-w mixing, no observable CP violation
or other flavour changing neutral currents are expected. This apparent vice can
however be turned into a twofold virtue:
Our alleged understanding of the elecnuweak forces in the charm sector allows
(9
us to use charm decays as a unique laboratory for studying the strong forces in a novel
environment.
c
(ii)
If -- connary to our jaded expectation -- an interesting weak phenomenon like
flavour changing neutral currents were observed we would have found unequivocal
WT
Tj &s
evidence for “New Physics” beyond the Standard Model. Of course, it would still be
ambiguous as to the precise nature of this New Physics.
0
Fig.9a
u
c
Fig.9b
In the following discussion of one-loop D decays and doubly Cabibbo
suppressed decays (hereafter referred to as DCSDl I will expand on these general
statements and make them more specific. But first I want to mention briefly two
technical complications that arise in treatmentsof D decays.
(9
Fig. 9a, b: Quark level transition operators with AC = 2 and AC = 1, respectively.
The one-loop AC=i,2 operators are non-local: the internal quarks that appear in
the diagrams of Figs.9 are lighter than the external charm quark
The strange quark can therefore m be integrated out to obtain a local effective AC=l,2
operator. The opposite situation arises for AS=2 etc. transitions.
There cannot be a trustworthy application of CWT. For the hadrons that appear
w
in these reactions, e.g.
D-tp+X
(5.2)
-53-
from different intermediate statesin (5.8). Describing D” -+ non the other hand by a
cannot be described as Goldstone bosons and “hard” momentum transfers appear
rn& p2 >> (4rrfJ2
A.
quark diagram that is analogous to the one in Fig.6a would presumably lead to a gross
underestimateof the rate.
(5.3)
Qne-looo Decay
Supersymmetry introduces the decay channel
There are quite a few processesthat come to one’s mind here
(5.10)
D-tnlp+R
D” -i )+a-
(5.4)
D” --+ yy
(5.5)
Do + n/p + “nothing seen”
(5.6)
Do + y + “nothing seen”
(5.7)
if the photinos 7 are sufficiently light. The relevant tree-level diagram is analogous IO
the one shown inFig. 4; the corresponding amplitude is subject to GlM suppression
- -that enters through the couplings of the internal squarks U = (u. c, t). Unfortunately -for the present analysis -- almost all SUSY models that are imbedded in a supergravity
environment exhibit the following property for the squark mass splittings:
(5.11)
Am2 (D) - d, 4
(5.12)
The GIM suppression that results from (5.11) makes considering D --f n/P + fi
(iii)
w
(5.13)
DO--+y+W
(5.8)
if the sneutrinos are sufficiently light. GIM suppression enters via the couplings of an
internal b squark where the more favourable scenario (5.12) holds. Yet even so it is
Since the first step representsa Cabibbo suppressednon-leptonic transition and
the second one a second order electromagnetic processone guestimates
BR(D’ + yy) 5 0 (tg%?s,a*) - 2.7 x 10’
Do + Y + “nothinr! seen”
SUSY again allows for a realization of such a mode, namely
In analogy to KL -+ yyone can describe this reaction as a two-step process
Do -+ “x, n, KK, K% 37tI...” + yy
a
completely academicaffair.
A few semi-quantitative comments can be added:
(0
4
Am* (ii) -d,
Unfortunately, one has to expect truly tiny branching ratios for these modes since more
than one suppression factor will typically intervene -- like helicity suppression in (5.4).
wavefunction suppression in (5.4,5,7) and GIM suppression in all four of them. And
in addition, the normal D decays are not -- unlike K decays -- Cabibbo suppressed.
hard
to
see
how
a
measurable
branching
ratio
could
result.
,.
I
(5.9)
::
This is probably a very generous number if not even a considerable overestimate
(which is why I used the “<” sign in (5.9)). For on general grounds one has to allow
for -- if not even expect -- sizeable cancellations to occur between the connibutions
-54-
:.’
l
Doublv Cabibbo SunmessedD Decavs -- DCSD
B.
These are necessarily non-leptonic decays. Thus one has to tackle the “Problem
of the Two Worlds” as described in Sec. IV, although it appearsin a less virulent form
here. Starting from the observation that almost everything is of order one in the strong
interactions -- the relative weight of higher order corrections, Clebsch-Gordan
coefficients etc. -- two thinkers arrived quite independently at the Ma-Ik Theorem: To
be off in one’s predictions by an order of magnitude or more one has to be
quite unlucky or
a)
rather dense or,
PI
most likely, both of these two requirements are fulfilled simultaneously.
Y)
The AI=]/2 rule is the classical example for case (a); everybody will know
examples of cases $3) and (y) from his or her own experience.
One consequenceof this theorem is that one cannot claim reliability for a model
just because it predicted a handful of decay rates more or less correctly. For a proper
evaluation one has to keep the wider theoretical and phenomenological landscape in
mind.
An expansion in l/N, N being the number of colours, provides a very compact
and rather successful phenomenology of Cabibbo allowed and once Cabibbo
suppressed D decays (a detailed description can be found in the literature (17)). It is
There exists a certain (though by no means large) potential for New Physics to show
up. For example, New Physics could be realized by the existence of charged Higgs
fields H the exchange of which leads to c + s(d) as well as c --f d(G) transitions. In
the first case the Higgs exchange produces a coupling proportional to mc*md (or
m+n,Jm~, in the latter one to me*ms/4.
The highly forbidden DCSD can thus
have a much higher sensitivity to New Physics than Cabibbo allowed D decays(‘9):
rate (“NP”)/rate (“Old Physics”) [c+d(uS)J
rate (“NP”)/rate (“Old Physics”) [c+s(u&l
DCSD of Do:
(a)
Invoking the l/N ansatz as rationale for including factorizable contributions
only, ignoring W exchange and putting the Bauer-Stech parameter 5 to zero one finds
(5.14)
BR@’ -+ K+p-)
- 0.5 tg” 0,
BR@” + K-p+)
(5.15)
+’
WD”
-+ K
n-)
_ 3 tg4 @,
(5.16)
BR@’ + K- * rt+)
quite natural then to apply it to DCSD as well.@)
It is of course the Cabibbo angle Be that sets the overall order of magnitude for DCSD.
The coefficient of tg%, which reflects hadronization effects is of order one -- in
Before I do that I would like to recall to your attention the four-fold motivation
for a detailed and dedicated study of DCSD:
accordance with the Ma-Ik Theorem; for example the enhancement in (5.14) can be
traced back largely to lfK/f#-1.6 etc. Furthermore
l
As is well known by now a good understanding of DCSD is relevant in searchesfor
Do-p
l
mixing.
As explained below interesting lessonscan be obtained on QCD
. Such lessons are of obvious significance for attempts to extract the values of the KM
parameter V(ub) from non-leptonic B decays.
.-_.
.:
,. : .-.,..I.
. ..
BR(D’ --f K+rr-, K+p-, K+‘x-) _ 1,2 _ ,,5
(5.17)
BR(D’= + K‘x+, K-p+, K- l n+)
i.e. summing over these channels yields an amusing (semi-quantitative) realization of
quark-hadron duality.
.. .
: :
.
(b)
DCSD of D+
The first factor -- fK/frt -- reflects SD(~)F, breaking in the K and n w;
the last one -- l/42 -- the Clebsch-Gordan coefficient that et
A rather intriguing scenarioemerges here:
..-:.
‘-.
._
BR(D+ --f K+tr’)
- 3 tg” 0,
BR(D+ -+ px+)
:
,..
..
..:-
wavefunction. The coefficients c+, c. finally denote the renormalizatio
weak quark couplings by QCD radiative corrections: c+-O.7, c-2;
term does not contribute to D+-t(S=-1) modes due to the destruct
(5.1R)
mentioned above (‘9).
(5.19)
Analogous effects occur in (5.19. 20). The expected enhance,
much larger, but also numerically more uncertain there: the destructi\
quite considerable in DC -+ K’*R+ and at the same time very sensitiv
changes in the model parameters. Comparing r(D’ --f ~*tt+)theo
(5.20)
BR(D+ -+ K+p’)
BR(D+ -+ ?T”p+)
suggest that the lower end in (5.19,20) should be favoured.
- 0.35 tg40,
(5.21)
Therefore I have to stress a general caveat concerning this ana
tinal state interactions have been completely ignored in the true spirit 01
While matters of practicality favour this procedure there is good real
universal wisdom. A detailed analysis of DCSD that is based on QC
quite desirable, but is not yet available at this time (1%
The apparently dramatic enhancement factors in (5.18-20) reflect actually the
destructive interference that occurs in the Cabibbo allowed D+ decays which in turn is
the main motor for the D+-Do lifetime difference (1%. Such a desuuctive interference
does not occur in DCSD and their relative weight is thus enhanced. This can be seen
most easily by considering the isospin of the final states rather than drawing cute
diagrams.
l
C.
The prospects of ever observing l-loop decays of D mesons
(9
gloomy since quite typically several concurrent suppression factor
mechanism, helicity arguments, small wavefunction overlaps, small I
The tinal states in D+-+ (S=-1) transitions carry a unique isospin, namely (I,l3) =
($, + 9;
these decays are therefore described by a single amplitude in isospin space,
etc.
namely (AI, AI3) = (1, +l). Interference can thus occur.
l
Resumeon Rare D Decay
(ii)
D+ + (S=+l) transitions on the other hand are described by the combination of two
Do-B0 mixing could be as “large” as to produce (18)
amplitudes that differ in isospin. namely (AI, AI3) = (0.0) and (1.0). This curtails the
possibility of interference.
New Physics could lead to
The coefficient in (5.18) can then be understood as basically due to
+0.1
(5.22)
(ii)
A detailed study of DCSD of D mesons appears to be
experimentally as well as theoretically. An intriguing and instructive patn
-56-
to emerge teaching us unique lessonson the strong interactions at the interface between
the perturbative and non-perturbative regime.
(iv)
VI “GUARANTEED DISCGVERIBS” - RARE B DECAYS
The B decays are simply “exciting” - even within the confines of the
StandardModel:
* A priori unknown KM parameters - V (cb), V (ub), V (td), V (ts) enter.
* B” B0 mixing had been predicted and - even better - it was observed (actually
Miracles can occur. Do not let them slip away by not watching!
*
*
-:-
“.’
:
on a higher level than anticipated).
B decays present the best odds to observe CP violation outside K decays.
Charmless decays like B +K*y will occur.
Since one is dealing here with reactions that typically require the presence of loop
processes, i.e., that represent genuine quantum effects, one encounters a rather
high sensitivity to New Physics in these transitions. The three generic scenarios for
New Physics that 1 am going to invoke are
- a fourth family;
an extended Higgs sector;
- Supersymmetry ( = SUSY).
Unfortunately there are a few technical complications we have to face here:
* ChPT is clearly not applicable in decays like B --f D p , B +K’ yetc.
* The two-body modes B -+ PP, PV, VV where P [V] denotes a pseudoscalar
[vector] meson are not the dominant decay channels anymore (although they are
not insignificant either) QCD sum rules that have been developed for these
l
exclusive modes are therefore of restricted use in B decays.
It seems that rare inclusive decays like B + (C=O,S = 1) are hard to measure.
This is quite unfortunate since theoretically they can be treated more directly.
A. KM suauressedtree level B decavs
There are charmless B decays that occur already on the level of tree
diagrams via the KM coupling V (ub). Among these there is a certain subset of
modes with a particularly clean experimental signature: two-prong, two-body
decays of beauty of which there are six channels
B --f x+x-, K+K(6.1)
-57-
.: ./’
I’
-,
B--+K’rr*
(6.2)
B+P?
(6.3)
3,-fprrr,pK(a)
BR(B,+rr+x-)<
BR @,-+K-x’+)
(6.4)
BR(B,+pF)<4
9x IO-~
CLEO
(6.5a)
s 9 x low5
CLEO
(6.6a)
~10.~
CLEO
(6.9a)
The bounds (6.5a) and (6.9a) have already reached theoretically interesting
territory as expressed by (6.5) and (6.9). The bound of (6.6a) appears to be
still an order of magnitude above it -_ yet, as already indicated -- this is a point
to which we will return.
Following the same procedure as in Sect. V.B - i.e. including factorizable
contributions only, setting 5 = 0 and ignoring final state interactions (hereafter
referred to as FSI)- we find (20)
(6.5)
(b)
t&I, BR (Ed -+ 11+x-
BR (Bd --f K-x+ ) z BR (B, -+ K+K-) ”
(6.6)
2
BR(3,+pn-)-3x
-3 ___
V Cub)
/VW !
10
tg2e,BR (3,+
BR(Bd-+p$)<fewx10-4
pn-) - 2.3 x 1O-4
V Cub)
K-x+ and Bs +K+K-
(6.10)
BR (B, --f x+x- ) << BR @, -+ K+K-)
(6.11)
BR(B,-,plj)<<<BR(B,~pjj)
(6.12)
The reason
for
that
is the following:
the decays
B,-+ K+ K‘ , B, + x+x- and B, + pp cannot proceed via simple tree
diagrams; instead they require the intervention of FSI (i.e., rescattering and
channel mixing), of annihilation or of KM suppressedpenguin contributions -
(6.8)
circumstances which are expected to reduce the rate (maybe I should add that
2
-V (cb)
BR (& -+ K+K-) << BR (i$ + x+r )
(6.7)
it is somewhat academic on this level to distinguish those three mechanisms).
(6.9)
A violation of the relations (6.10-12) might not necessarily amount to a
disaster for theory - after all we have included factorizable conuibutions only yet it would at least represent an acute embarassment for our theoretical
description of heavy flavour decays.
Cc) The three modes
2
< 0.05
These processes, in particular B,+
There are three more of these decay modes, but they should be further
suppressed, i.e.
can receive
contributions from Penguin graphs which we have ignored here; this point
will be re-addressed later on. Altogether we estimate the uncertainties due to
on the other hand could be significantly enhanced over the rates given in (6.5-
the hadronization process to amount to factors of 2 3 roughly.
None of these rare decays have been observed yet -- which is not surprising
in view of the predicted tiny branching ratios. The present 90 % C.L. upper
6.8) due to the intervention of FSI, annihilation and/or KM favoured
penguins. Let me sketch just one scenario involving a two-step process
limits read as follows (for a more detailed discussion seeRef. 4):
-58-
_ -.
-:.: __
:::.:
..
Bd+“D,
-c*)
D
C),,
*K-X+
(6.13)
The first transition has a huge enhancement factor over the &xcJ process
Bd+ K-K+ :
EF w-
:
. ‘2. _ ” .,.
(6.14)
..,
The re-scattering efficiency for the second transition in (6.13) will certainly
be quite small; yet we do not know how tiny it is. A re-scattering efficiency
of 1% might not represent an inflated number - after all the process takes place
less than 1.5 GeV above the DI D* threshold; even then this two-step process
would dominate the Be -+ K-x+ mode in view of (6.14).
:’ ._.
-:
.--
Ypzig
Clearly more theoretical work is needed here. A refined analysis based on
QCD sum rules appears quite promising, be it only to give a theoretical
underpinning to some of the rather ad hoc phenomenological assumptions made so
Fig. 10: Quark level diagram for induced FCNC.
far.
In any case, dedicated experimental searchesfor these decay modes should
receive a high priority, Determining their branching ratios will yield new and
unique informations on the hadronization process and thus on QCD. For that
purpose it is not essential to obtain these branching ratios with high precision - I
would consider a 30% measurementas quite adequate: on the other hand it is hi&.&
desirable to obtain data on&of
thesedecay channels.
These informations on hadronization can then serve as essential input for
even more ambitious searchesin these rare B decays, namely for BO-ED mixing
and - ultimately - CP violation. (32)
tand rd Model
3B On -I
Fig. 11: Quark diagram for b + “w” s + ys
(a) Generalities
The generic diagram for Q + q + yor Z or g is shown in Fig. 10 where the
loops with a charm and a (virtual) top quark have been singled out; the u quark
contribution acts mainly as a GIM subtraction. It is understood that the photon or
the gluon can be on- or off-shell (a somewhat murky distinction for the gluon).
The dependence on the KM parametersfor such a transition with an internal t quark
:
I
:
I
is then given by
-59-
:.
.:
1.
rate (b + s + y/Z/g ) = b’ (lb) v (ts) f = A2 A4
of this width on the KM parameters can be eliminated by considering the ratio
r (b + sy) / r (b + c” V ) since 1V (tb) 1 r 1 , 1V (ts) 1 z / V (cb) I. One then
(6.15)
finds (23)
rate(s+d+yNg)=
tV(ts)V(td)?zA4h10((1-pf+q2)
(6.16)
2x 10”
r (b -+
where I have used the Wolfenstein representation (21)of the KM matrix. Therefore
we find for the branching ratios
BR(b-+s+y/Ug)=
r(b-+sy)
C
” C) =
1O.3
m,= 65 GeV
for
m,= 150 GeV
(6.21)
:_ . .
‘. .-.:
Equating r (b + c”v) with the measured width T(B -+ “v X) one obtains for the
1V (tb) V 0s) r” = 1
branching ratio
(6.17)
m, = 65 GeV
for
1V (cb) f
BR(s-+d+y/Z’g)=
m,ll50
GeV
(6.22)
=A4hs((1 - p?+Tl*)
Yet - as discussed before what is measured are (exclusive) transitions involving
- (1 - 2 ) x 5.5 x 1o-6
hadrons rather than free quarks.
Gauge invariance again implies
I-(B+Ky)=O
Iv (us) f
(6.18)
(6.23)
The mode B --f K*ycan proceed; since BR(B --f K*y) can neither be 100% nor 0%
i.e., these rare decays of beauty have a much higher sensitivity to the presence of
heavy quarks - the top quark in particular - than rare decays of stangeness. This
one “infers” as an application of the Ma-Ik Theorem
BR@+K’y)
I 5-10Q 0
(6.24)
BR(b+sy)
a guestimate that is “confirmed” by computations (24)employing specific models for
makes them such an exciting field of study ! cz2)
the hadronic wave functions. The final estimate then reads
(b)B-+y+(S=-1)
2x d
BR(B-+K*y)-
m,z 65 GeV
for
(6.25)
1 x 1o-5
rn,ll50 GeV
1
This steep dependence on mt does not allow us to make a reliable prediction on the
branching ratio. Yet such an apparent vice can swiftly be turned into a virtue by
noting that a measurement of BR (B + K*y) would in turn give us a good handle
(i) Quark-level results.
From the diagram in Fig. 10 we obtain (23) the effective coupling for the
auark-level transition b+sr
(6.19)
I eB(b -+ sy) = G,mb bL oPv q, A, s I?, (q’ ; m, m, ; KM param.)
4-i
where Av denotes the photon field and q, its momentum. Gauge invariance tells us
that for q2 = 0, i.e., real photons, there can be only one form factor, namely F;.
on Nature’s value of ml! Before however jumping to this conclusion it behooves
us to pause and think whether such a strong dependence indeed makes senseor not.
After all, we have considered mainly quark level diagrams so far, i.e., shortdistance dynamics.
It depends, due to the GIM mechanism, approximately on the square of the internal
quark mass, i.e.
F; (top) = 3
>
(6.20)
6
This makes the charm contribution numerically quite insignificant and at the same
time introduces a strong sensitivity of T(b + sy) to the top mass. The dependence
(ii) On the impact of long-range dynamics Duality lost?
The authors of Ref.25 addressed the question whether there is another
mechanism leading to the same final state; in particular they considered a two-step
processa la Vector Meson Dominance
-6O-
__
.:
-
(6.26)
One can make a very crude estimatefor its branching ratio
BR(B+yK*)-BR(B-t”y/‘K*)
xProb(“W”-+y)
-(5x10-3)x~-10-5
-
Diagrams like the one in Fig. 12 produce “soft GIM suppression”, i.e., actually
an enhancement - log (MJm$ which is particularly effective for mt < Mw.
(For mt > Mw also the expression in (6.28) yields an enhancement. This at
first sight paradoxical result is due to the coupling of longitudinal W bosom).
New and more leading log terms emerge for mt - o(Mw) since
(6.27)
a, Cm’)
The point of this exercise is not to produce a reliable prediction, but to point out that
there could be a contribution to B -+ yK* that is indeuendent of mt, yet of
---L
n
m2
log * 5 1
%
in that case.
Putting everything together and including leading log terms only the authors of Ref.
26 found the results shown in Fig. 13. From it we draw the following conclusions:
* The QCD radiative corrections am very large indeed.
* They decrease somewhat in relative importance as mt increases: e.g., for mt =
50 GeV they produce an enhancement by a factor 17 whereas for mt = 125 GeV
this factor has shrunk to 4.3. As discussed above such a trend was to be
expected since the biggest difference between soft and hard GIM suppression
occurs for small values of mt.
. lhe dependenceon mt therefore becomes less steep.
This makes it doubtful that the decay B + K* ycould reveal information on the
comparable magnitude to the numbers listed in (6.25). Furthermore these two
contributions are coherent; therefore their amplitudes could add or subtract thus
influencing the overall result quite dramatically. Such an observation -- namely that
there is a numerically significant contribution to B + K*y that is not produced by
the diagram in Fig. 10 -- would spell trouble for the applicability of quark-hadron
duality in B decays if it were true.
(iii) QCD radiative corrections Duality regained!
The suggestion made above that there is no quark-level diagram
corresponding to (6.26) has to be examined more carefully. The diagram shown in
Fig. 11 would fit the bill and it merely represents a permissible distortion of the
charm loop in Fig. 10. However we had argued before that the GIM mechamism
relegates this diagram to numerical insignificance!
l
*
A more careful analysis of the GIM mechanism will help here: If two
quarks Q and q with masses mQ and nk, respectively appear in a loop diagram
*
together with W bosons then such a diagram has to yield a vanishing contribution in
the limit mu = m,+ However this czanhappen in two different ways:
m* -m
Q q
.
Ampl. = 2
(6.28)
MW
this is usually called “hard” GIM suppression(at least for 4, mi C M$),
l
presenceof a fourth family.
The lowered sensitivity to mt implies that the charm-loop contribution becomes
numerically much more significant.
This means that the concept of quark-hadron duality escapesthe disaster it was
facing before QCD radiative corrections were included.
These radiative corrections obviously contain sizeable numerical uncertainties;
for example, the appropriate normalization scales have not been uniquely
determined so far. Yet the fact that they are large or even dominant per se does
not make them completely untrustworthy. For - as discussed before - we do
understand on fairly general grounds why in this particular case these correction
terms are so large: it is fvstly the conversion of hard GIM suppression into soft
GIM suppression; secondly the appearance of large logarithms log rnf which
Ampl. = log z4
(6.29)
9
which is commonly referred to as “soft GIM suppression” although it actually
amounts to an enhancementfor 4 << n$
.
have been summed to all orders on the leading log level. Higher order terms
which have been ignored so far cannot benefit from additional enhancements
over the terms already included. The situation here has something in common
with the one encountered in e+e- annihilation: the two-photon process
Returning to the case under study here: as already stated, the diagram in Fig. 10
reproduces hard GIM suppression, (6.28). However QCD radiative corrections
change the situation very significantly:
-61-
:
dominates the one-photon reaction at the highest presently available energies;
yet nobody claims a breakdown of perturbative QED since we understand the
structural reasons behind the prominence of the two-photon process.
As an (optimistic) reference point we can then state:
BR (B --f K*y)-
3.3 x 10m5 for
rn,= 150GeV
This is to be compared to the upper bounds (4)
2.9 x lO-4
WBd4’
y)-4
2.8 x 10
ARGUS
CEO
Cc) B --f “+“- + (S = -1)
Some new features emerge in a treamlent of the transition b + s “+“- :
* It can proceed due to the exchange of a photon in b + s “y” -+ s ‘I+“- Since
this photon is off-shell a new form factor that is not present in b + s y appears
Fig. 12: QCD radiative corrections that produce “soft GlM suppression”.
*
here; it is usually referred to as Fl,
The lepton pair “+‘‘-can be produced from an intemlediate Z” or W+W- pair as
well. This introduces new terms for which there is no analogue in b -+ sy, for
heavy top quarks, say ml > Mw, they actually yield the dominant contribution
(which is due to the coupling of the longitudinal Z or W bosons to the top
quarks that appear in the loop ).
0.003
Putting these ingredients together one obtains (27)
0.002
0.000
I 3.5 x 1o-6
_*--
0.001
m
_ --50
__--
__--
__--
1 6.4 x 1O-6 form, = { loo}
125
100
75
I 1.0x 1o.5
I50
GeV
(6.30)
I1501
mt( GeV)
QCD radiative corrections treated in a leading log framework(28) enhance these
numbers considerably, in particular for moderate values of mt:
Fig. 13: The ratio r (b + sy) / r (b -+
CLV)
with (solid line) and without (broken
I 7.3 x 1o-6
1ine)QCD radiative corrections; from ref. 26.
BRQcD (b --f s e’em)= ( 1.1 x 1o-5 for m, =(
( 1.4x 1o-5
A few observations should be added here:
-62-
PO 1
lm}
I1501
GeV
(6.31)
(i)
Theoretically this represents a truly lovely mode whose branching ratio
increases very strongly with mt (the virtual photon contribution is of course absent
here). For mt = 100 GeV one finds (30)
(6.35)
BR(b+svv)r2x10.5
The QCD corrections while considerable are not nearly as huge as the caseof
b -+ sy. That is not surprising: it was pointed out before that the transition
b -+ sy depends on a single form factor in a very restricted way and does
represent the exception rather than the rule. In b -+ s “+“- on the other hand
several short-distance contributions appear, as discussed before.
(ii) Information on the underlying dynamics is contained not just in the branching
ratio, but in the di-lepton mass distribution as well; details can be found in
Ref. 29.
(iii) The virtual photon has a definite preference to materialize in an e+e- rather
than a p+j.t- pair. The rate for b + s p+p- is thus suppresssedrelative to b -+
which is twice the value of BR (b --f se+e-)for this mt. This should not come as a
surprise since one sums over the three neutrino species (and the 2’ couples more
strongly to neutrinos than charged leptons). Unfortunately it appears that the
experimental signature for such decays, even for exclusive channels like
B --f K’ v? is not sufficiently clean.
s e+e- beyond the mere phase spacereduction; for details seeRef. 29.
Exclusive decay modes exhibit a cleaner experimental signature, while
introducing further theoretical uncertainties in the treatment of hadronization. Two
channels have been studied in particular, namely B --f K e+e- and B + K* e+e- ,
(e) B + (S = 1) + glue
On the one-loop level there are four types of quark processes in this
category, namely b + sg, b?j+ sq, b -r sq?jand b + s gg. It is actually the latter
two that dominate and altogether one obtains (3*)
(6.36)
BR(b-tsiglue,qq)-l-2%
for which the following estimateshave been given (29)
BR (B + K*e+e-) _ o.2
BR(b-tse+e-)
(6.32)
BR (B + K e’e-) _ o,05
BR(b+se+e-)
(6.33)
for mt 3.30 - 200 GeV, i.e. the branching ratio exhibits fairly little sensitivity to the
top mass.
There exists a second source for charm-less final states with strangeness,
namely the KM and Cabibbo suppressed transition b --f uiis. A crude estimate
yields
V(ub) *
(6.37)
BR (b --f u iis ) - 2tg* 8, V(cb)
s 1%
I
i
where the factor two reflects the phase space advantage of b --f u over b-t c.
combining these numbers with (6.31) we arrive finally at
BR (B + K*e+e-) - [1.5, 2.2, 2.8) x 1O-6
The rates for these two reactions, namely the one-loop process b + s + glue
and the tree-level process b + ulis , are therefore of a magnitude that is not very
(6.34)
BR (B + K e+e-) - [0.3, 0.6, 0.841 x 10e6
dissimilar. Not only is this interesting by itself, but it also creates very favourable
conditions for the emergenceof CP asymmetries in this class of 6 decays. (32)
for mt = [ 50, 100, 1501GeV.
These are tiny numbers indeed, but not zero. And they could be enhanced
quite considerably if there is a fourth family.
CLEO has obtained the following upper bound:
BR(B++K’e+e-)<
Alas, we have to face up to the usual unpleasant business of hadronization.
Gluon fragmentation
2%+ g&T.nri
is “soft” thus transforming the original (virtual) masses of up to a few GeV into
high hadronic multiplicities. It is therefore a multitude of exclusive channels that
5 ~10.~
builds up the not-so-small inclusive branching ratio given in (6.36). To make this
(d) B-+fl+(S=-1)
-63-
._,
:-
..:.
-..I .‘:
‘:
.: -.
:
.:
‘-
also add a short remark on light Higgs scenarios although they could be realized in
the Standard Model as well.
statement more quantitative we have at present to rely on phenomenological models.
They tend to yield numbers like (33)
BR (Bd+ K-x+) - few x 1O-5
(6.38a)
BR(~d-fi?~)-fewx
1O-5
(a) Non-minimal Higgs sector with Natural Flavour Conservation
The Standard Model contains one complex SU(2) doublet Higgs field.
Three of its four degrees of freedom are transmogrified into the longitudinal
(6.38b)
A comparison of (6.38a) with (6.6) shows the considerable impact Penguin-like
contributions can have even on the branching ratios. In particular the number
components of the weak bosons while the fourth one emerges as the physical Ibggs
field, which is neutral.
quoted in (6.38a) is relatively close to the present experimental upper bound.We do
not have a reliable method for gauging the theoretical uncertainties in these
predictions, but we have to suspectthey are large, say a factor of three or so.
For the same reason we have to conclude that the sensitivity to the presence
of a fourth family is submerged in this “theoretical noise”, at least as far as
exclusive decay modes are concerned
Since flavour changing neutral currents are highly suppressedin nature one
does not want to enlargen the Higgs sector in a reckless manner. Instead one
introduces new Higgs doublets in such a way that they couple either to the up- or to
the down-type quarks .(x6) For two doublets we are left with five physical Higgs
fields, two of which are charged and three neutral. (CP invariance is still
maintained; it is broken spontaneously if three Higgs doublets are introduced.)
Even with this imposition of natural flavour conservarion we are dealing
with a high-dimensional spaceof new parameters. To identify an interesting comer
in this parameter spaceone can turn to B, - Bd mixing.
C. One-looa AB = 1 Processeswith New Phvsics
The predictions given so far for these one-loop B decays contain two types
The ARGUS and CLEO findings do not establish a need yet for New Physics in the
AB = 2 channel; on the other hand it cannot be ruled out that New Physics does
of uncertainties:
. The “embarrassing” uncertainties that enter into our estimates of branching
ratios for exclusive modes in particular they are due to our less than satisfactory
provide the dominant motor of B”-Bo mixing. It is thus legitimate to consider that
part of the parameter spacewhere Higgs exchangesdominate AB = 2 dynamics and
mastery of hadronization.
The “good” uncertainties concerning parameters of the quark world, in
particular the top mass. The unknown value of mt severely restricts the
l
then search for sizable enhancementsin AB = 1 reactions.
Such an analysis has been undertaken in Ref. 37
numerical precision of our predictions; yet a measurement of the relevant
branching ratios would produce a lower and an upper bound on mt.
We have reason to entertain even bolder hopes, namely to searchfor the presence of
imagination stretcherrather than a realistic dynamical scenario.
New Physics in these B decays which represent classically forbidden processes. In
the preceding discussion of subsection B I had already included one such scenario,
namely the Standard Model with one additional, the fourth family. There we had
encountered the one general impediment for such an analysis: due to the
“embarrassing” uncertainties we can hope to perform a successful hunt only, if
.
.
.,--.
some big game is waiting for us out there, i.e., if the measured rate is considerabl\C
h
The authors’
conclusions for two quite different models with two Higgs doublets are
summarized in Table IV. One should add here that model II serves as an
than the expected rate.
I will briefly review the situation with two other realizations of New
Physics, namely a non-minimal Higgs sector and supersymmetry ( = SUSY); I will
-64-
Assuming
transition
BR[in %]
Model II
Model I
EnhancementFactor
I
II
b -+ sy
few x 0.1
22
0 (10)
0 (100)
,, + s”+“-
< few x 10e3
2 few x 10e2
0 (10)
0 uw
b -+ s g(*)
$4
5 100 (!)
2-4
0 (10)
q 2 80GeV
(6.40)
as the raison d’&tre for a light Higgs one infers from the available limits on such B
decays(41)
(6.41)
mH > 3.7 GeV
There is still another window open, namely
0.3 GeV < rn~ c 2 GeV;
it can be closed only by making more detailed theoretical assumptions on the
relevant Higgs decay channels. Those can be checked (or challenged) by further
Table N
These numbers have to be taken with a grain of salt since radiative QCD corrections
have not been included here. Yet even so they show how large a discovery
potential there is in these uansitions.
experimentation.
D. Resume on Rare B Decays
B physics is “full of promise”; there is tantalizing “poetry in beauty”! All of
(b) Supersymmetry
There is one feature of particular relevance here (38): gluino exchanges
mediate flavour changing neunal currents with a strength of order a,, i.e. the
this is of course a euphemism for saying that B physics has not reached the maturity
level yet, neither experimentally nor theoretically.
Experimentally: as a theorist one cannot help but complain that measurements
of inclusive B decay rates have so far produced rough numbers only.
Theoretically:
- As far as inclusive decay rates are concerned there is still some homework to
strong rather than the elecaoweak coupling. This enhancesthe rates for b --f sy and
b -+ sg(*) by an order of magnitude for moderately heavy Susyons, i.e. if M
l
(gluino, squarks) - MW (39)! Again, QCD radiative corrections have not been fully
included.
l
be done:
QCD radiative corrections have to be included properly and
comprehensively (42); more detailed thinking should be applied to the question
of whether one can trust quark-hadron duality in B decays on the 10% or only
on the 50% level.
- More formidable tasks await our dedicated attention in exclusive B decays:
most hadrunization prescriptions -- like potential models - are of untested
reliability; trustworthy results from lattice Monte Carlo computations are still a
few years away; it appearsthat an application and refinement of QCD sum rules
(c) Light Higgs scenario
It was already mentioned in Sect. III that an arbitrarily light Higgs boson
can emerge in the presence of heavy quark fields Q, i.e. if MQ > 80 GeV. The
decay b + sH is dominated by the loop diagram containing the top quark and is
roughly proportional to rn: : one factor of mt enters through the Yukawa coupling
of the Higgs, the other is produced by the chiral structure. Therefore (40)
BR ( b + sH) = rn:
a la the Blok-Shifman treatment of D decays is the best available technology.
- As far as numbers are concerned one should keep in mind that the sxclusive
branching ratios for these rare B decays are typically of order 10-6-10-5; the
inclusivt transitions on the other hand command branching ratios that are &
(6.39)
by a factor lo-lOO!
-65-
,_
..:
.,
.:.
-:
.:
. .. .
:’
.. .
In summary: if we apply the principles on which the Napoleonic campaigns were
built
i.e. employ large numbers, i.e. t 107 B’s, spend a small fortune (but get
Aoaendix A: Long-distance dynamics in K-+ xvv
others to pay for it) and, very importantly, rely on “fortune” in the French sense then we are faced with the prospect of guaranteeddiscoveries!
The diagrams in Fig. 3 generate a local AS = I operator which - as stated in the text
can then be related to the operator that underlies K 4 rrev decays. However there exists
another mechanism which is of relevance, at least in principle, namely the two-step process
VII - OUTLOOK
We should keep in mind how much New Physics has been unearthed in K
decays: parity violation, suppression of flavour changing neutral currents, CP
violation and the existence of the internal quantum numbers strangenessand charm
(and even top quarks). There is no reason to believe that the potential for indirect
discoveries of New Physics has been exhausted in any way. Yet there are two
K+ -+ “R+” + R+VV
Since such states
are not necessarily far off-shell, they can propagate over typical hadronic distances; the
process (A.l) therefore represents long-distance dynamics and it is not included in the
reference reaction K + rtev to the same degree(M) (it appearsthere as a radiative correction
important lessons we should draw from the past:
(1) A careful and continuous evaluation of our theoretical tools has to take place:
lattice Monte Carlo computations will answer all these questions sometime in
only). An analogous situation is encountered when one attempt@) to compute the longdistance contribution to K”
the future; for now (and for some time to come) we have to rely on a judicious
and detailed application of different theoretical technologies: ChPT for K
mesons, QCD sum rules etc., for D and B mesons.
(2) We have to pursue a comprehensive experimental program: for example the
relevant quark mixing angles could be completely different for down-type
quarks --like s and b -- than for up-type quarks -- like charm. Therefore one
En mixing. Using similar arguments one estimates that the
process (A. 1) could be numerically significant if top quarks are only moderately heavy,
i.e., mt < M,.
has to study also rare D decays in a dedicated fashion to obtain a complete
picture even though one needs a gambler’s luck to find New Physics there.
Dedicated searchesfor and studies of rare B decays are “assured” to yield a rich
harvest. Yet even so one should view studies of rare K and rare B decays as
perfectly complementary, a
(A.11
R+ represents an intermediate state with S = 0: R = I, p, At,rcn, 3x,
as competing.
Acknowledgements
I have benefitted from enjoyable discussions with G. Ecker, H. Galic, A.
Pith, E. de Rafael, B. Stech and R. Willey. Thanks are also due to the organizers
for their customary successin creating a very pleasant environment.
-66-
:
References
Appendix B: Some technical remarks on the basics of ChPT
1) W.Buchmiiller and D.Wyler, Nucl.Phys.B268 (1986) 621.
2) J.C.Anjos et al., “A Search for Flavour Changing Neutral
Current
Let go (qR1 generate the transfomlation of the fields under the action of the group
SU(.I)L [sum).
The unitary matrix u as defined in (4.17) then obeys a simple
3)
4)
5)
6)
7)
8)
transformation law:
Y + gt2u g;
under Sum
Processes
in
lk’~yS
of Charmed Mesons”, XXIVth International Conference on High Energy Physics,
63.1)
x SU3)R.
(B.1) is so remarkable because it shows that the matrices u and u+ are the
appropriate building blocks for constructing chirallv invariant Lagrangians. There is then a
Munich (1988).
J.Adler et al., Phys.Rev.Lett. 60 (1988) 1375.
See the lectures by K.Berkeimdn, these Proceedings.
See the lectures by A.J.S.Smith, these Proceedings.
T.Inami and C.S.Lim, Prog. Theor. Phys. 49 (1973) 652.
S.Bertolini and A.Masiero, PhysLett. 1748 (1986) 343.
R.S.Chivukula and A.V.Manohar, preprint CTP#1580, BUHEP-88-7 (1988).
transformations since those are global) and take the trace; the simplest non-trivial
9) S.Bertolini and ASantamaria, preprint CMU-HEP88-2 (1988).
10) For a recent review, see: F.Gilman, lectures at the SLAC Summer Institute 1986.
11) See for example: H.Georgi, Weak Inreractions and Modem Particle Theorv,
expression one can write down reads
(2)
I
- tra,va,u’
Benjamin/Cummings Pub. Co., 1984.
12) .l.Gasser and H.Leutwyler, Nucl.Phys.m(l985)
465.
13) G.Ecker, A.Pich and E.deRafael, in preparation (private communication).
simple prescription: form pairs au au+ (the derivative operator commutes with chirdl
(8.2)
(1987) 363; preprint CERN-TH.4853/87 (1987).
15) L.SehgaI, preprint PITHA-88/2 (1988).
16) J.F.Donoghue, B.R.Holstein and G.Valencia, Phys.Rev. ~
(1987) 2769.
17) A.J.Buras, “The l/N Approach to Non-Ieptonic Weak Interactions”, in:
, i.e. has dimension of an
inverse mass. Thus we are dealing with a non-renom~alizahle interaction.
1
14) GEcker, A.Pich and E.deRafael, Nucl.Phys. Q.9-I (1987) 692; PhysLctt. 189R
The matrix u can be expressed by an expansion in powers of the Goldstone boson
fields Q, see (4.17); the expansion parameter contains l&
..
It is then
completely obvious that loop, i.e. quantum corrections will necessarily introduce new
” CP Violation”, C.Jarlskog (ed.), World Scientific, 1989, with references to
coupling terms like
I
earlier work.
18) I.I.Bigi and A.I.Sanda, Phys.Lett. m
(1986) 320.
19) For a recent review on D decays, see: I.I.Bigi, preprint UND-HEP-88.BIGOI,
to appear in the Proceedingsof the Ringberg Workshop “Hadronic Matrix Elements
(B.3)
and Weak Decays”, 1988;
M.Wirbel, preprint DO-TH 88/2 (1988), to appear in Progress in Particle and Nuclear
with a relative weight that is completely undetermined by chiral invariance. Going to
Physics.
20) I.I.Bigi and B.Stech, preprint SLAC-PUB-4495 (19X7), in: Proceedings of the
Workshop on High Sensitivity Beauty Physics at Fermilab, 1987;
higher loops will enforce couplings 1(G),1(@etc. where the superscript denotes the number
of derivatives.
M.B.Gavela et al., Phys.Lett. m
(1985) 425.
21) L.Wolfenstein, Comm. Nucl.Part.Phys. 14 (1985) 135.
22) Fore recent discussion, see: A.Soni, “Aspects of Rare B Decays”, in: Proceedings.
-67-
:
:.,.,
.,
:
-.
of the B-Meson Factory Workshop, SLAC, 1988, SLAC-Report 324.
23) W.-S.Hou, A.Soni and H.Steger, PhysLett. 192B(1987) 441;
N.Deshpande et al., Phys.Rev.Lett. 5e (1987) 184.
24) N.Deshpande and J.Trampetic, in : Proceed. of the International Symposium on
Production and Decay of Heavy Flavours, Stanford, 1987, E.Bloom and
A.Fridman (ed.), Ann.N.Y.Acad.Sci., Vol. 535,
25) E.Golowich and S.Pakvasa, preprint UMHEP-293 (1988).
26) B.Grinstein, R.Springer and M.Wise, PhysLett. 202B (1988) 138.
:
‘_
._
..,.
.,”
I
27) N.Deshpande et al., Phys.Rev.Lett. x (1986) 1106;
J.O’Donnell, PhysLett. m
(1986) 369;
W.-S.Hou. A.Soni and R.Willey, Phys.Rev.Lett. 58 (1987) 1608.
N.Deshpande and J.Trampetic, preprint OlTS 379.1988.
28) B.Grinstein, M.Savage and M.Wise, preprint LBL-25014, 1988.
29) Ref. 28; N.Deshpande and J.Trampetic, preprint OITS 379,1988.
30) W.-S.Hou, A.Soni and R.Willey, Phys.Rev.Lett. 58 (1987) 1608.
31) For a recent discussion, see: W.-S. Hou, preprint MPI-PAE/PTh 7/88, 1987.
32) M.Bander, DSilvennan and ASoni, Phys.Rev.Lett. a (1979) 242;
I.LBigi et al., “The Question of CP Noninvariance -- as seen through the Eyes
of Neutral Beauty”, preprint SLAC-PUB-4476, 1987, in: “CP Violation”,
Clarlskog (ed.), World Scientific, 1989.
33) M.Bauer, B.Stech and M.Wirbel, Z.Phys. c34 (1987) 103;
M.B.Gavela et al., PhysLett. m
(1985) 425.
34) This emerged from an interesting discussion with R.Willey.
35) I.I.Bigi and A.I.Sanda, PhysLett. 148B (1984) 205.
36) S.L.Glashow and SWeinberg, PhysRev. D15 (1977) 1958
37) W.-S. Hou and R.Willey, PhysLett. 2028 (1988) 591.
38) M.J.Duncan, Nucl.Phy@&l
(1983) 285;
J.F.Donoghue et al., PhysLett. 128B (1983) 55.
39) SBertolini, F.Borzumati and A.Masiero, preprint CMU-HEP88-08, 1988.
40) R.Willey and H.L.Yu, Phys.Rev.m (1982) 3086;
R.M.Godbole et al., PhysLett. 1948 (1987) 302.
41) B.Grinstein, L.Hall and L.Randall, preprint LBL-25095, 1988.
42) The results of Ref.26 have been criticized by R.Grigjanis et al., preprint UTPT-88.11.
. .
_:’ ,, -.
:-
SUPERCONDUCTING
FOR MONOPOLES
AND WEAKLY
DETECTORS
INTERACTING
PARTICLES
B. Cabrera
Physics Department, Stanford University
Stanford, California 94305
In our laboratories at Stanford, we have undertaken several research programs to
search for dark matter candidates in our galaxy with laboratory based detectors. The
first effort is a search for magnetic monopoles in the cosmic rays. These would be
supermassive (IOtb-1019 GeV/c*) and a density of only one per lo-10,000 km3 would
be sufficient to account for the local dark matter around our galaxy. We have been
operating a 1.3 m2 times 4n sr detector utilizing eight SQUIDS. It is the largest
superconductive monopole detector. The second effort involves the development of
large mass (-1 kg) elementary particle detectors capable of sensing weakly interacting
particles. These utilize silicon crystals at temperatures below 1 K, have spatial
resolution in three dimensions and would measure the total energy deposition. Such
detectors will be used for direct dark matter searches and for neutrino experiments
capable of setting better limits on the neutrino mass.
@B. Cabrera 1988
-69-
._-_
.-
PART
SEARCH
FOR MAGNETIC
catalysis. It has been shown theoretically that the supermassive monopoles arising
from many grand unification theories would catalyze nucleon decay processes. If the
cross section for such events is of order the hadron cross section, as has been
suggested,then all attempts a: direct detection of the monopoles from such theories may
be doomed to failure. Arguments based on x-ray flux limits from galactic neutron
stars, which assume a strong interaction cross section for proton decay catalysis, lead
to an upper bound for magnetic panicle flux of about loo*’ cm-* ST’ s-l. There remain
unanswered questions concerning the detailed theoretical understanding of the catalysis
cross section and concerning the astrophysical arguments based on our incomplete
understanding of neutron stars. In addition, proton decay has not yet been observed.
Thus, from an experimental point of view more weight should be given to the less
A:
MONOPOLES
IN THE
COSMIC
RAYS
Introduction
In 1931, P.A.M. Dirac proposed the existence of magnetically charged particles
to explain the observed quantization of electric charge. He showed that only integer
multiples of a fundamental magnetic charge g (Dirac charge) = hc/4se are consistent
with quantum mechanics. Many years of experimental searches produced no
convincing candidates. In 1974 ‘t Hooft and independently Polyakov showed that in
all true unification theories (those based on simple or semi-simple compact groups)
magnetically charged particles are necessarily present. The modem theory predicts the
same long-range field and thus the same charge g as the Dirac solution; now, however,
the near field is also specified leading to a calculable mass. The standard SU(5) model
predicts a monopole mass of 10’6 GeV/c*, much heavier than had been considered in
previous searches. More recent unification theories based on supersymmetry or
Kaluza-Klein models yield even higher mass values up to the Planck mass of 1019
GeV/c2.
Such supermassive magnetically charged particles would possess qualitatively
different properties from those assumedin earlier searches. These include necessarily
nonrelativistic velocities from which follow weak ionization and extreme penetration
through matter. Thus such particles may very well have escaped detection in earlier
starches based on heavy ionization of relativistic monopoles.
Although GUTS theories are very clear in their prediction of the existence of
monopoles, cosmological theories based on GUTS lead to impossibly high or
unobservably low predictions for monopole particle flux limits with the latter results
being exponentially model dependent. Thus, only astrophysical arguments provide
guidance For the relevant detector sensing areas for experiments. An upper bound of
10 iT c& sr~’ s-1is obtained assuming an isotropic flux from arguments based on the
existence of the 3 microgauss galactic magnetic field (Parker bound). The Parker
bound becomes less severe linearly with monopole mass for masses above 10”
GeV/cz. In addition, several authors have demonstrated that models incorporating
monopole plasma oscillations would allow a much larger particle flux, approaching in
some cases the local galactic dark mass limit. All of these bounds assume particle
velocities in gravitational Gal equilibrium, i.e., very near 10.”
Much more severe astrophysical limits can be obtained based on proton decay
::
_’
:
model dependent astrophysical limits.
Superconductive technologies, many developed at Stanford LJniversity over the
last decade, have led naturally to very sensitive detectors for magnetically charged
particles. These superconductive detectors directly measure the magnetic charge
independently of particle velocity, mass, electric charge and magnetic dipole moment
[I]. In addition, the detector response is based on simple and fundamental theoretical
arguments which are extremely convincing. Because of their velocity-independent
response, these detectors are a natural choice in searches for a particle flux of
supermassive (and therefore slow) magnetically charged particles. By far, the most
definitive positive identification of a magnetic charge would be made with a
superconductive detector. Other detectors, though larger, are less satisfactory for
positive identification of monopoles since the interaction of monopoles with matter
through ionization processesis less well understood [2]
Detailed reviews of the theoretical, the experimental and the astrophysical work
can be found in Magnetic
Monopoles
[R.A. Carrigan and W.P. Trower, eds.,
Plenum 19831 and Monopole ‘83 [J. Stone, ed., Plenum 19841.
Operation
of Three
Loop
Detector
Between February, 1983 and March, 1986, we operated a three loop coincident
superconducting magnetic monopole detector 131. The rms current noise levels in an
effective noise bandwidth of = 0.16 Hz were 0.02 $JL in all three loops, less than 1%
of the signal expected from Ihe passageof a Dirac magnetic charge through one of the
two turn loops (4 $I&). The sensing area based on this low noise operation was 476
cm2 (7 1 cm2 loop area and 405 cm* near miss area) for events greater than 0.1 $& in
C.
-7o-
:.
at least two of the three loops. The data were extremely clean and no candidate events
were seen. Based on the 1008 days of accumulated active running time, these data set
an upper limit of 4.4 x 1O-t2cm-* sr-t s-I (90% C.L.) on any uniform flux of magnetic
monopoles passing through the earth’s surface at any velocity [3].
-.:.
I.
.
.
.~,.,.
_.
New Large Area Octagonal Detector
Our group at Stanford, consisting of B. Cabrera, M. Huber, M. Taber and R.
Gardner, has designed, constructed, and brought into continuous operation an eight
loop detector [4] with a cross section averaged over 47t sr of 1.3 m* for double
coincident events and a signal-to-noise ratio of 30 for the passage of a single Dirac
charge. This detector shown schematically in Fig. 1, is composed of eight planar
superconducting detection coils arranged around a cylinder with an octagonal cross
section. Each coil is a gradiometer 16 cm wide and 6 m long and is connected to a high
sensitivity rf SQUID current sensor. The entire assembly is surrounded by a
superconducting lead shield and housed in a dewar which is enclosed in a w-metal
shield. This detector has a sensing area 30 times larger than that of the three loop
detector.
A very important design feature for the large scale use of superconducting coils as
monopole detectors is the use of a gradiometer winding pattern [5,6]. The sensitivity
of a gradiometer to external magnetic field changes is substantially reduced over that
from a simple coil whereas the sensitivity to the passageof a magnetic charge remains
high since the particle passesthrough only one element of the gradiometer pattern. We
have utilized computer calculations to optimize our coil design under constraints from
dewar size and minimum acceptable signal to noise ratio. The optimum pattern which
we have used for our design is shown in Fig. 2. The conducting elements are NbTi
ribbon, 2mm wide and 50 pm thick. It is a repeating rectangular pattern with an aspect
ratio of 0.6 to 1.O. A further improvement was achieved by breaking the loop up into a
number of parallel elements which are connected together to one SQUID. This
technique reduces the coupling lossesto the SQUID from a l/L proportionality to l/c
where L is the inductance of the single series loop [7].
The new 1.3 m2 monopole detector requires eight low-noise SQUID systems,
T-*-l
SUPERCONDUCTING
--
SHIELD
-- 7
:‘.:.
..,>,.
.:,..
one for each panel of the detector array. We have chosen to use rf SQUIDS
manufactured by Biomagnetic Technologies Inc. [B.T.i.], (formerly S.H.E. Corp.)
together with rf electronics from Quantum Design. A shield of high magnetic
permeability metal (p-metal) has been designed and constructed to shield the detector
Fig. I. Schematicdiagram of octagonal detector.
-71-
from the earth’s magnetic field during the initial cooldown, as the inner
superconducting lead shield goes through its transition temperature. The external shield
consists of 0.038 inch-thick sheets of p-metal mounted on an aluminum frame. The
shield provides an absolute field below 10 milligauss throughout most of its interior.
We are utilizing a Model 1200 closed-cycle liquid helium refrigeration system from
Koch with the new octagonal detector. We have modified the operation of the helium
liquifier to maintain a constant dewar pressure relative to atmosphere. This
modification eliminates SQUID signals resulting from the pressure variations of the
original cooling-capacity control system. A very slow drift remains, caused by
atmospheric pressure changes, but it is well below the bandwidth of our detection
system and poses no degradation of our signal to noise ratio for monopoles. There are
two significant advantages derived from using this system: lower long-term operating
costs, and the virtual elimination of disturbances that are produced by liquid cryogen
transfers. Now that the new system is cooled down and stabilized, we achieve
essentially 100% live time.
The geometry of our detector provides greater confidence in coincidence
correlations for true monopole events than our earlier detectors. A monopole can
intersect no more than two loops, and the only trajectories intersecting one loop are
those passing through the detector ends (which are not covered by detector loops) or
through small gaps between the panels. We thus exclude from consideration all signals
appearing in one loop only or in three or more loops. The response of the detector is
calculated from a numerical simulation of a uniform flux of cosmic ray monopoles.
This response is shown in Fig. 3 for positive signals in both loops; it is symmetric in
the other quadrants and includes trajectories which intersect one or two wires.
A computer and strip-chart recorder collect data at 10 Hz and 0.1 Hz,
respectively, from the SQUIDS, strain gauge, and other anti-coincidence
instrumentation. The strain gauge sensesmechanical disturbances which sometimes
induce spurious offsets. Also recorded are a line voltage monitor, ultrasonic motion
detector, and flux-gate magnetometer in the anti-coincidence instrumentation. We also
have added a wide-band radio frequency voltmeter for EM1 anti-coincidence.
We began obtaining low noise data on May 5, 1987 [8]. Figure 4 shows typical
filtered data (one point every 10 set) from the computer data acquisition system.
Included is a calibration signal showing the signal to noise for a Dirac size magnetic
charge. Figure 5 shows the high bandwidth data available around any events. This
particular event was caused by a bump of the dewar system clearly seen in the strain
\ \
521.2cm
”
-1
Fig. 2. Loop parameters for octagon01detector.
-72-
;
_.,
:.:..
‘.
._
,
,-::
.,
:’
-
-1
-
-E C41
T--------------N
[%I 13
2 dl -
-
-1
-
N
z
-I
.-I:0 O
;/
:
_.‘.
31-J’JL-87
gauge and external flux-gate magnetometer channels. As of July 14, 1988, we have
accumulated 6,OCKlhours of live time. A preliminary analysis of these data [S] contain
no candidate events and set a limit of 7.8 x lo-13 cm-2 srt s-1 (90% CL.) for any
particle flux of magnetically charged particles passing through the surface of the earth.
We intend to run the detector continuously for at least three years.
>
a
a
-
Particle
Flux
Limits
From
Our
Detector
Exposures
In Fig. 6 we summarize the current status of our research efforts with respect to
astrophysical bounds. The Parker bound as modified to include supermassive
monopoles has a mass independent floor at -10-1s cm-2 ST-ts-t and rises linearly with
mass above -1017 GeV/c* until it intersects the local dark matter bound around the
Planck mass (1019 GeV/c2 ). Since more recent unification theories suggest a
monopole mass approaching the Planck mass, searches at a flux level of -lo-t3 cm-2
sr-t s-t are particularly important. Also shown in Fig. 6 are possible monopole particle
I.
.
’
‘.
‘I’
&.-----------It
I
.
,
‘.
”
.
flux levels 2 to 3 orders of magnitude above the Parker bound. These models are based
upon monopole plasma oscillations within the galaxy. Detailed computer simulations
performed by the Cornell group confirm the stability of such solutions and to my
knowledge they are not ruled out by any galactic observations.
The particle flux limit obtained from our three loop superconductive detector was
4.4 x lo-t2 cm-2 ST-t s-t at 90% C. L. Four other groups (Chicago-FermiLabMichigan; IBM, Yorktown Heights; Imperial College; and NBS, Boulder) had obtained
similar limits, for a combined world limit of 1.4 x lo-12 cm-2 sr-t s-t at 90% C. L. In a
preliminary analysis of 15 months of data from our new octagonal detector, we find no
candidate events for the passage of a monopole through the detector and set an upper
limit on such a particle flux of 7.8 x IO-13cm-2 ST-1s-t (90% C.L.). In addition, the
IBM, Yorktown Heights group is operating a 1 m2 x 4tt sr sensing area detector and
“1
-;
has reported a similar preliminary result in slightly more run time. The combined world
limit for velocity independent detectors is now - 3 x lo-13 cm-2 sr-1 s-t (90% CL.) and
is shown in Fig. 6. Also shown is the limit our detector will achieve after three years
of operation.
These data effectively rule out the plasma oscillation models and approach the
mass-dependentParker bound near the Planck mass.
Fig. 5. High bandwidth data (twenty poirlts per xc) from trigger showing
the eight SQUID channels, the strain gauge channel and the
external flux-gate magnetometer channel. This disturbance was
caused by a bump to the &war.
-74-
-_
Acknowledgements
\
,
Our group at Stanford has included 9. Cabrera, M. Huber, M. Taber and R.
Gardner and J. Bourg. This research is funded in part by DOE Contract
DE-AM03-76-SF00-326.
1982 (0.001 m2)
,
World Limit (Late 19881
I
lOI
I
lOI
10IX
10IY
I
102O
I
IO*’
Monopole Mass (CkV/c2)
-_
.:
__:.;
._
Fig. 6. Cosmic ray particle flux limitsfrom our superconductive detectors
compared with varicw astrophysical limits.
-75
i
. .
PART
SILICON
CRYSTAL
ACOUSTIC
The decay rates are very strongly dependent on phonon energy (=v5) and for
wavelengths of several hundred lattice spacings further decays are entirely negligible.
These longer wavelength phonons propagate throughout the crystal with little scattering
and no dispersion. This mode has come to be called the the ballistic phonon mode
II:
DETECTORS
FOR NEUTRINOS
Introduction
[121.
Semiconductor diode particle detectors now provide the highest energy resolution
(- 3 keV FWHM for 1 kg) and the lowest thresholds available (- 5 keV) for large mass
detectors. In this energy range less than 30% of the deposition energy is converted
directly into electron-hole pairs which produce the observed signal in the
semiconductors, the rest forming phonons. The characteristic energies of these
phonons is - 1 meV, 10s less than the excitation energy for an electron-hole pair in a
semiconductor (- 1 eV). Thus in principle, energy resolutions over an order of
magnitude better are possible if the phonon signal is used.
Recent work on
bolometers, which sense the thermal phonons, has demonstrated an improvement in
energy resolution (most recently 17 eV, FWHM, by Moseley, McCammon, et al [9])
by measuring the temperature rise in a small ultra-low heat capacity sensor (- 10m5g of
silicon). B. Cabrera, L. Krauss and F. Wilczek IlO] suggested scaling such
bolometers up to a mass - 1 kg.
Motivated by this suggestion, our group, now composed of B. Cabrera, B.
Young and A. Lee at Stanford and B. Neuhauser at San Francisco State University, has
proposed direct sensing of the ballistic phonons produced by an event in a large
insulating single crystal [I 11. Since this wavefront carries information on the event
total energy and location within these silicon crystal acoustic detectors (SiCADs),
substantial improvements in background rejection are possible over detection schemes
which measure total energy deposition only. A threshold of 1 keV or better is
important for our primary interest in using SiCADs as neuuino detectors. For example,
at power reactors all nuclear recoil signals from elastic neutrino scattering are below 10
keV with 60% above 1 keV, and a 1 kg SiCAD with a I keV threshold would register
an event rate of - 100 events/day.
An interesting and important aspect of ballistic phonon propagation is that strong
focussing effects occur within the crystal, although the propagation is dispersionless.
These focussing patterns, which have been well verified experimentally, permit three
dimensional reconstruction of event locations within the crystal and can resolve tracks
or multiple scattering events. We have performed Monte Carlo calculations on these
effects [ll].
Figure 7a shows the result of such a calculation for a point energy
deposition within a silicon cube with all faces cut along [loo] axes. The number of
phonons used in the calculation is for a 1 keV energy deposition at a point within the
crystal. It is clear that information on the event location as well as tracking information
is available. We call such a detector a SiCAD (silicon crystal acoustic detector).
We have considered several phonon sensor configurations for the surface
readout. The most promising to date consists of parallel strips on each face and
provides spatial resolution based on the intensity and arrival time profiles across the
sensorson each face (Fig. 7b). The sensorson the front and back faces perpendicular
to the x (y and z) axis have their sensorsparallel to the z (x and y) axis and thus can be
used to determine the y (z and x) coordinate of the event location. As an example, the
phonon energy flux intensities incident on each of the 384 strips for the event location
in Fig. 7a is shown in Fig. 8. As can be seen, sharp peaks in each of the face intensity
profiles locate the event to better than the width of a sensor and there is always at least
one sensor with an intensity greater than - 2 % of the total energy in the event. To
obtain a 1 keV energy threshold for event detection within a 1 kg SiCAD cube (for
example to detect neutrino-nucleus elastic scattering at a reactor) then each parallel strip
sensor must have an energy sensitivity of - 20 eV.
Ballistic
Superconducting
Phonons
from
Point
Events
in Crystal
Cubes
For a deposition of energy in a well localized volume within a single crystal of
silicon, a thermal-like spectral phonon distribution is generated with a characteristic
.;....2
Phonon
Sensors
During this past year we have worked on two phonon sensor designs which
utilize superconductivity. The first, called a transition edge sensor, is a simple single
layer thin-film patterned into a series superconducting circuit and biased with a constant
temperature of lo-20 K. This spectral distribunon arises from the rapid decay of
electron-hole excitations to the band edge, first generating very short wavelength
phonons, which quickly relax to longer wavelength phonons within less than -10 nsec.
current. A phonon flux incident on the film will drive those portions normal where the
phonon energy density has exceeded a critical phonon energy density. Then a voltage
-76
‘,.
.‘__
:
..
._
II
.::
:
:
.‘..Y.
‘..
la
0
20
40
CHANNEL
mrrurr
x on 2 ,rcrs
60
0
20
40
CHANNEL
M~as”r.
Y on x ‘ace*
60
0
20
40
60
CHANNEL
Pleasure 2 on Y frcrs
: :.:-.
,__ -_
._
Fig. 7. (a) Calculatedphonon energy densip incident on silicon cube with
[IOO] faces from point source within the crystal. (b) Arrangement
of parallel xenon on crystal faces.
Fig. 8. Simulated signals from 64 channels per face. Lower two rows
correspond to time evolution of peak channel on eachface.
-77-
deposited on the surfaces of the silicon crystals and biased with a constant current.
For currents below a latching critical current, self-terminating voltage pulses are
observed. These pulses are caused by the heating of line segments above the
superconducting transition temperature. Last year, we demonstrated this technique
using aluminum films with alpha particle sources [13], and most recently we have
obtained a factor of one hundred improvement in energy resolution and threshold using
titanium films in x-ray experiments [ 141. These most recent sensors are made by
depositing 40 nm of titanium on crystalline silicon wafers which are 1 mm thick. The
polished wafer faces are perpendicular to the [ 1001 axis. The meander pattern, shown
schematically in Fig. 9, was produced using conventional photolithographic techniques
and consist of 299 parallel lines each 2 ttrn wide with 3 pm space between lines. The
pattern is aligned parallel to the [I IO] crystalline axis of the wafer. The active Xcd of
the pattern is 4.5 mm long and 1.5 mm wide. The normal resistance just above their
superconducting transition temperature (T, = 312 mK) is - 18 kW per line. These films
have sharp transition widths of 2 5 mK (from 10% to 90% of the resistive transition),
indicating homogeneous properties across the film. A typical superconducting to
normal resistive nansition for one of these patterns is shown in Fig. 10.
Here we describe two recent x-ray experiments. These were performed by Betty
Young with a 24 pC source of xt Am. The decay spectrum of z4tAm is dominated by
two alpha particle energies at = 5.5 MeV. In addition to these two alphas are a nuclear
gamma at 60 keV and two atomic x-rays at 14 and 18 keV. An appropriate absorber
placed in front of the source readily stops all of the alphas and essentially all of the 14
and 18 keV x-rays before they reach the sensor; however the 60 keV gamma rays,
being much more penetrating, pass through the absorber attenuated in number by - 0.5.
We used ,005” (125 Frn) thick foils of Sn and Pb as absorbers.
Using a cryopumped 3He refrigerator at 0.3 K (described below) we biased the
is seen across the circuit providing a signal which is proportional to the length of the
circuit driven normal. If the current is below a latching critical current, then
self-extinguishing pulses are seen,otherwise the resistive heating of the normal state is
sufficient to expand the normal region across the whole circuit. Such a system is
straightforward to manufacture using photolithographic techniques, but the physics
governing the response is non-linear and complicated. Below we discuss this point in
more detail.
A second device, the superconducting tunnel junction, possess the opposite
properties. These are more difficult to manufacture, but the physics is more linear and
simple. Such a device consists of two superconducting films separated by a thin oxide
bartier (typically l-2 nm). This device is biased with a constant voltage given by A/e,
where A is the superconducting energy gap. Phonons from an event within the crystal
reach the surface and enter the superconducting film. Once inside the superconducting,
those phonons with energies greater than 2A (most) are strongly absorbed by breaking
Cooper pairs and forming electron-like excitations called quasiparticles. In fact for
phonon energies well above threshold, several Cooper pairs will be broken. These
quasiparticles will tunnel across the oxide barrier providing a signal if the tunneling
times are short compared to the quasiparticle recombination time. This condition is
satisfied for T < TJlO, where quasiparticle recombination with thermal quasiparticles is
negligible. For these devices the tunneling current is proportional to the energy
absorbed by the film as long as the quasiparticle density produced by the phonon flux
remains dilute so that little self-recombination of the quasiparticles occurs prior to
tunneling.
Given the results of our experiments during this past year and calculated
improvements, we now believe that transition edge detectors can be used successfully
to construct SiCAD detectors capable of a 1 keV energy threshold. Such devices will
become our central focus during this next year for our first generation detectors.
However, we also believe that better ultimate resolution and thresholds will be obtained
with tunnel junctions, and we will maintain a parallel effort to develop this more
difficult technology over a longer time scale. As available, we will substitute the tunnel
junction technology into future generationsof the SiCADs.
Experiments
with
Titanium
Transition
Edge
Sensors
on Silicon
titanium/silicon devices at the foot of the resistive transition in temperature and below
the latching critical current in bias current, and we observe self-terminating voltage
pulses when the film is bombarded by phonons produced by the interaction of an
incident x-ray (or gamma ray) within the Si substrate. These pulses occur because
enough phonon energy from the photoelectron in the silicon reaches the Ti film to drive
portions of the film normal. To estimate the threshold energy density E, necessaryfor
this superconducting to normal state transition, we integrate the heat capacity of the
Wafers
superconductor from the bias temperature to T,:
Our first generation of SiCADs will utilize superconducting transition edge
devices as phonon senors. These devices consist of thin superconducting lines
-78-
: -:. .,-. -.:
-,
-:-
q
.
.
.
.
.
.
.
.
.::
‘,
,’ ‘. ‘,
‘G’,,~:,
.’ .,,
/
.,:‘c::
E, = lTTc C,,(T)dT ,
where C,, is the electronic heat capacity below T, as given by the BCS theory. We
assumethat the time constants are sufficiently long to allow quasi-thermal equilibrium.
The asymptotic form near T, is:
En = 5N(O) Aaz (l-T/T, ) ,
where Au is the gap at T = 0 and N(0) is the density of states at the Fermi surface in the
normal metal.
For our Ti films, N(0) = 4 x 10” cm-3 eV-1 and A a = 47 peV, yielding Et, = 22
eV/pms at T/r, = 0.95. In terms of the energy density per unit area of film, E, we get
E, = (22 eV/pm3) x (40nm) = 0.88 eV/pm 2. We may also estimate the minimum
detectable energy for a Ti sensor as follows. In our current experimental setup we use
a cryogenic GaAs MESFET voltage-sensitive amplifier (described below) which
introduces an ampiifier noise level of AV,, = 1 nV/@z at 1 MHz. At T/r, = 0.95 and
a bias current (It,) of 60 nA we can detect a minimum sensor resistance of ARr,,
=AV,, & = 17 R. At T ;: T, the resistance of our sensor is - 18 kfZ per 2 pm wide
line 5 mm long, or 8.5 fi per 2 pm x 2 pm square of the Ti film. Therefore the area of
film which corresponds to a normal area resistance of A& = 17 R is (17 n/8.5 Q)
(2 pm x 2 pm) = 8 pm2. The minimum detectable energy deposited in the Ti sensor is
then AE,, c: E, x Area- = (0.88 eV/pmz) x (8 pm2 ) = 7 eV. The inequality holds
I...,....,..
0
(a)
5
Tie
‘I...‘..“‘(.‘.(
10
15
(microsec)
20
x
becauseJoule heating contributes to the actual area driven normal.
Figure 1la shows (for I, = 120 nA and T = 286 mK) some typical single pulses,
of - lo-15 psec duration, resulting from the interaction of 60 keV gamma rays (from
24tAm) in the Si substrate of a TE sensor. In Fig. 1lb (for I, = 60 nA and T = 299
mK), we have expanded the time scale to show the leading edge of each pulse with
electronics-limited risetimes of - 140 nsec.
We mounted the 24tAm source such that its active area faced the backside of the
299-line sensor, and investigated the effect on detector response when various
absorbers were placed between the source and sensor. We chose two convenient
absorber materials (Pb and Sn) and used appropriate thicknesses such that we could
study the TE response primarily due to 60 keV g-a
ray radiation with zero incident
alpha-particle flux, and essentially zero 14 and 18 keV x-ray flux. The measured count
rates for all spectra obtained, for various operating temperatures, bias currents and
Fig. 11. (a) Individnal pulses from 60 and 25 keV x-rays. (b) Leading
edges of pulses wirh 140 n.srise time.
-8O-
absorbers, were consistent with the calculated values.
Figure 12a is a pulse height spectrum obtained for the case of a ,005” (125 pm)
thick Pb absorber. The prominent peak towards the center of the spectrum is the
photopeak due to interaction of 60 keV gamma rays in the Si subsnate of the detector.
The sharp feature at 11 keV is consistent with the position of the Compton edge for 60
keV gamma rays in silicon. In Fig. 12b, we show a pulse height spectrum under
similar running conditions, but with a ,005” Sn absorber. We note that the prominent
features due to the 11 keV and 60 keV interactions appear, as expected, in the same
positions as they did with the Pb absorber. Furthermore, in the Sn absorber spectrum,
we observe an additional peak around 25 keV. This peak is readily recognized as that
due to secondary emission of & x-rays from the Sn.
We can qualitatively reproduce typical pulse height spectra (such as those shown
in Figs. 12a and b) by applying Monte Carlo methods to a simple model of the detector
response. We assume that an incident photon, if it interacts at all, interacts in the
silicon substrate only once, and that this interaction is point-like. We imagine that, to
first order, the phonon energy generated by such a scattering event spreads spherically
outward through the crystal, producing heat spots on the surfaces. The energy density
(per unit area) of such a heat spot is then given by
F
10 Min Run
0
100
(a)
1
200
Channel Number
EG (p.z) = z Ea /[4~(z*+p*)~~]
where p is the radius of the heat spot, z is the perpendicular distance from the Si
surface to the location of the scattering event, and Ea is the total energy of the heat spot.
Defining E,, as the (minimum) critical energy density required to drive the detector film
normal, we find that the areadriven normal is given by
A(z) = x p* = z [(zErj4xE32fl-z2]=
x ~2 [(z&$m- (z/z#]
0
100
200
(b) Channel Number
where rc2 = Ee /(4 x E,,).
The amplitude of the voltage pulse resulting from an interaction in the crystal is
simply proportional to the amount of line driven normal, and the number of interactions
producing pulses is proportional to (dA/dz)-1 for events uniformly distributed in z. For
incident particles of given energies, we can then plot a theoretical pulse height spectrum
for the Ti transition edge response -- as shown in Fig. 13a for the case of incident 30
Fig. 12. (a) Pulse height spectrum for z4/Am source using Pb absorber.
(b) Pulse height spectrum for same source and geometry using Sn
absorber.
and 60 keV photons.
-81-
22
8
4
,
I
30 keV
I
I
Another interesting and very useful plot is generated by graphing the calculated
normal area A as a function of interaction depth z for incident particles of a given
energy. By considering various initial particle energies, one obtains a family of curves
as shown in Fig. 13b. Assuming this simple heat spot model is valid to first order
(i.e. neglecting focussing effects), we can extract important spatial information about
events by comparing such curves with those obtained experimentally. We are in the
process of carrying out the more computer intensive calculations which fully include
phonon focussing effects.
We are currently working to fabricate 1 and 2 mm thick, double-sided (Ti
I
10 Min Run
meander patterns on both sides of the Si wafer) transition edge devices. These devices
will enable us to do timing experiments and to obtain spatial information about each
event occurring in the detector. We shall also be able to experimentally measure Fig.
13b and obtain an energy for each event. These improvements will take us one step
closer towards our goal of developing a = 1 kg scale SiCAD.
(a) Channel Number
Cryopump 3He Test Probe
We have performed these experiments using our laboratory-built fast-turn-around
probe for device testing down to 250 mK and we are delighted with its performance.
The probe was designed by Barbara Neuhauser, and we cannot overemphasize the
importance of quick and inexpensive accessto ultra-low temperatures for the successful
development of both transition edge and tunnel junction devices. Until a well
characterized design is available, many devices are either defective or do not perform as
designed. We are now able to rapidly test a range of different devices and we have
significantly increased our rate of progress.
This refrigerator is based on a sealed 3He and charcoal cryopump design. In a
typical run we begin precooling in the morning and by early afternoon we can begin
taking data at - 270 mK. The initial liquid 4He transfer (- 5 liquid liters) lasts
twenty-four hours allowing more than twenty hours of data below 300 mK.
/-
. ..-
200
0
(b) Chazl
Low
Number
Noise
JFET
Preamplifiers
Operated
Another important component for our recent progress has been the use of
cryogenic preamplifiers in the titanium sensor SiCAD experiments ]15]. These were
designed and constructed by Adrian Lee. The peak resistance of the titanium line,
typically - 3 kR for 60 keV x-rays, would produce a large “RC” time constant if the
fist stage of amplification were at room temperature. This time-constant can have two
Fig. 13. (a) Monte Carlo generated puke height spectrum from simple
model. (b) Pulse height versus distance from titanium sensor
function used in Monte Carlo.
-82-
:
Cryogenically
..:.
:
:.::::-L
..
_-
adverse effects. First if the rise-time is long compared to the signal duration, the signal
will be truncated since the input pulse will start to decay bet-orethe output can reach its
full Jlulse height. Second, a long time constant will make it harder to resolve the
leading edge of the pulse. The spatial resolution of the detector will, in the future,
depend on being able to resolve timing differences between different channels, which
makes a long time constant undesirable. Mountmg the first stage of amplification
down in the cryostat reduces the capacitance seen by the amplifier dramatically. The
GaAs MESFET (Plessy P3S-IlOl), which we use, has the advantage of operation at
1.5 K and has very good noise above 100 kHz.
The total power dissipation of this amplifier is about 14 mW. The bandwidth of
the amplifier is IO MHz. but the rise-time is dominated by the RC time at the input.
The gain of this device 1svery low, about 15 into SO0, which necessitatesa low noise
room-temperature stage. We use a Trontech WSOATC instrumentation amplifier with a
noise voltage of - 1.2 nV/&& and a bandwidth from 10 kHz to 50 MHz.
Superconducting
Tunnel
.Junctions
as Phonon
- I5 pee were observed.
In fact, this sensitivity is already sufficient for our detection threshold requirement
of 1 keV in a 1 kg SiCAD. However, the area of each parallel strip sensor needs to be
- 1 cm2, a factor of - 104 greater than used by the S.I.N. group. We are pursuing
several techniques for obtaining comparable energy sensitivity in these much larger area
tunnel junctions.
Conclusions
Ballistic phonon focussing effects greatly enhance the spatial resolution in silicon
crystal acoustic detectors (SiCADs). Utilizing titanium superconducting transition edge
devices as phonon sensorson the crystal surfaces, we believe that an energy threshold
of - 1 keV can be achieved for a 1 kg SiCAD. Such a detector would be of great
interest for a number of experiments including dark matter searches for weakly
interacting neutral particle candidates and low energy neutrino experiments to set better
limits on the neutrino mass.
Detectors
On a longer time scale, we believe that the most promising sensors for high
Acknowledgements
sensitivity phonon detection are superconducting tunnel junctions. For our proposed
application as a SiCAD readout, we are beginning the development of aluminum
junctions. These are formed by a - 200 nm thick aluminum film deposited directly onto
the surface of the silicon crystal, followed by the formation of a thin oxide tunnel
barrier (- 1-2 nm thick) and then deposition of a second aluminum upper film.
Phonons from an event within the crystal reach the surface and enter the aluminum,
which has an excellent acoustic match with silicon. Once inside the superconducting
aluminum, most phonons have energies greater than 2A (where A is the
superconducting energy gap) and are strongly absorbed by breaking Cooper pairs and
forming electron-like excitntions called quasiplutxles. Tnfact for phonon energies well
above threshold, several Cooper pairs will be dissociated. We have performed junction
tests down to a temperature of 250 mK utilizing the sealed 3He system with a charcoal
cryopump. Ultimately we intend to operate at T < T,/lO (-100 mK for aluminum),
where quasipartxle recombination with thermal quasiparticles is negligible.
Recently several European groups [ 16,171 have reported excellent energy
sensitivities and resolutions for X-rays. The S.I.N. group [ 161in Zurich, Switzerland
The work at Stanford has been performed by B. Cabrera, C. J. Martoff, A. T.
Lee, and B. A. Young. Also, B. Neuhauser now at San Francisco State University has
participated extensively. This work has been funded in part by a Research Corporation
Grant, a Lockheed ResearchGrant and DOE Contract DE-AM03-76.SFO@326.
has reported - 48 eV EWHM for the detection of low energy x-rays (- 6 keV) using a
100 pm x 100 pm area Sn Sn oxide - Sn junction at - 0.38 K. Pulse rise times of
-83-
:.
:.
-::,
._
‘._
,;
. ‘.
::;
::,
::
.,
References
[l]
[2]
[3]
[4]
IS]
[6]
[7]
[S]
[9]
B. Cabrera, Phys. Rev. Left. 48, 1378 (1982).
See the review article by D. E. Groom, Phys. Rep. 140, 323 (1986).
B. Cabrera, M. Taber, R. Gardner and J. Bourg, Phys Rev Lerr. 51, 1933
(1983); and R. Gardner, B. Cabrera, M. Taber and M. Huber, to be submitted to
Phys. Rev. D.
R. D. Gardner, Ph. D. Thesis, Stanford University (1987); and M. E. Huber, Ph.
D. Thesis, Stanford University (1988).
S. Bermon, P. Chaudhari, C. C. Chi, C. D. Tesche, and C. C. Tsuei, Phys.
Rev. Left. 55, 1850 (1985).
J. Incandela, M. Campbell, H. Frisch, S. Somalwar, M. Kuchnir, and H. R.
Gustafson, Phys. Rev. Left. 53, 2067 (1984).
S. Somalwar, H. Ftisch, J. Incandela, and M. Kuchnir, Nucl. Insr. A226, 341
(1984).
M.E. Huber, B. Cabrera, M.A. Taber and R.D. Gardner, Jap. J. of Appl. Phys.
26, 1687 (1987); and M.E. Huber, B. Cabrera, M.A. Taber and R.D. Gardner,
Proceedings of Applied Superconductivity Conference, San Francisco, Aug.,
1988, in press.
S.H. Moseley, J.C. Mather and D. McCammon, J. Appl. Phys. 56, 1257
(1984); D. McCammon, S.H. Moseley, J.C. Mather and R.F. Mushotzky,
J.Appl. Phys. 56, 1263 (1984).
[lo] B. Cabrera, L. Krauss and F. Wilzcek, Phys. Rev. Lett. 55, 25 (1985).
[ 1I] B. Cabrera, J. Martoff and B. Neuhauser, Stanford Preprint No. BC44-86.
[12] See for example: Nonequilibrium
Phonon
Dynamics,
ed. W.E. Bran,
NATO AS1 Series B124, Plenum Press, N.Y., 1985. An excellent review of
recent developments in phonon physics.
[13] B. Neuhauser, 8. Cabrera, C.J. Martoff and B.A. Young, Jap. J. of Appf. Phys.
26, 1671 (1987).
[14] B. A. Young, B. Cabrera, A. T. Lee and C. J. Martoff, Proceedings of Applied
Superconductivity Conference, San Francisco, Aug., 1988, in press.
[15] A. T. Lee, Stanford Preprint No. BC73-88.
1161 D. Twerenbold, Europhys. Lett. 1, 209 (1986).
[17] H. Krauss, T. Peterreins, F. Probst, F.v. Feilitzsch, R.L. Mossbauer and E.
Umlauf, Europhys. Lett. 1, 161 (1986).
:
.;,
.,
-84-
. .
..,.
:....
1
.:
:
:
!
Cosmic
Relics
F’rom The Big Bang
Lawrence
*
J. Hall
Department
of Physics
of California
University
and
Theoretical
Physics
Physics
Lawrence
Berkeley
1 Cyclotron
Berkeley,
Group
Division
Laboratory
Road
Cal~omia
94720
Abstract
A brief introduction
given. Dark matter
to the big bang picture
is discussed; particularly
tary particle physics. A classification
of the early universe is
its implications
for elemen-
scheme for dark matter relics is given.
;..
‘This work was supported in part by the Director, Office of Energy Research, Office of High
Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy
under Contract DEAC03-76SF00098 and in part by the National Science Foundation under
grant PHY8$15857.
@L.J.
-85-
Hall 1988
..::.
.:I.
..-
Table
remarkably
of Contents
about
(I) The Importance
(II)
A Brief
(III)
Dark
of Cosmic Relics
Introduction
to the Big Bang.
electric
Perhaps
we even learnt
per century
Scheme for Cosmic
charge,
Relics.
placed
from
Importance
Of Cosmic
It is probable
that
physics
will
come from
unexpected
particles
accelerator
described
There
experiments.
are two clear examples.
the origin
physics:
of electroweak
and the discovery
Accelerator
symmelry
breakdown.
evidence;
is crucial
It will also shed
that of searching
masses are
typical
done for other
What
reasons:
the next
major
and cosmology.
the questions
as supernova
the most exciting
What
of galaxies,
form clusters
thing
have their
about
However,
in these lectures
hope to learn about
I want to take a more limited
particle
For example,
free paths
its surface,
of various
scalar
could be emitted
so the existence
the best example
SN1987A[l].
astrophysical
particles
with
unanswered
viewpoint;
matter:
questions.
ments
containing
powerful
deal of evidcuce
[3,4]. It is worth
A new experimental
form:
of its const,it,ucnts.
“surely”
for example,
A
mass
st,ars in the local
in our and other
spiral
in the whole universe,
galaxies,
it does
Since we have not detected
dynamics,
it is completely
this
we call it dark matter.
no constraint
the nature
at
01~ then asks
more, unobserved
see it, surely it could be anything.”
which restrict
looking
field is opening,
be sure of its foundation.
stable system or whether
clouds
that
a system will be observat.ionnlly
and even for galaxies
the word
constraints
of dark matter
the eye. I will not discuss this
guess that there is virludly
“if we cannot
have
now
m&s
by means other than this gravitational
You might
is
what can we
objects
open. We can certainly
to place limits
a mass of less than
from the entire
volume
of these particles
is the supernova
Although
For a particle
and cosmology
it
can be
on the nature
As with
false.
of dark
most state-
We have thrcv
very
of dark mat.tcr:
physics from astrophysics?
In fact this still leaves a wealth of possibilities
understanding
matter
We
on the qu&ion
seem that a great deal of extra mass is required.
clustering
limits
is a great
[5], and we shoukl
hydrogen
l&Lime
backgrounds.
it. For a. great many systems;
galaxies
a supernova
If I,, is heavy
There
the mass and velocities
of our galaxy,
hot gas in elliptic
why do they have the
of galaxies?
to determine
neighborhood
How did the
than
has the following
this is a gravitationally
is needed to stabilize
is
own intrinsic
triggered
astrophysics
that there seems to be an endless succession of interesting
whether
physics
and cosmology
and quasars?
of the universe come about?
size they do, and why do they themselves
in particle
Most astrophysics
why are there so many varieties
perhaps
advance
being addressed
is the nature of such objects
observed mass distribution
into galaxies,
that
plrysics.
for dark matter
I,,.
[2].
it over for yourself.
piece of evidence
with
case very st,ringcnt
there are now several books on the subject
the evidence and thinking
analyzed
possible
the gala.xy
currents.
v,. Since we are now
we now know that
on X and r-ray
there is much more to the universe
of new
physics
for particle
of 11,: its
and right-handed
v, than we did about
in these decade old limits
and its implications
possibilities:
at the very least we can learn how fermion
will come from astrophysics
physicist
are many
of particle
at the TeV scale.
It is also quite
worth.
in our understanding
decay modes of Ii, D, B, p, r, Z particles
on flavor
limits
mixing
a supernova
is populating
observational
we (lid learn a. great &al
about other propertics
I will reduce my scope again, and concentrate
the next leap forward
at high energies
in unravelling
light
Relics
from
y or e *; in either
decay giving
espcriments,
We lcnrnt
moment,
more about
in our galaxy
great confidence
(1) The
magnetic
sure of the size of v emission
MaLter.
A Classification
physics from SN1987A.
lifetime,
could
(IV)
close t,o that from la.boratory
particle
which
the mass limit
dark matter
on new particles.
a keV and long mean
2.‘We
of a star, and not just form
is severely
constrained.
went off in a nearby
or ve from
1. We know the location
use our
galaxy
this event turned
of the dark matter.
in locations
know that
it is dark.
in the local neighborhood.
Perhaps
mass m it is raining
last year,
and we just cannot
out to be
-86-
This is especially
important
If the dark mat,ter
down on us with
see it.
(Of course there could also be
other than those we have st,udied.)
for the dark ma&r
is composed
of particles
a flux of N 107/(m,/GeV)cm-2s-’
of
,, ._
:: . . . .,
..
3. Dark
matter
start
should
result
from a reasonable
the big bang off with
they typically
with
annihilate
the observed
big bang cosmology.
a given set of particles
and do not survive
abundance
until
with
today.
is a very powerful
dR is the usual element of solid angle, t the proper time at any location
If you
given interactions
and r is a dimensionless
Requiring
at TA and r~ at time t is given by
constraint
survival
coordinate.
The proper
distance
of fixed r,
between fluid elements
: _,
-.-..: ;I:.
: -,ry:....:
(24
object.
To implement
the third
constraint,
it is necessary
of the hot big bang model of the early universe.
this picture,
3’K
which emerges uniquely
microwave
SU(3)
x SU(2)
background
to have an understanding
In the next section
from three cornerstones:
the general
radiation,
x U(1) gauge interactions
of relativity
of the elementary
on the experimental
baryonic
or whether
stable objects,
In Section
and finally
Why
a classification
and experimental
particles.
have I chosen to orient
that we have for particle
A Brief
The
cosmology
on ideas rather
A simple
cessional
expanding
stituents
the standard
Big
Many
references,
cal. Although
could be
and isotropic
temperature
for species i pz(T).
of the plasma
of the 3’K
candidates
and
with 1/2~ZhSl.
of cosmic relics?
plasma.
T(t),
of the big bang
details
in terms of the Robertson-Walker
d?
scale factor
microwave
at
will be
= dt2 - R(t)’
galaxy
radiation
an early
which
then H = n/t
picture
is helpful.
at time
has been measured
to be
H;’
(2.3)
sets the scale for the age of the universe.
and to = nH;’
is given by some power law
N nh-‘lO’Oyr.
of the expanding
Cornmoving
tA with
universe
coordinates
wavelength
tA and
as the surface of an inflating
are fixed to the surface of the balloon.
XA will have a stretched
Th e red-shift
received at TV is defined to be (Xn - X,)/X,
wavelength
at some
of a photon
emitted
and for tn >>
ta this just
becomes R(&)/R(t,).
re-
dynamics
general relativity
of the expansion
applied
is given
to the metric
by Einsteiu’s
of equation
field equations
for
(2.1)
is that
(2.4)
at
where G is the Newtonian
of the con-
gravitational
sity at any point in the homogeneous
itself is described
equation
appears in the metric:
expansion
is inspired
+ da’)
by Newtonian
of a small spherical
nate radius r <<
&
it is frequently
era of a hot
can be described
from a knowledge
The expansion
R(t)
If
if k = 0 it is criti-
of the universe
of the universe
later time tn given by XB/XA = R(te)/R(ta).
will be omitted
Emphasis
law for distant
This system
Th ese are determined
In many cosmologies
The simple
its pressure p = p(p), and the chemical
and their interactions.
behavior
parameter
suppose the expansion
R = &(l/to)“,
balloon
[6,7,8].
from
vanishes or has unit magnitude.
it is open, while
H,, = 1OOh km s-~,,,,-~
for dark matter.
The
and has evolved
for the future
being the spa-
early times and can be set to zero.
The present value of the Hubble
A photon
red-shift
k either
H = h/R
I will scale the coordinate
are the best evidence
the framework
important
constant
parameter.
is closed, if k = -1
k is crucial
during
from this, with
Hubble
exotic
model.
elsewhere
of the Hubble
is expanding
homogeneous
the dimensionless
unimportant
Bang
is to present
and of the isotropy
universe
any era by the plasma
potentials
In Section
directly
but time dependent
k = +1 the universe
than formalism.
interpretation
velocities
the present
with
at the question
and dark non-baryonic,
and brief way.
together
T so that
I give a few
to include
law, ci = Hd, follows
constant
For example
these lecture
To The
of this section
in a simple
and can be found
and its implications
scheme for dark matter
physics beyond
Introduction
purpose
physics
of the
and the
the dark matter
of particle
tially
signatures.
Cosmic relics, both visible baryonic
(II)
I discuss whether
I consider inflation
IV I introduce
give examples
results,
it requires an extension
Hubble’s
we discuss
the isotropy
theory
III I discuss three general points which have to do with dark matter.
remarks
:.
on any relic
constant,
and p is the total energy den-
fluid at time t. A useful mnemonic
ideas as depicted
cornmoving
I. The sum of its kinetic
in Figure
the
region with a unit test mass at coordiand potential
where A4 is the mass enclosed in the unit sphere, is just
-a7-
for this
1. Imagine
energies d’/2
-k/2.
- GM/R,
Thus if k = -1
;_
:‘..
‘: -.:,...
:
:
the total
energy is positive
not correct
from general relativity.
mology
However,
is flat, k = 0, equation
today
I like to interpret
of the universe
I
I
I
J (r,is)
\
\
is driven
in driving
by energy
the driving
the expansion
density
today;
\
I------+
I
I
content
of the universe
cosmological
constant).
to the critical
we know that
Defining
O(lO-‘).
When
during
a previous
era:
that
of Hubble’s
today it is probably
density
mnemonic
dominated
so the expansion
We do not
term.
EM
components:
i.e. the electro-
microwave
radiation,
and V to vacuum
of density
energy
If 00 is larger
v
ie. a
in any component
galaxies
(2.6)
and for very light neutrinos
law which is dependent
observations
R, =
we see them as and where t,hey were
when the detected
photons
left them.
on the deceleration
measurements
This
leads
parameter
of qo lead to CL,S2. Hence
that
10-%noS2.
of k/R
If Gp,
the invisible
has various
baryons,
by the 3’K
0, = pi
PC
Rvs = O(lO-*)
1
for interpretation
R-’
curvature.
only through
today
is visible
to dark matter
= Ro12. Experimental
we know from very direct
Newtonian
than
R; to be the ratio
we observe distant
qo = -RR/k*It,
rather
density
OEM N 0(10-5),
to a violation
Figure
DM
(2.4) as the terms which
Gp >>
it could be the curvature
of ~0. The energy
refer to massless neutrinos,
i relative
If the
(2.5)
side of equation
po = pvs + PEM + py + PDM + pv (VB
,--. f ,(rvc4)
//
of big bang cos-
at any time.
N 10-5GeVn-3.
the right-hand
or dark components
/ --\
is
(2.4) can be solved to give p 0: HZ. This critical
At early times we know that
know what dominates
magnetic
equation
is expanding
picture
as it follows
is
drive the expansion.
dominates
The Newtonian
(2.4) is correct
It is about the most important
pc = &Hi
77
/
is open.
equations
since it tells you how fast the universe
universe
density
and the universe
for the whole system.
than CLVB the difference
is predominately
(2.7)
due to the presence of
dark matter.
At early times during
number
densities
to maintain
the big bang the temperature
thermal
equilibrium
rate to be fast enough to maintain
than the expansion
-88-
was high so that particle
in the plasma were large enough to give reaction
between many species of particle.
thermal
rate of the universe,
equilibrium
rates sufficient
For a reaction
it should basically
be faster
that is the mean free time for interactions
.I...
should
be less than the age of the universe
example,
for a reaction
time t requires
at the era under
AB -+ X to keep particle
the reaction
consideration.
A in thermal
era: t - M,,/T2.
For
equilibrium
The constant
of proportionality
does have a weak dependence
on T. Near an MeV:
at
(2.12)
rate
How does this hot plasma at T > eV evolve into the universe
rastx
=
%+AE-XUAE)
>
r,,,(t)
=
H(t)
=
At first
where
R,,J,(~)
thermally
are particle
averaged
perature
T(C).
member
cross section
In thermal
densities
times
at time t and (cr,.~~+xu~s)
relative
equilibrium
speed for this process
the particle
number
densities
of spin states of particle
and 3~1 refers to fermions
ij’ + mf.
and bosons.
Useful order of magnitude
i,p,(T)
The particle
approximations
mass ni
is perfectly
are given
enters
inhomogeneous
reaction
does the expansion
via E2 =
electromagnetic
are
temperature
prevent
- 573
(2.10a)
n!“(T
*
<< m,)
N (,,qq+‘-“‘v~.
(2SOb)
only
relativistic
hot big bang model p is dominated
species (with
there is a plasma
which
about 1 eV. Although
long-lived
exotic
T >>
m;, so n; - T’s) for virtually
is thermally
coupled;
era is a very important
or with
periods
one. During
have p - T4, so that Einstein’s
k/R
of inflation,
scattering
which
cosmologies
with heavy
that
calculate
T, we
exotic
The calculation
particle
(2.11)
This is equivalent
(one which grows as R3) being constant.
most circumstances,
with
which
(2.11) allows for a solution
in a cornmoving
The gas is expanding
so that RT = constant
only when there is a mechanism
gether
to the entropy
Using k/R
for T(t)
the radiation
= -T/T
growth.
clustering,
it can
and stars,
are
we see should
particles
abundance
particles
contain
into
What
in the universe
determines
today?
Is it
p, e, y in the observed ratios?
theories
of particle
physics
can we
in the universe?
of these abundances
is very simple
[9].
n,(T)
of the last such reaction
will be given by equation
since the i particles
Consider
changes the number
equilibrium,
(for example
from the hot plasma to the
(2.9).
Suppose Ti, is
to be in thermal
equilibrium.
do not decay and assuming
by the decay of some other
a stable
of i particles
they are
species) we have n,(t)
N
to the temperature
T;J.
(R(t)lR(t,))3n~“‘(t,)
wh ere t, is the time corresponding
After freezeout the remaining i particles are just diluted by the volume expansion.
under
and is violated
creates entropy.
during
volume
adiabatically
holds more generally,
once the
gravitational
that we must address.
temperature
not produced
era the relationship
about the evolution
the freezeout
and R(t).
is that RT is constant.
there is some
Furthermore,
such as galaxies
is in thermal
ship between
dominated
out”.
of the resulting
species i. As long ss a process which
At lower temperatures
the radiation
of the plasma
for each reaction
systems,
universe
stable
their present
expands it does work and hence cools; there must be a relationDuring
picture
stable
the universe
When the universe
T(t)
so that
of all the stable fundamental
If we introduce
dominated
- T=IM,.
As the temperature
- n < ou > fall much more rapidly
in the plasma from undergoing
cold, inhomogeneous
reasonable
has the form
- (Gp)“’
it
evolve into a
processes freeze out, there is no longer any pressure to
stop once gravitationally
the abundance
above
this era, since n - T3 and < E; >-
equation
we 6ee a
we have come to realize that
it is “frozen
we are far from a complete
observed
all times for which
the radiation
hot-spots,
formed.
from
that is for all temperatures
this is not the case for non-standard
particles
by contributions
universe.
rate I’,,(T),
There is a very basic question
In the standard
local
also it is grossly inhomogeneous
However,
rates I’,q(T)
beneath
mass perturbations
Although
from
that the plasma of the hot big bang should
cold, non-interacting,
than
apart
interactions,
drops all the particle
critical
>> m.)1
different:
with few particle
reasonable
potential
nI”(T
they seem very
on all scales up to at least 50 Mpc.
at tem-
is the chemical
sight
very cold universe
is the
(2.9)
where g; is the number
we see today?
;
Since R - T-i
to-
dominated
-89-
it is convenient
n,/T3
which
become independent
which
is still relativistic
to consider
of
at freezeout
t
“reduced”
after freezeout.
(m; < Tq),
ny)(Tf)
number
densities
Note that
k(t)
=
for a particle
is given by (2.10a)
so
that
the relic abundance
at freezeout
which
rzp’(Tf)
can reflect
and mi >>
f, N 1. However,
is given by (2.10b)
an enormous
Boltzman
process,
which
be seen by numerical
particle
I for which
Ignoring
a possible
n,
The physical
integration
since freezeout
ideas are correct
of the rate equation.
for small
chemical
the rate equation
potential
p*
as a
as can
consider
a
process to freeze out is xz +
is
< c7AtJ >zp+.,. (12 - nq
has be en numerically
This
is treated
however
For example,
changing
is shown in Figure
abundance
- m,)/Tif)
at freezeout
the last z number
= 12~ = n.
behavior
suppression
are approximate
it is not.
dn
3k’
- = ----1xdt
R
where
was non-relativistic
TX,.
The above relic abundances
sudden
if the particle
so that f; N (F)s”exp((/l;
2. A useful analytic
(2.13)
integrated
and the freezeout
approximation
for the freezeout
is
(2.14)
where 2 = m&~(u~v),
the freezeout
temperature
T, ‘Y nz.~ / in Z and the result
is valid for large 2.
For very large 2, fxf N Z-l,
so that R, N (m,f,r/Tof,~)R,
or
Q,-b&&&T
This result has one astounding
if XF annihilation
~53
proceeds
on dimensional
consequence
via strong interactions
grounds.
Hence 0,X2
I
sible to have a stable fundamental
is encouraging,
possible
if the dark matter
to push their
particle
increasing
which is rarely
with
nz,S103TcV.
cannot
only be avoided by having
a phase transition
by < ~Aav >
than 10”Z’eV.
particles
small.
i
It is not pos-
mass larger
be made arbitrarily
Z
Even
of fundamental
high, and consequently
sity and flux at the earth
mentioned.
it will be bounded
implies
is composed
mass arbitrarily
(2.15)
their number
This
This
m
it is not
bound
denFigure
could
give a mass to z after it has already
Schematic
frozen out at a low abundance.
What
are the relic abundances
we believe to be stable?
,f, = O(l),
Photons
we have observed.
The photons
of the four known
particles
(I/, y, e,p) which
are massless and have relativistic
are the only relics which were relativistic
They play a crucial
2
role in determining
freezeout
at freezeout
which
the age of the universe.
-9o-
illustration
of particle
abundance
freezeout
behavior
We believe the observed
of the hot big bang.
they
maintain
universal
These photons
a thermal
expansion:
distribution
relativistic
roughly
with
T(t)
wavelength
temperature
stretched
which
equation
describes
light
but
need this:
1OsTs N 30eV they would
%(nz,
give &(m,
the
then gives the age
domain
of p with
If m,
relativistic
freezeout
of a heavy neutrino
< a~v >-
p. Although
trons
to write
of the universe
mean that
To obtain
accurate).
MeV,
then
to other
about
This is excluded
v, must be unstable.
astrophysical
30eV.
implications.
Equat,ion
annihilation
occurs
At temperatures
applies
is completed
picture
number
to any neutral
and the baryon
get trapped
for baryon
number
typically
lead
to be less than
fermion
Such a particle
whose dominant
with
mass in the
interacting
is carried
int.o quark
predominantly
supercooling
nuggets
t,he baryon
for example.)
are in
of p and I,
vanishes,
{LB = 0, then the freezeout
abundance
(2.14),
and fin is given by (2.15).
Since < oav >-
is given by equations
this gives R,3 - lo-*s.
We conclude
/LB # 0, i.e. it requires a cosmological
that the standard
potential
for lepton
asymmetries
carried
it is necessary, just before the QCD phase transition,
(n, - ni;)/ np = 0(10-s).
big bang framework
should
be. The asymmetry
all anti-protons
initial
Although
today
is enormous
come across a proton
small it is of crucial
somewhere.
condition
The imporhow big
and obvious
to annihilate.
However
It also implies
the nature
..) is pure speculation
that
processes occurred
of the phase transition
interactions.
that
particle
physics
at some
gauge symmetry
of the main events in the hot big
by the SU(3) x SU(2)
asymmetry
x U(1) model of pai-tick
gauge
3. This model should be good up
GeV so this is where we begin.
the cosmic baryon
an
at the moment.
These even& are shown in Figure
to a few hundred
during
phase transitions
(inflation,
and
a randomly
in a non- thermal
because it implies
additional
I will end this section with a brief summary
as inspired
it is not just
it must have been generated
This is fascinating
model.
importance:
Assuming
to the universe,
environment.
the standard
‘bang cosmology
-91-
asymmetry.
it is non-zero
effect.
have come from
breaking
baryoii excess to be present, by T = 50 MeV.
The absence of antimatter
in a billion
early era, although
big bang scenario requires
pr, = pn, since
by neutrinos.
it was a one part
beyond
m;s
number
does not
early on in the big bang it would not have been very obvious,
such as
potential
such
in clec-
This
is that it allows us to calculate
equilibrium
by p and n. (The
Reactions
domains
incorporating
implies that the cosmic asymmetry
era of the universe when CP and B violating
particles
If the chemical
such enormous
cosmology
tance of the standard
it must
could take place or baryon
distributions.
could produce
This
over-annihilation
cosmic baryon
adjusted
u,d and s quarks
Way
symmetric
today would lead us to expect a non-zero
because essentially
cosmological
lepton
asymmetry
such an asymmetry
assume that by T = 50 McV the phase transition
number
therm&e
< 35
for the dark matter.
could be much more complicated;
could
m,,
with the eight gluons, and these strongly
For simplicity
@ --t n(rr) ra.pidly
I expect
< m,
have very exciting
above the QCD phase transition
equilibrium
are all relativistic.
would
via W and Z exchange.
range l-10 GeV is a good candidate
thermal
problems:
to the contrary
(2.16)
If 1 MeV
In this case the decay products
or cosmological
Evidence
(2.15) and (2.16) are not numer-
for a stable heavy vr.
could be baryon
at least for a closed universe.
the chemical
0~ = 0(10-s)
to have a quark
ically
in the
and some anti-baryonic.
down a complete
in protons,
there could be additional
factors of 4~ equations
universe
some baryonic
an era of inflation
is equal to that
necessarily
(2.15)
gives
(Since we have dropped
that we would
anywhere
a scheme.
For the non-
G$mZ, and equation
anti-matter
in the cluster of galaxies of which our Milky
domains,
it has not been possible
= O(1). This could also be true
non-relativistically.
about the nature
must have existed at T - 50 MeV to prevent
structure
Charge neutrality
I,, would freezeout
assumpt,ions
argue that it was obvious
The only way that the entire
is if there are enormous
of the
that they also were
tau neutrino.
is above 1 MeV,
You might
we do not see any evidence of primordial
is a member.
= 0) = O( 10e5), If their mass were
= 30eV)
by more complicated
solar system or indeed anywhere
fy - 1. If they are stable and massless they contribute
at decoupling:
is not altered
of the QCD phase transition.
by the
Of the neutrinos
to be sufficiently
This conclusion
relic
to any plasma,
being
of To = 3’1;.
v, and vP are known
is the photon
coupled
from Einstein’s
the observation
the same to ps as do photons:
for a light
radiation
are no longer
distribution
Knowing
to from
model,
background
X 0: R, so the effective
T cc R-r.
of the universe
standard
3°K microwave
It is likely,
but not necessary,
exists even at this high temperature.
At a
::-’
:.
temperature
dam.?)
near 250 GeV there is a phase transition
acquire
a mass
as well as all the quarks
is light
considerable
phase transition.
supercooling
(but
cosmological
consequences
below Mz, Mw, mb, m,, and m,
they freezeout.
footprints.
so the baryon
to the plasma rather
than a miniscule
is possible
at this
of this pbsse transition
which
As the temperature
are depleted
essentially
asymmetry.
so that
every anti-baryon
in reducing
the neutron
energies are O(MeV)
mediately
is as given
decay becomes
number
density
it also becomes possible
photodisassociated
and ‘Li.
The abundance
from a variety
important
ratio.
experimental
for T < 1 TeV.
support
cess has important
is especially
for deviations
Hence the interacting
tons in the ration
1 : 1 : O(lO’),
plasma
to cool until
as the reverse photodisintegration
plasma
dark
He,
in the stan
abundance
inferred
success; there is direct
big bang and
could
the light
now contains
T = O(eV).
matter
electrons,
process freezes out.
the photons
decouple
just the electron
protons
the heavy nuclei.
At this point
be baryonic,
neutrinos
down to essentially
and also contains
by a factor of E 3000 until
At all temperatures
-92-
primordial
At O(MeV)
the plasma ceases to be interacting,
red-shifted
which escape
ending up in *ff:
from the standard
to the issue of whether
and e+e- --+ yy depletes the charged leptons
formed
binding
for the big bang model back to times of 0(1 EC). The succonsequences
important
continues
(2.12).
are not im-
by nucleosynthesis
with
energy
an MeV
Since nuclear
This is a very important
as we will discuss in the next section.
excess.
beneath
Most of the neutrons
of these nuclei predicted
of observations.
radiation
in equation
to form nuclei which
by the plasma.
dard hot big bang are in good agreement
events in the hot big bang cosmology
if
This era, like the pre-
by relativistic
relation
neutron
to proton
driven
decay are processed into 4He nuclei, with trace quantities
Important
annihi-
component
which could effect primordial
events take place.
rate k/R
the time-temperature
Since m, - mP = O(MeV)
3
until
no observable
The QCD phase transition
inhomogeneities
At the MeV era many important
Figure
drops
by annihilation
decays, again leaving
;,;. i: : :
;)
,:. :_ ‘. .,
of the light elements.
vious ones, has the expansion
density,
boson
inflation)
excess now becomes an important
it is first order may lead to density
abundance
rapidly
the QCD phase transition
a baryon
If the lliggs
today.
particles
these
Any relic abundance
After
lates with
or attribute
the W, Z bosons
leptons.
insignificant
I know of no feature
leads to observable
at which
and charged
ep -t Hy
Once neutral
and phoThis dilute
takes place
hydrogen
now free-stream
is
and are
the present era.
smaller than O(lOMeV)
we havepB
= n~rn~
- 10-9T3mn
:-
:. ,:
:,
:’
‘:
and p-, = n, < E, >-
T4. At T = lMeV,p.,
p7 = ,DB when T - 10-9m~
drops until
an era when R/R
RT = constant,
is driven
by the hydrogen
Einstein’s
equation,
nated era. If k = 0 this behavior
curvature
dominated
The plasma
continues
radiation
mogeneities
last scatter
in the baryon
stars must have evolved
present
a late phase transitions
structure
which
cosmological
critically
distribution
during
this energy density
so it is sensible
sentially
identical
native
classification
underlying
(III)
particle
Dark
together
galaxy
many
aspects:
energy density
Elementary
of the universe,
as to its nature.
of the dark matter
particle
active
candidates
which
scheme for dark matter;
one which is motivated
that one component
universe
of dark matter
[3,4,5].
may be fairly
should
be given
u(r)
The form of this dark matter
particles,
such as monopoles,
chunks of solid material,
etc.
configuration,
visible
= GM/r’
where
From the
and it is frequently
about
dark matter
be cool stars
on
distributed
over the
of particle
onic density
particular
burnt
examples
be in
clouds provide
only
the rotation
speed
mass.
In fact constant
Thus
one
values of n(r)
to a spiral
galaxy,
that
of
as r out to very large distances,
the first
Examples
or perhaps
not revolutionary.
thought.
is related
planetary
it would
larger
of how such objects
option
are formed
are, to varying
be interesting
(4He,‘Li)
to ask
would
of cold
for particle
mean that the baryonic
asymmetry,
simply
is larger
because we do not
is a mistake:
formation
of
so the nudeosynthesis
[ll].
As the bary-
reaction
rates are
(2H,3 He) since they are more fully
whose abundances
range of Rn from a comparison
:A..
.:;:
degrees, not understood.
on Qn comes from big bang nucleosynthesis
mass nuclei
question
dark matter
sided lumps
to the cosmic baryon
To ignore the baryonic
at the MeV era is increased
to the higher
important
of baryonic
It would simply
This depletes the low mass nuclei
crease. The preferred
-93-
physics
low luminosities
abundance,which
One constraint
increased.
from the
should
that the halo mass is an order of magnitude
all types of stars and galaxies
It could be a
Since the galaxy
out to very large P (up to 100 kpc).
If this were the dark matter
but certainly
have an understanding
energy, topological
The H clouds distant
component
increasing
is: is it baryonic?
with
than previously
These
mass.
From the viewpoint
into
have M(r)
estimated
center and
of the spiral arms.
M is the galactic
This has not been seen.
It should
limit
mass of the galaxy,
the dark halo.
that
near the galactic
and since these distant
to the total
by u’/r
axis.
and since
more by the
and each of these classes has many
spiral galaxy.
the symmetry
for many spiral galaxies
an alter-
different
they yield masses in the range of 10” - lOi*
there is an additional
evidence
vacuum
about
the visible
This suggests
for dark matter
is not known.
beyond
4. Together
cx r-i/s.
than the visible
are many
15 kpc from the
component
have been observed
give es-
There
such as our own.
areas of
solely from its gravi-
smootldy
galaxy
depends
and indirect
..‘ :;
it is the lo
arms of stars; the sun is in such an arm about
center rotate
freezeout
to groups of galaxies,
is of most importance.
There is also a spheroid
in Figure
solid material.
There is direct evidence
as our own galaxy
is the disk con-
clouds, which extend
physics,
is inferred
interest
of dark matter
There
a small contribution
by
Matter
gas of elementary
center.
which
to a spiral
a stable gravitational
physics.
whose existence
with galaxies of quite differI will make a few comments
detection
expects
can be divided
hot, warm and cold. In the next section I introduce
the spiral
galactic
need be known,
candidates
for example.
of direct
times the solar mass for a typical
and
in baryons
the clustering
taining
are sketched
of the universe.
produced
components
hydrogen
Hence the inho-
fluctuations
is associated
and spirals,
the viewpoint
density
visible
galactic
of this background
perturbations
and from
cal dark matter
We know this
galaxies
elliptic,
.
is spiral
once the peculiar
clusters,
dwarf,
on the case of spiral galaxies [lo], which is of particular
domi-
the origin of this large scale
those dark matter
effects is called dark matter.
defects
ent types:
if R < 1 then a
Lo have is one of the most
only a few properties
all scales from the solar neighborhood
entire
today,
or large density
of the dominant
Any form of energy density
tational
The photons
could be small density
It is a field with
behavior.
three such groups:
However
to be isotropic
for.
seen
at T = O(eV)
to group
There is evidence that dark matter
enters
- Ts12 and
to a very high degree.
is dark there are only speculations
of clustering
DC T and
this matter
this last factor of 3000 in redshift
we see the universe
on the nature
viewpoint
until today.
at T < 1eV. Understanding
research.
Since fi
t*13in
at the era when T = O(eV).
The seeds for this inhomogeneity
or dark matter
rest mass.
background
has been accounted
have their
p-,/p~
IeV the universe
(2.4), gives R -
at 1eV was homogeneous
of the earth
pn, however
Beneath
R - t is reached.
era with
because we see the 3OK microwave
motion
>>
= IeV.
consequently
of big bang nucleosynthesis
in-
,,
.I,‘,.’
-
with
the observationally
inferred
are many uncertainties
and consequently
known
one cannot
dark matter
It is widely
believed
underwent
produce
that
process
history
which
There
increase
(d/R)’
presumably
:.
to many
times
Gp dominates
initial
condition
amount
of entropy
I will
cosmologists.
describe
for the rate of expansion
Direct
observations
also
and reheats
the way in which
of the universe;
today
era) while R-’
by an enormous
incrcnscs
amount.
for evolution
it has the
tell us that the curvature
times p increases first as T3 (matter
required
scale factor
era would
problem.
equation
dominated
:
reasons ie to why this quite bizarre
term cannot be larger than about ten times the energy density
As we go to earlier
:
than the
This era is ended by some very non-
releases a stupendous
- Gp - l/R’.
T4 (radiation
that all the
larger
[12, 131. This inflationary
(RT = const.).
solves the “flatness”
Recall Einstein’s
form
at some temperature,
are several theoretical
is attractive
inflation
there
observations,
began an era when the Robertsor1-Walker
very rapid cooling
adiabatic
However,
of the various
use this alone to rule out the possibility
a very rapid
the universe.
is a few percent.
(RD,~~ 1: .l) is in fact baryonic.
weak scale, the universe
R(t)
abundances
to do with the interpretation
term:
l/RZ~lOGp.
dominated
era) then a~
only as T*. Thus at very early
In fact at t,he Planck
to reach the present
universe
scale the
is
(3.1)
Figure
4
A much more natural
Schematic
that
view of spiral galaxy.
case the universe
R = t. Furthermore
Since p -
Thus
universe
is reached
open universes
might
the l/R2
RT = constant,
P/G
at a time
to avoid
This is avoiding
term negligible
initial
would be for this ratio to be unity.
become curvature
-
-
-
10-l’
this problem
just
implies
= l/R
This
In
or
7’ N t-‘.
in this universe
n(7’)
t.cmperaturc
-
of the
implies
this is not our universe.
set k = 0 (I took k = -1
that,
You
in the
h- = 0 is the same fine tune as making
wit.11 Gp.
is sketched
in Figure
at T - MP. A curvature
takes place, but long before the present, era, the l/R2
-94-
condition
sec. Naturalness
certainly
to this problem
Gp - l/R’
lOem.
R.
the issue: putt.ing
solution
condition
l?/R
the initial
to N T&’
compared
dominated:
12”p’P we find that
become cold very quickly,
The inflationary
natural
condition
when T = To = 3”K,
argue that
above).
with
II” and pC -
T2/Mz.
initial
will rapidly
curvature
5. There is a
dominated
era then
term is made very
:
:_
: ‘-:
:.
-.:
-:.
.
small by inflation:
recall that inflation
since T drops rapidly
during
inflation
p is dominated
It is true that the radiation
of inflation
After
than R-’
GP
I
I
percent.
c:
energy density.
drops faster
a fine tune.
Hence inflation
Known
gives
dark matter
In view of the theoretical
it seems to be a small step to assume that further
particle
nucleosynthesis
physics this is the crucial
too small.
cosmological
problems
new particle
physics
step: standard
since the deuterium
Inflation
beyond
the standard
which contribute
perhaps
tic scales (I’ll
call this the diffuse dark matter
physics which is responsible
it not only
There
should
component).
solves
considerable
be new exotic
90% to R and are not clustered
for the vacuum
is
of
allows 0~ = .I,
but it dictates
model.
stable objects
dark matter
is then three orders
exciting:
problem
contri-
motivation
from the viewpoint
abundance
is tremendously
such as the flatness
a new idea which
plays the role of inflation
In this case there is no need for the diffuse
Figure
,_ ,_. ,.
we are now in the era when they are
It is also clear that we should tread very carefully:
t
t,
Inflation
that
However,
>
to
t1
to radiation
out there and that R is really very close to unity.
the particle
:.
is constant.
on galac-
There must also be
energy which drives the
inflation.
R-2
I
I
pv which
Gp subsequently
to R are a few percent.
but 0~ = 1 really is excluded
I
I
that
i.e. it gives R = 1.
give an R of ten to twenty
of magnitude
think
is not correct;
pv - ‘P does drop, however at the end
because pv is converted
The visible contributions
from inflation,
That
energy density
indeed this would itself constitute
Rm2 today,
butions
increases R. You might
Gp is much larger than Rm2. While
there is no reason to expect
comparable,
Gp >>
by vacuum
energy density
it is replenished
inflation
rapidly
p would also decrease catastrophically.
5
solves the flatness problem.
R = 1.
component
of dark matter.
In this
dark matter.
exotic,
for. It is also worth
and both forms are worth
Both
theory
issues.
dark matter
homogeneities
created
of observation
theoretical
question
nucleosynthesis
era with
are predicted
sufficient
homogeneity
it seems that in a small region of parameter
with
the standard
currently
size to radically
assuming
model.
stressing
under
or
that the
of nucleosynthesis.
have many interesting
at the QCD phase transition
dances which
It could be baryonic
also relies on our understanding
and interpretation
An important
searching
invents
does not require
case there is still the issue of the clustered
case for exotic
-95-
suppose somebody
but which
study
unresolved
is whether
in-
could have persisted
to the
alter the conventional
abun-
[14]. This is not yet resolved;
space s1B = 1 might yet be consistent
:,
..
:
A more radical
element
question
abundance
is whether
dances for 2H,3 Hq4 He and ‘Li
particle
decaying
is rekindled
during
the keV era to produce
ble exotic particle
or exotic.
it is important
Such late decaying
sLi than the standard
It is possible
complicates
model,
that
over an unstable
a higher
The clumped
in gauge theories
I will divide
their
typical
contribute
about
.l to R. They
components
contribution
be something
If there
could be baryonic
to R is certainly
like relativistic
is a dark
matter
in the earth?
how stars form in a galaxy.
occurs only because the components
gravitational
molecular
kinetic
potential
collisions
energy is radiated
gravitational
the earth
collapse
to dissipate
particles
this kinetic
the galaxy.
by dissipating
for example)
their
are sufficiently
Presumably
energy, they have no option
particles
particles,
gas cloud
is
in the halo,
7~. This allows a cross section
from baryons
as large as a millibar*,
a few simple
estimates
of event rates which
of our halo is composed
of particles
curves of our galaxy and other observations,
of halo dark matter
to try and observe
from
is .3 GeV cm-‘.
the nuclei
this enormous
of the detector,
Thus with
speeds of
Suppose
flux.
that
If the dark matter
of mass mu,
of detector
of mass
the best estimate
at the earth is N 107n-2s-‘(GeV/nz~).
cross sections
are non-relativistic
and only
build
For example
is crucial
the rates could
experimental
with
with
some cross
is
be enormous.
challenge.
(3.2)
However,
detect-
Since the dark matter
p = 10e3, their kinetic
of this will
appear
for any
been performed
approximate
excluded
Most interesting
is that the
that they are unable
orbits
with
energies are
low background
necessary
annihilation
-96-
1 < mn
this region
Ge detectors
is to
Searches have
which have mssses of
< 10 GeV, which
is so interesting
can be read from
such as a Dirac
neutrino,
equation
(2.15).
Q is a known
6.
has not yet been
is straightforward.
cross section oA for a cosmic relic to survive
R E .I today
candidates,
The challenge
of O(keV).
designed to search for double beta decay. The
is the region
The reason that
interesting
recoil.
region in the mn, os,~~ plane is shown in Figure
excluded.
and contribute
Since they are dark, these particles
as nuclear
which can measure energy depositions
O(11Cg) and which were originally
the reason why
but to move on bound
a fraction
detectors
already
on de-excitation:
of dark matter
weakly interacting
This is quite reasonable.
For large enough
can sink in the
energy.
This dissipation
quantities
:‘
this it is useful to
of a pre-stellar
modes which give photons
enormous
dissipation
particle
(g$) =(2.1~:m2)
(g) (Z).
it should
of exotic
To understand
(HZ molecules
away from the cloud.
scatter
with
ing the events is a considerable
composed
A condensation
of a dark matter
os,~, then the event rate per kilogram
which
energy.
to form a stable dense object.
and sun do not contain
halo dark matter
around
of the cloud
excite rotational
The components
To avoid clumping
halo in our galaxy
why do we not see these particles
remember
or vacuum
cross sections for these particles
for a halo stable against
scattering
if the dark matter
a detector
particles
section
velocity
particles
the flux expected
up to R = 1. Such a large,
not baryonic.
particles
infall
requirement
:
escaping from the galaxy.
or exotic.
scales could contribute
on
that the scattering
this section
From rotation
we build
are elementary
this is the typical
The clumped
on galactic
are clumped
weakly
. . . .:
be longer than the age of the galaxy,
for the local density
into two
their interaction
a weak cross section.
lo-sc
Faster speeds would lead to the particles
smooth
mn.
which could survive
If these components
speeds will be O(10e3)c,
should
could be expected
we know
Presumably
they are often called WIMPS:
that the mean free time for collisions
I will finish
certainly
these components
into a galaxy.
are not clumped
This
to think
A sufficient
< afi > for dark matter
of
and those which do not.
components
U(@,).
hardly
but it is not unreasonable:
scales and hence are non-relativistic.
particles
I?‘,
is baryonic
abundance
has several components.
formation,
the big bang and would be dark today.
galactic
primordial
and this can be searched for [lS].
the dark matter
clump
It is a mistake
simply
interactions.
of the weak interactions;
massive particles.
is really
one. Form the viewpoint
or not the dark matter
is that
interacting
it is not clear that a sta-
schemes predict
which arise quite naturally
classes, those which
physics,
have strong or electromagnetic
strength
abun-
have an exotic
to know whether
issues such as galaxy
of many objects
acceptable
showers in which nucleosynthesis
of particle
should be preferred
cannot
the main era of light
to reproduce
with Rg = 1 in schemes which
[15]. From the viewpoint
of observation
we have identified
in the big bang. It is possible
The
the big bang
For several
function
of nn
-. :-: :::
:‘. c.
._: :
.
and hence one can predict
mn and it turns out to lie in this region of a few GeV.
Furthermore,
if the annihilation
by a crossing
relation
nucleus
N : US,N. Putting
the event
the dark matter
depositions
large.
(3.3).
to directly
Typically
The problem
Future
and will explore
explanations.
detectors
Figure
6
with
seeing these events can be
this crucial
Excluded
responsible
region
region in the mn/as,o.
corresponds
overburden.
plane assuming
for the local dark mass.
The upper
to the cross section
The plot is taken from
of a double beta decay Ge spectrometer.
a Dirac neutrino
with conventional
for scattering
Ref.
22
the particle
is
Scheme
For
relics can be classified
on the earth can have a variety
from
of the remaining
the rock
and results
from use
The curve labelled
vn is for
transitions
the signal is too feeble.
Cosmic
according
Relics
to the way in which
equilibrium
and they underwent
three classes were produced
and were never in thermal
and the classification
they are pro
until today.
(IV.l)
Plasma
relics are elementary
couple.
no -
That
All relics of
photon
is still relativistic
plasma
relics which
for dark matter,
is excluded
Plasma
today.
greatly
thus destroying
they cannot
relics which
and would clump.
could therefore
are relativistic
density
is no
Z’,” so no -
is the best illustration
-
when they deTz,
and today
10-s.
The three
of a plasma
relic
If the masses for v, are less than L?” they are also
are relativistic
Hence although
not be clustered,
We discuss each class in turn
which
number
background
since they would
cleosynthesis.
today
particles
their
today.
unless there were O(10”)
of nucleosynthesis,
Relics
in the table at the end.
mass is less than To then p0 -
degree microwave
which
equilibrium.
process.
events such as phase
Relics
is at decoupling
7’2. If their
a freezeout
in catastrophic
scheme is summarized
Plasma
weak interactions.
-97-
of
I am aware fall into one of six classes. For three of these classes the relics
were once in thermal
edge of the shaded
energy of
to such low energy
region.
detect dark matter
duced in the big bang and the way in which they survive
which
-+ QQ, then
cross section from
it is either that os,~ is too small, nan is so large that the
A Classification
Cosmic
eg 00
will be sensitive
event rate is too low, or mn is so small that
(IV)
matter,
the scattering
The lower value of mn decreases the kinetic
particle.
Our failure
to calculate
these values of mn and QS,N into (3.2) one finds that
rates are quite
seen from equation
process is to ordinary
it is possible
Such plasma
such species.
increase
relics are not important
This bizarre
p and therefore
the successful
predictions
k/R
of primordial
plasma relics which are still relativistic
contribute
today
nuwill
much to R.
have masses larger
than
7’s would
Any of the three neutrinos
make an important
possibility
at the time
contributions
be non-relativistic
could have such masses and
to R.
:
.:
(IV.2)
Freezeout
This important
are particles
were made recently
Relic
case was discussed
the reactions
which
contribution
change their
a freezeout
as Dirac
neutrinos
Consider
baryons
into a bound
Although
these candidates,
. with
neutrinos
shadow
QED.
carrying
shadow
arises with
l/A”.
energy
of shadow quarks
These baryons
If nb is the mass of the shadow
Asymmetric
Asymmetric
greatly
number
Dark
matter
would
reason that the visible
matter
abundance
In particular,
of the surviving
way below what
of the antiprotons
would
produced
abundance
asymmetry.
Protons
that the dark matter
a cosmic
asymmetry
solution
have survived
until
today
for precisely
while the chemical
potential
major
the minor
component,
have survived
with
seen in cosmic rays survived
directly
initially
component
zero chemical
which
are initiated
does this oscillaton
directly
be an interesting
which
temperature
while
signature
the
rest; ‘00 = nm.
expands
None
aho
from the big bang, they
If 4 has strong
V. easily, so the equation
is strongly
damped.
the equation
of motion
In the limit
that
-98-
physically?
governing
On the other
it rolls to
couplings
the damping
represents
Of course, equation
density
hand,
if 4 has only
particles
(4.1)
would
survive
These oscillatons
until
Because the oscillatons
a uniform
carries
had only a small contribution
today.
no momentum.
correct:
gets diluted
However,
What
are the same at
distribution
(4.1) is not quite
due to the expansion.
and the
can be neglected
the field 4 creates.
of these particles
it
t.he evolution
will have small damping
it is a mode of the field which
in the oscillaton
the number
which
by the phase transition
has a time dependence
relativistic
in
for
for this field
at the phase transition
4 = g everywhere.
represent
locations
energy density
is annihi-
potential.
I$ = 0 everywhere,
of the potential
where m is the mass of the quanta
a chem-
determines
would
How-
(now much higher
c$(Z, t) = 0 + (b@P
the same
including
which
the solar opacity.
neutrinos
relic
buildup
To a phase transition
will be oscillatory.
all spatial
calculation
in changing
in high energy
a freezeout
will prevent
Relic
is
in baryon
did.
[9] freezeout
While
potential
very weak interactions
has been
[17].
temperature
the high energy solar
by the sun, xz +
to be important
can radiat,e the energy density
asymmetry
the central
in Fig. 7. then at some critical
the minimum
that it has done the same for some other quantum
It is fun to redo the Lee-Weinberg
ical potential.
anti-particle
It is very plausible
we know native
B, so it is reasonable
number.
relics whose survival
because of a cosmic particle
relic:
lepton
will occur:
particle
so that R,, N .l
problem
the con-
relics could
a scalar field d(?, t). If the zero temperature
of 4 has a solution
are the best examples.
an asymmetric
zero shatlow
the lightest
an/m:,
Relic
relics are freezeout
enhanced
and electrons
electron,
charge, then e’Z’ -+ y’y’ has < ~AZ) >z
is as sketched
does not deplete
produces
....:--_ -_.
relic candidates.
Oscillaton
Consider
U(1) gauge group:
the solar neutrino
than usual solar neutrinos)
(IV.4)
rate which
them
up in the sun,
masses such bound
of the sun, decreasing
may itself result
some freezeout
can annihi-
could have built
t,hat for certain
opacity
is au asymmetric
by scattering
Over the age of the sun sig-
relics so that sz +
the reaction
concentration
particles
the sun.
particles
can also be trapped
ever, IZ -+ .
If A’ N 300 TeV these shadow
a world with a new unbroken
m,, 2 a’300 TeV, again taking
(IV.3)
thus solving
(no asymmetry)
which has an asymptotically
mass O(A’).
< ~AV >-
one could imagine
to the thermal
of a sufficient
shadow &CD,
of dark matter
It has been found
contribute
such
bind dark matter
as they pass through
of the sun and decreasing
they are not
arises if the halo dark matter
they are asymmetric
centration.
so that R, N .1
are quite plausible,
orbit
concentrations
providing
dependence
possibility
The sun can gravitationally
nificant
the
would give R N .l even if there were no cosmic D’ asymmetry.
Similarly
lated
Their
relic.
5’ which acquire
+ x’
relic.
t,han lo” TeV. For
which gets strong at A’ causing confinement
q’ into shadow baryons
1at.e int,o r’ : Ui?
to be lighter
photinos
a new version of &CD,
free gauge coupling
freeze out.
cross section < ~Az) >E G$mz
results with mz N O(GeV).
freezeout
densities
A very intriguing
relics
when
Since < gnu > ZZl/n22 even for a strongly
or supersymmetric
the only possible
number
relic is expected
with a weak annihilation
for halo dark matter
Freezeout
(2.15) f or any such species z. Although
cross section.
particle,
a particle
sections.
and are non-relativistic
in R,, their is almost always implicit
nxass does not appear explicitly
via the annihilat,ion
equilibrium
comoving
to R is given by equation
interacting
in the previous
which were once in thermal
in high energy collisions.
The
of 4 quanta
at
as the universe
n -
l/P,
so do
even if these non-
to p at the phase transition
., :::..:
‘_
po(T,)
<<
~(2’~) they could easily dominate
by today
era. This is illustrated
8. The most well know example
dominated
an oscillaton
is the axion.
Goldstone
boson
the potential
parameter
results
symmetry,
for the symmetry
they
from
the breaking
at some scale f.
of a global
The QCD
U(1)
result
of
breaking,
from
V, is f.
symmetry
However,
breaking
with
symmetry,
interactions
7, V, - A4 where A is the QCD parameter,
of Fig.
frequently;
if T, falls in the radiation
In the absence of QCD the axion is in fact a massless
which
the Peccei-Quinn
in Figure
i’ :. :.-._--
and the order
oscillatons
a weakly
:. ._ ._
produce
occur
coupled
very
scalar,
and are much more general than the axiom
(IV.5)
Secondary
Relics
So far we have assumed that relics are stable, or at least that their lifetimes
sre longer
than
so far could
the age of the universe.
have lifetimes
stable decay products
for obtaining
I will call secondary
Sl = 1 in a smooth
None of the first
relativistic,
today
potential
for an oscillaton
via small
today
which
is bot.h
relic could
be
primary.
The inflaton
gets suppressed
by exp(-l?t).
example,
is an oscillaton.
How-
because it is unstable
In this sense, everything
to t.he decays of inflatons
to R.
they clump.
violating
interactions.
which
plasma photons
radiation
the majority
which
theories
although
One example,
relics.
e* and demonstrate
The e* lose energy
However,
electromagnetic
supersymmetric
9. This gives e*, v as secondary
from the background
background
consider
we take to be the photino,
of the relativistic
significantly
-99-
interest
size clumping.
a secondary
its oscillation
R parity
the evolution
(< IO-‘).
matter
to describe
which
t,rated in Fig.
relic
galactic
of secondaries.
As another
Typical
cosmologically
is a sec-
reheat.ed t,he
after inflation.
superpartner,
7
without
even if it came from a non-relativistic
relic, we owe our existence
universe
Figure
distribution
Their
They are of particular
(4.1) is insufficient
so the oscillaton
ondary
relics.
and gives R = 1. However,
There are many examples
ever equation
any of the relics considered
few classes of relic lead to dark
unclumped
relativistic
However,
less than the age the universe.
today
X and y rays observations
rapidly
where
the lightest
long lived does decay
? +
e+e-L/,
is illus-
In this case we can follow
that they cannot
by inverse
Compt.on
contribute
scattering
ey -+ cy. Once the e’ are non-relativistic
of the photino
rest mass has ended up in
would
be ,Y and y rays.
We know from
that R
in these components
are very small
As usual, one finds that the big bang is a tightly
constrained
frame-
:.-.
:.
.’
.,_ .:.
.;
‘\
‘A
e-
e
violates
Lad
RG\
<
Figure
Figure
Temperature
baryons.
evolution
The oscillatons
8
of p in oxillatons
are produced
Photino
and p in radiation
at T,. At ‘I&,
decay via lepton
”
9
and R parity
violation.
and
prodiot,m and phrva
are equal.
-_
::
..
.I
-lOO-
.,.~
.
work.
The majority
do not work.
of new particle
(N.6)
Soliton
By “soliton”
Relics
has a potential
stable defects:
consider
V(4)
= X(4’
field 4 takes on a vacuum
- 2).
the minima.
This
domain
wall contains
made complex
and the theory
J~(m’4 - 2’)‘.
In this case a pattern
configuration
8(c).
as shown
in Fig.
to be localized
in the monopole
A simple
a potential
example
The calculation
in particle
is a theory
the U(1)
V($)
Suppose
that
while at ‘I’, 4 makes a transition
where it vanishes.
length
the horizon
there will typically
The subsequent
However,
E3
under
for domain
where
rapidly
density
p today
evolution
certain
is n,o(T,)
is dominated
as shown
in Fig.
conditions
by domain
other contributions
one-dimensional
which has
to I$1 = o everywhere
of 4 is random
except
on scales of
Hence, as an order of magnitude
volume
less than
at T,.
of defects can be very intricate.
pnw
-
R-l,
p. N R-’
I know of no complete
walls or cosmic
strings.
Cosmic
strings
and PM N
cosmologies
Domain
walls
quite unlike our
which
10
stable defects ( a ) a two-dimensional
string
the arrows represent
for a phase transition
to p and lead to universes
own, unless they can be made to disappear.
Topologically
- 2).
N Ce3. Since C is certainly
of the collection
walls, strings and monopoles.
overwhelm
at a point
be many defects per horizon
simplified
A
group
defects is not straightforward
The direction
f, of the phase transition.
the defect number
be gauged.
at T > Z’,,I$ = 0 in each of the
above examples,
the correlation
Figure
of this field
symmetry
Simple estimates
near the defects
estimate
should
=
in a
internal
= A(&
rates for vacuum
of
V(4)
result
of three real scalar fields ($iv2(ps)
or in the big bang.
in the big bang can be made.
then
In fact for the energy
invariance:
B, then
If the 4 is now
field configurations
when a non-Abelian
of production
collisions
phase invariance
case the defect occurs
which has an SO(3)
near region
a U(1)
8(b).
degenerate
4 is not at either
field energy.
of vacuum
which
takes place such that the
wall at which
on the line defect
arises in gauge theories
is broken,
has two discrete
localized
processes
[I&
a real scalar field 4(Z,t)
This potential
by a domain
Some s&ton
and monopoles
value +o near region A and -g
will be separated
monopole
and which is produced
walls, strings
10(a), if a phase transition
these regions
string
domain
a theory which contains
As shown in Fig.
t,opological
localized
This is not the same as other uses of the term.
relics are topologically
191. For example
cosmic relics simply
quite unlike our own.
I mean energy which is spatially
at a phase transition.
minima.
physics ideas for creating
They lead to universes
self-intersect
-lOl-
S (c) a point monopole
the direction
domain
wall (b) a
M. In csses (b) and
of the scalar field in internal
(c)
space.
“.
and produce
loops which
be problematic.
one finds R,Xu/Mp.
provide
can then disappear
by gravitational
radiation
may not
At any era p. then scales the same way with R as pror,.+n.
For o of 10’s GeV it is possible that the string
the inhomogenities
If monopoles
about which galaxy
clustering
first
are made at a very early phase transition
must be depleted
by a subsequent
era of inflation
may
density
the universe
will not
with magnetic
charge
and mass near the grand unification
scale is depleted just enough to be the dark
matter
a flux of monopoles
today.
This would
been experimentally
monopole
which
produce
excluded.
carries
It is possible
have become
topological
stabilized
solitions
and which
logically
nuggets
I describe
In Fig.
assuming
matter
There are regions
nuggets.
nearly
that
the picture
medium
the QCD phase transitions
phase transition
it is first order,
as indicate
phase are nucleated
Since the vacuum
would
by lattice
equal numbers
Tc,ns
of quarks
and antiquarks,
However,
and antiquarks
II(b).
c <<
at T, is maintained.
When the phase boundary
be swept
along
with
although
if the critical
must annihilate
N np z (Tc.mg)wP-~=
equilibrium
bubbles
11(a).
quark
phase.
plasma
because in the hadron
transport
/
had
The cosmological
hadron
phase at
The q?j annihilation
quark
can
excess tends to
number
across the boundary
energy must be found
to create the baryon
degree it is therefore
energetically
for the quark excess to remain
11
QCD phase transition
(a) nucleated
bubbles
of
into the quark plasma
(b) shrinking
bubbles
of
phase.
:.
.:I
..
:.:
_.
..
the quark excess.
This is because for baryon
phase expand
Figure
:(
energy over large distances
Now imagine following
favorable
Subwithin
is say 100 MeV
moves into the quark fluid the quark
the boundary.
The bubbles
there was a quark ex-
temperature
T,” (see 2.10).
9’
@
is lower
are collapsing
The original
At
homogenous
half of space is filled by the hadronic
as shown in Fig.
cosmo-
calculations.
energy of these hadronic
occur to vv via the Z, and since neutrinos
thermal
proceed
in the previously
is that regions of quark phase which
cess of one part per billion.
the many quarks
9/ H
63
These non
H
how the QCD
and coalesce until
the hadronic
of false vacuum
or charge.
than in the quark phase the bubbles expand as shown in Fig.
sequently,
has
be a
The most well known exam-
which could arise during
of hadronic
quark gluon plasma.
will collide
which
could
below [20].
11 I sketch
first small bubbles
relics.
by the presence of matter
I will call false vacuum
ple is that of quark
at the earth
the dark
-:
Z” .
some other charge.
There is a second class of &ton
which
that
.A:.
‘.il
:,
‘j
.k.,
:
occurs.
their number
otherwise
evolve to the one we see. It is not possible that a monopole
Today
network
to go
mass. To some
in the
-102-
y.
”
..,
quark plasma.
If this e&t
shown in Fig.
11(b) will eventually
pressure
of the quark
at temperature
is quite powerful
excess inside the bubble.
just
even if quark
possible
category
eflect of the
baryons.
were formed
However,
at zero
evolution
from
Jecoupled
7, to T = 0, rather
nugget of another
phase transition
n > T,,
they
it is
the universe
issues.
which
the need for a cosmic
would
The standard
we observe.
Most additions
to the standard
the correct
restrictions
an enormous
the Table.
Plasma
particle
of candidate
and freezeout
equilibrium
which
relics.
P, e
CI’ violation
Abundance
UD
New quantum
asymmetry
and there is
Oscillation
Very
weakly
cou-
pled scalar
description
New phase
I3ifficult
transition.
\Neakly couplet 1.
relics have been proposed.
these cosmic relics,
An approximate
jion
,Other
symmetry
1llcts
(including
asymmetric)
with the plasma of the hot big bang.
techniques
Oscillatons
and solitons
are directly
associated
field theory, and occur in a surprising
in the Table,
understanding
are planned
turning
there
for the future.
point
particle
Soliton
in
which
are many
variety
with
in cosmology.
physics beyond
Defects from phase
Domain
New phase
Direct sear&
transitions
walls
transition
Gravitational
with
localized energy.
Secondary
phase
Strings
ing
Monopoles
Gravitational
NugRets
ation
of forms.
ways to search for the various
Several searches have been done for many years and new ones with
be a major
y, X ray signs. Is.
I have introduced
relics are particles
The discovery
It would
the standard
TABLE
novel
A cla.ssiIication scheme for cosmological
of any of these relics would
also give us solid guidance
decay prod-
of X1 may giv e
Nevertheless
and it is summarized
as
4xion to y colnver-
of 0.1 N R N 2 places conthe relics.
I direct detectic
number
give cosmic relics do not give
which generate
of I
by cosmological
arise from the decay of any of these three types of pri-
in the quantum
As indicated
model which
The requirement
scheme to describe
relics are particles
relics.
m > To
determined
physics
does not lead to
The cosmological
detectio
11cts
physics gave rise to an era of inflation,
on the interactions
were once in thermal
transitions
abundance.
number
a classification
mary
if particle
P
I 1etection
grew very rapidly.
them with
siderable
apparently
I Cect
,veak scale
sun or halo.
a simple and elegant
is the need for baryogenesis
relic to be the dark matter.
also be more acceptable
when R(t)
gauge theory
There
VW physics at
f mm annihilati
Summary
on cosmological
IVM.D
contributes
in which to study the effects of various gauge models of particle
as low
Bosons
Ion-relativistic
Lsymmetric
provides
I )ifhcult
e
“. : :
froze out while
to the dark matter.
The hot big bang model of the early universe
%z,v light
>articles eg
;oldstone
that
it seems that quark nuggets are not the dark matter,
some false vacuum
I
temperature,
it has been argued
I )ctection
‘ossible
mplications
at Z’, and even if they were stable at T = 0,
the cosmological
[21]. While
framework
1Examples
A quark nugget has been formed
such nuggets would be stable
decay to ordinary
nuggets
that
7-
Zharacteristics
n < T,
they do not survive
evaporate
by the stabilizing
T,.
We do not know whether
they might
then the collapse of a quark bubble
be prevented
in
model.
-103-
relics.
S
lensrad-
16. L. Brown
References
1. L. Okun,
Proceedings
of Neutrino
‘88 Conference,
Boston
17. W. Press and D. Spergel,
MA, MIT-CTP-
1606 (1988).
2. S. Falk and D. Schrarnm,
3. J. Kormendy
and J. Knapp,
117 (1987);
Universe,
J. BahcaIl,
Jerusalem
4. J. Binney
Phys. Lctt.
79B, 511 (1978).
Dark Matter
T. Piran
Winter
In The Universe,
and S. Weinberg,
School Volume
and S. Tremaine,
Gala&i
4 (1987).
Dynamics,
IAU Symposium
Dark
Matter
World
Ch.
and D. N. Schramm,
Fermilab-Pub-88/20-A.
Astrophys.
J. 296, 679 (1985).
18. T. Kibble,
J. Whys. A9,
1387 (1976).
19. J. Preskill,
Phys.
Rev. Lett.
43, 1365 (1979).
20. E. Witten,
Phys.
Rev. D30,
272 (1984).
In The
21. C. Alcock
Scientific.
10, Princeton
and E. Farhi,
2.2. D. Caldwell
Univer-
et al., Phys.
Phys.
Rev. D32,
1273 (1985).
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sity Press, 1987.
5. Proceedings
fo the Workshop
1988, Ed. E. Norman,
6. S. Weinberg,
Gravitation
7. M. Turner,
Proceedings
mond and R. Stora,
8. E.W. Kolb,
Cruz,
Wiley
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1985, Ed. P. Ra-
Holland.
of the TASI in Elementary
9. B. Lee and S. Weinberg,
Dec.
(1972).
of Les Houches Summer
North
Berkeley,
Scientific.
and Cosmoloa,
1986. Ed. H. Haber,
10. V. Rubin,
on Particle-Astrophysics,
World
World
Particle
Physics,
Santa
Scientific.
Plays. &v.
Lett. 39, 169 (1977)
Science 220, 1339 (1983).
11. R.V. Wagoner,
W.A.
Yang, M.S. Turner,
Fowler
and F. Hoyle, Astrophys.
G. Steigman,
D.N. Schramm
J. 148, 3 (1967); J.
and K. Olive,
Asrophys.
J. 281, 493 (1984).
12. A. Guth,
Phys.
Rev. D23,
347 (1981).
;
13. L. Abbott
and S. -Y. Pi, Inflationary
Cosmology,
World
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1986.
.:
._
.
.,
:.
14. J. Applegate
15. S. Dimopoulos,
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R. Esmailzadeh,
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L. Hall and G. Starkman,
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60, 7 (1988).
-104-
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1. Introduction
The ueutriuo
only
is distinguished
weak interactions.
decays.
Like other
v,,, and I+ associated
type of neutrino
are concerned
concerning
neutrinos
with
is known
neutrino
addition
it is quite
electroweak
massive
ably providing
with theoretical
it clear that
theoretical
natural
as one introduces
the dark
physics
matter
discussed
sources, in particular,
In the first lecture
seriously
evidence
2. Mass
the gauge theory
is that
on theoretical
Terms
do not interact
links
by SU(2)
proportional
ativistic
all fermions
invariance.
Conversely
to the SU(2)-breaking,
transform
fermions
field theory
the right-handed
The existence
particles
embodied
fields $~(z).
particles
of left-handed
particles
by fundamental
in the CPT theorem.
The usual Dirac
principles
of rel-
One can similarly
field G(z)
is related
by
try
(2)
flux
In
conceivHall.
A techuical
Also
point
of importance
from the charge-conjugate
is that
one can define a right-handed
field
of +L
of neutrinos
the sun.
ideas and then I will turn
mass.
will be gauge theory;
are introduced
and so must
antiparticles.
of right-handed
left-handed
the minimal
by Prof.
gauge theory.
and so must. transform
the left-handed
quantum
Here br, annihilates
neutrino
in Gauge Th.eories
discussion
the existence
5
ev-
on new physics.
from
neutrino
A crucial
fernlions
as doublets.
as singlets.
to the right-handed
This is the field which,
when expanded,
and creates left-handed
particles.
and T is transpose;
the particular
in partic-
the correct
trausformation
feature
emphasize
that
alternative
way of writing
as massless chiral
The reason for this, of course, is that left-handed
which
implies
evidence
in cosmology,
change the detected
x U(1) electroweak
dard weak SU(2) interactions
bidden
window
in the lectures
concerning
of our theoretical
SU(2)
term
and di creates right-handed
We
we will
beyond
as
a small mass. Thus neutrino
the neutrinos
I will concentrate
and prospective
ular, the standard
acquire
could be of great importance
from astrophysical
fernlions
where the sum is over momentum
Each
experimental
However,
physics
as a possible
mass could
fields.
vc,
partner.
in favor of a non-zero
are massless.
model that neutrinos
in particle
neutrinos
The framework
“flavors”
ideas and experimental
argument
fields may be expanded
it has
e, IL, and T respectively.
there is no defmitive
all neutrinos
effects of neutrino
t.o available
to exist in three
chiral
of weak
write
by making
mass is of interest
leptons
in that
as a result
mass.
It may well be that
standard
are believed
the charged
idence and no compelling
to show that
fermions
in the laboratory
to be much less massive than its charged
in these lectures
I must start
mass.
from other elementary
It is produced
fermions
The free left-handed
of
(Weyl)
Lorentz
right-handed
anuil~ilates
right-handed
anti-particles
(Here C is the Dirac charge conjugation
way this is written
property.)
fernlions
Note
guarantees
matrix
that
4;
I use the subscript
are annihilated,
but in fact 4;
+!I;. In the same way an alternative
has
R to
is just an
to v& is
have the stan-
d$ = C(4dT.
Right.-handed
The
usual mass
fernlions
is for-
the mass of all the usual fernlions
is
It. is asual t.o imroduce
a set of fields in,
introduce
however,
interactions,
and anti-particles
or weak, scale.
110 $Rj
-126-
without
we don’t
and another
set. $~,(r).
know the difference
so we could (and sometimes
loss of genera1it.y.
(36)
Before we
between
do) start only with
particle
a set $~i and
.:,-_ I -.
::.p.:.
,_.:: _.
-.
Let me first
acquire
their
handed
singlets
review
mass.
how the other
The fernlion
ferulions,
quarks
and charged
fields are the left-hauded
doublets
leptons,
and Z becoming
and right-
the fermions
massive.
One also introduces
)
,
(2)
Y = (Doublet
where
i = 1,2,3
charged lepton,
associated
is the generation
and Vi, D, are the quarks.
SU(3) of QCD.)
will be discussed
in detail
The interactions
are dictated
The question
neutriuo
(We ignore throughout
of whether
The Yukawa
the original
interaction
chi-
is SU(2)
@)r(Duubld
FL)z(Singlet
FR).
(8)
and
Considering
color and the
to inlroduce
fields.
only the coupling
involving
the neutral
a0 we have
the fields NiR
later.
of the fermious
with the four gauge bosom
by the gauge principle
weak interactions.
IV, aud Li represent
index,
Dirac
between
invariant
(4)
F -kyUiR,DiR
interaction
and the Higgs bosons as a means of converting
ral massless fields into massive
(:f
a Yukawa
In particular
c
of SU(2) x U(1)
and lead to the usual electromagnetic
the charged
g WA
current
‘%;r. TX D,L
interactions
where the sunl over repeated
indices
is implied.
Using Eq. (7) and setting
and
have the form
(5)
+ h.c.
we have
1
The fields of Eq. (4) defuse the weak eigenst.ates,
be the mass eigenstates.
leading
to the standard
assignment
To make a sensible
the standard
bosom
version
The right-handed
theory
fields
of electric
it is necessary
of the standard
which
ss we shall see may not
have only
U(1)
interactions
to introduce
the Higgs bosons.
model a single complex
doublets
In
of Higgs
Here ‘p represents
is introduced
tion with
/m+\
(64
The antiparticles
Comment:
also form a doublet
IIiggs
boson 0” acquires
a vacuum
expectation
x U(1)
symmetry
(124
breaks down to the electromagnetic
the physical
Higgs boson field and Y(q)
the fermion
for the quarks
interac-
and the charged
Weyl
In Eq.
fields.
(12) the fermion
Considering
fields
the leptons,
are actually
for example,
Dirac
fields rather
one obtains
directly
., I,
..: : .
: r., ,. ; -
the aid of Eq. (2)
value (VEV)
<w>=v
the SU(2)
A4c = h,jvLiLj.
‘p. The A& are now the mass terms
from Eq. (9) with
the neutral
(126)
1eptons.
than
When
A4u = g*j*UiUj
charge.
(7)
U(1)
with
provided
W
without
-127-
the matrix
h is hennitean.
loss of generality
In fact one can always choose h,j hermitean
by redefining
the basis for the right-handed
fields.
they are required
D, = (v,)jdt
in many extensions
of the standard
to give neutrinos
a mass term completely
and quarks
(12) )
(Eq.
equivalent
Uj = (Vu)jt%
._
:
:.
;.:
+
This is referred
When
we
Eqs. (14) into Eq. (5) we find
to construct
WA~LjYXujrdL.r
to as a Dirac
can be combined
term.
mass term
since, as discussed
to form the four-component
a mass term
We ca.n coustruct
Dirac
where
U is the famous
Note that
in the case of neutrinos
here as hermitean),
thus 18 arbitrary
these end up as observables:
(three
in its gauge sector
and ugly in its Yukawa
(16)
d
(KM)
two arbitrary
parameters
quark
3x3 matrices
for the quarks,
Notice
The standard
model which
(only two coupling
constants)
mixing
(chosen
vation
for the other
violate
the total
lepton
number
but only 10 of
sector.
For the charged
leptons
is so economical
becomes
with
and
extravagant
we have similarly
where the l’, are the usual e, p, 7. Because the neutrinos
standard
model we can redefine them by operating
the lepton
(or degenerate
analogue
massive)
Let me return
model
we never
On the other
the doublets
the lepton
now to the neutrino.
them.
introduce
on the original
of U is just the unit matrix.
neutrinos
the fields
hand the symmetry
remain
mixing
Therefore,
way
the Majorana
mass
called
weak isospin
matrix
with
leptons
of Eq. (4) may suggest that there really
and quarks
should
to lepton
by one unit
This term
- N(L+)).
does
However,
charge since it is not associated
of neutrino
number
mass the fundamental
violation.
(since it annihilates
to MD which violates
a Majorana
- N(N)
changes the
by charge conser-
for neutrinos.
+ N(L-)
like electric
and therefore
be forbidden
weak isospin
The term
or creates
by f unit.
ML
two NL
It is also
mass term from NR
f h.c.
V, so
Characteristics
massless
of the standard
N,R since we have no essential
between
to construct
(N(N)
ME = /L:ITRiNij
V, is unobservable.
In the usual presentation
is related
1s = f) in contrast
+ NLNL
would
In most theories
also violates
+ h.c.
but is conceivable
number”
symmetry.
NiNi
Such a term
fermions
“lepton
introduced
massless in the
N;L with
proportional
by two.
L is not sacrosanct
a gauged
possible
Lj = (Ve)ji&
number”
new physics
with
that
that this is really
“particle
the six quark masses and the four KM parameters
angles and one phase).
elegant
contains
above, Nr, and NR
There is another
(15)
3x3 Cabibbo-Kobayashi-Makawa
the Lagrangian
field.
a mass term using only NL
ML = pijNLtN;11
matrix.
(18)
11.~.
(14b)
where d, = (d, s, b) and u; = (IL, c, t) are the usual “mass eigenstates.”
u = v’vu
It is then possible
(14a)
MD = m,j~~,Nnj
substitute
model.
to those for charged leptons
need for
as seen in
be NOR and indeed
-128-
of those three types of mass terms are summarized
in Table 1.
_._.‘..
-.._
If we have only t.he Majorana
will be massive
particles.
In their
rest frame these particles
the anti-particles
and Majorana
are identical
mass terms.
set of t,wo-component
viewed
simply
obtained
from
IELSS term,
say hf~,
but still have only two components.
MR.
More
terms can be found
It is possible
In this case in general
details
neutrinos
solution
from
formulation
those
of neutrino
mass
beyond
the standard
the NJQ so as to get the Dirac
the simplest
While
conceptually
considered
as the sole origin
the smallness
of neutriuo
2. Do not, include
to leptons.
1.
a four-component
Majorana,
The reason is that neutrinos
h&city
part
neutrinos
(whether
in general
(E
>>
requires
almost
m).
observations
distinction
is that
all models
we can imagine
the Dirac
“standard
model”
with
suppressed
neutrino
discussed
(18).
While
not
of neutrino
mass because it provides
:. :
>...I.
.:
.,
.:
..
:
no insight, into
NR~ but add a Higgs triplet
a Higgs mechanism
that
has a Yukawa
for producing
coupling
the Majorana
version is the Gelmin-Roncadelli
mass
model3
Dirac
viulation
from
which
of lepton
number
we will pursue
at a large mass scale M, in particular
which results in Majorana
lriplet
mass terms.
the
It is this idea
in most detail.
The basic idea of the Gelmini-Roncadelli
and this
An important
moment
effects of new physics
(GR)
model is the addition
of the
will1 the charge states
pLv but in
and so very smaIl.
T = (To, T+, T++)
In the
.
Bohr
coupling
of T to the product
of two lepton
doublets
is
(21)
magnetas
is much too small to be detected.
An indirect,
but very sensitive,
come from the observation
a change of lepton
Witherell
the virtual
The amplitude
rather
indication
of neutrinoless
number
As discussed
exchange of a Majorana
is proportional
of a Majorana
double beta-decay,
by two units.
to the diagonal
neutrino
element
where $1~ is the leplon
mass for V, could
doublet
from Eq. (4). Looking
just at neutrinos
a process involving
in the lectures
yT
of Prof.
could induce this process.
pee of the Majorana
When To acquires
mass
IV;
a vacuum
-
k&;NL,T”
expectation
(22)
+ h.c.
value VT Eq. (22) yields the mass term
of Eq. (19) with
than to a mass eigenvalue.
3. Models
In the standard
vided
of Eq.
mass, it is usually
mass solely due to film one finds2
I‘” = 3. lo-‘9 m,(ev)
matrix
neutrino
below.
The gauge invariant
which
ways to get a
mass.
This provides
3. Consider
left-handed
$$)
(m/E)‘.
can have a magnetic
to m,
from a
of the right-handed
the anti-particle
by a factor
pL, is proportional
a neutrino
with
to distinguish
the character
$n or just
The
indistinguishable.
completely
In order
one needs to determine
it is the new particle
is very different
they are practically
are produced
and at high energies
Majorana
Dirac neutrino
experimentally
mass term
way t.0 get a non-zero
term of Eq. (19). The most interesting
two-component
model.
,.:
will be a
iV1~ with
is uo physics
1. Include
this provides
term in this case may be
obtained
on the general
in Reference
and (3) there
11011-zero m, are:
to have both Dirac
the final
The Dirac
particles.
the Majorana
particles
have the usual t,wo spin states and
to the particles.
Majorana
as mixing
then the final
These are called Majorana
SU(2)
of
Neutrzno
x U(1) gauge theory
(1) there is no NR, (2) there are no IIiggs
P t, = k, L’T.
Mass
the neutrinos
are massless pro-
Note that
bosons other
thai
quantum
the doublet,
-129-
given its charge structure
number
of T) the triplet
(corresponding
to the choice of the U(1)
does not couple to the quarks.
The smalhress
.:..,
.,
of neutrino
mass is “explained”
constrained
by astrophysical
The Yukawa interaction
nunll,er
by or related
argumeuts4
ton nmnlxx
theorem
there results
a massless spin-zero
usual Higgs boson this boson remains
uumber
is not a gauge symmetry.
are many
interesting
emission
of a majoron
discussed
boson (essentially
This particle
One of these is the possibility
Let me now turn
to the idea that
interactions
Sucli interactions
that
typically
uot renormalizable
Of interest
and ax
Indeed
mass arises from
There
the neutriiio
particles
of the nortnal
handed
the major
to be used ady
in lowest-order
interaction
tlmt
nornml
Equation
(23) violates
-. .>.. :-:
. . ., __ :.I..:
-.,.::_..
lepton
this is due to the new physics
at
because the larger M the smaller
comes in theories
NR~. One assumes that. these neutrinos
mass given
assume that
singlet
by Eq.
(20) with
the plj
the magnitude
of fife
acquire
a very large
M
z). Because
of order
>>
defines the scale M at which
We now assume that in addition
magnitude
with right-
there is no reason for the @Ij to be of order
(similar
to quarks
Then the form of the mass matrix
of new physics
there is a Dirac
and charged
leptons)
v and we
lepton
number
mass term
MD of
but keep ML = 0.
is
of M.
particles
NL
Ni
N;
0
MD
NR
Q
MD
Mn
with
interactions
perturbation
f
of the see-saw formula
as au efTective four-
Such effective
ouly Al’=
and it is presumed
realization
fifR is an SU(2)
new physics
The
mass.
neutrinos
Majorana
see-saw fonnula.7
arises because, as shown in Table 1, ML requires
SU(2) x U(1) variety.
cm be described
I.0 [m (iv)]-‘.)
to us here is the effective
virtual
to v2 necessarily
The simplest
with
to some power
Gell-M~ln-Ramotld-Slansky-Yallagida
by t,wo units
is broken.
involving
Mr. of Eq. (19) with
mass scale M. This is called a see-saw formula
to fine tune V(T, @)
proportional
arise out of diagrams
proportional
double
x U(1) scale the consequences
(At a lower mass scale the weak interaction
interaction
uumber
because leptm
are so much fum5 The main disad-
neut.rim
mass term
A? = 1 whereas < @” >= v provides
the
beta-decay
are inversely
masses of the order M but external
fernlion
unlike
of neutrimless
lectures.
proport.ionalily
sun11 value of (VT/W).
at a large scale M. At the SU(2)
are effective
Imp);
particle
and it is necessary
the Majoram
This is the famous
when To ac-
such a massless
of the GR model is that majorons
is t.bat it has lit.tle motivation
lep-
By Gold&me’s
is called the Majoron.
Witherell’s
we obtain
T has a leptoll
co*~sequeuces of having
in Prof.
in order to create the necessary
broken.
&s a true physical
l~lieiioi~ienological
particle.
advantage
provided
V(@, 2’) also conserves
value, L is spontaneously
is
in the GR model.
A s a consequence
L (there is no t.erm of the form cP9T).
expectation
of VT/V, which
1V7
I+ conserves lepton number
of two, In the GR model the IIiggs potential
quires its vacuum
vantage
to the smallness
to be less than
are
Diagonalizing
theory.
particles
t.llis we find for AiD <i
characterized
by nii,
and light
n,f~ that
neutrinos
there are heavy
with
a mass matrix
Majoram
given by
of the forn16
(26)
Mu = DTM;‘D.
.
.
‘...C.
Note this is part of a gauge invariant
bined to form a triplet
a t.riplet.
When
together
a0 acquires
term made of two fennion
wit11 two Higgs doublets
a vacmun
expectation
value
dorlblets
also combined
(Eqs.
corn-to form
where m.~ is the Dirac
(7) alld (10) )
A,JR were zero.
-130-
mass, that
Since rn~ conxs
is, the mass the rleutriuo
from expressions
like Eq.
would have had if
(la),
it follows
that
:_.
_ ::
.-
Eq.
A ssuming
(27) has the general form of Eq. (24).
as the mm
lhe factor
of a quark
or a lepton
we see that
mg
is of the sane order
the neutrino
mass is reduced
(31)) the fields e;, etc., are really the charge conjugates
by
to the present
(ma/M).
showing
discussion
up in the form
the 16 of SO(10)
Ni.
contains
The conjugate
of Ed, etc. Of importance
both
NL and NR, the Iatter
fields 416 transform
under
SO(10)
. .
The
motivation
quarks
which
mass term
standard
for this
suggests
sinlilar
approach
there should
to that of other
is the symmetry
be NR and that
fernlions.
model is a weak phenomenon,
and the mass of the charged leptons
the NR are completely
it becomes
SU(2)
that
possible
breaking
scale that
the large ratio
large ratio
neutral
with
respect
that
electromagnetic
x U(1).
A disadvantage
introduces
in SU(3)
The Yukawa
is not equivalent
to 16 (just as 3 and 3 are not
).
-7.
::.f:..:.
interaction
:.
._.
2,
:
:_
:
involves
so
interwhich
t,ransforms
as 16 x 16 which
As a consequence
mass much larger
M and Y is t~echnically
is needed in any theory
in the
of SU(2),
the NR and all other fermions;
to SU(2)
rn~.
equivalent
be a Dirac
13, which
to their strong interactions
a Majorala
determines
between
should
and
mass generation
to their
between
for NR to acquire
leptous
with the breaking
is unrelated
There is, of course, a difference
there
Note that
associated
that the mass of quarks does not appear to be related
action.
between
as the representation
however,
new physics
representations
16x16=10+120+126.
than the
of this approach
uxznatural;
breaks down to irreducible
is
Higgs bosons that
such a
we can write
can couple
the Yukawa
to fernlions
interaction
are thus &lo, &o,
and 4126 so that
of SO( 10) in the form
at a large mass
scale.
The original
idea for t.he see-saw formula
of (25) comes from the SO(10)
in which
down
down
to U(1).
different
to SU(3)
parts
are different
x SU(2)
The
weak,
conlpouents
The simplest
GUT
on SU(5)
16-dimensional
Ill
one starts
x U(1) just
fermion
(GUT).
with
SU(5)
11xre
eventually
interactions
Similarly
quarks
that
breaks
are just
two
are no NR.)
different
(A simpler
representat.ions,
The fernlions
The Dirac
the bottom;
are united
GUT
mass terms
the Majorana
based
The Higgs field ~$10contains
which
normal
in SO( 10) form
mass terms &s
well as Dirac terms can arise when the Higgs bosons acquire vacuum
values.
of a single generation
Eq. (28) into Eq. (29) one can see t,hat Majorana
By substituting
and leptons
field.
is based on the group SO(10).
into
(29)
GUTS are models’
x U(1)
and strong
in which all the fernlions
divided
of mass matrix
a single gauge group
as SU(2)
gauge interactions.
of a grand
has the fermions
ululatural.
theory
electromagnetic,
of the original
in a single representation
Seellls
grand unified
at a high mass scale lLf~u~
breaks
and for the form
Higgs while
mass matrix
a
expectation
(28) couples
to
mass terms when Nr. couples to itself or N,” to itself.
two SU(2) doublets
&20 contains
schematically
arise when t.he top row of Eq.
an SU(2)
0, that can play the role of the
triplet
T aud a singlet
S. Thus the
;. .. .
:: :.~.:.I”...z .: -:. .. :..:
._,.
__
_-’
take the form
representation
(28)
which reduces
where a is the color index.
We show only left-handed
fields, but as shown in Eq.
to the form (25) i f we, some&at
arbitrarily,
value of < S > and thus of M can be equal to the GUT
-131-
set < T >= 0. The
scale (2 1015 Gev) but
In fact the SO(10) model with only two mass scales ~JG~T and
could be smaller.
v tends to have the failures
of SU(5) in predict,ing
1.00 fast. a rate for proton
and too low a value of sin’ Bw. Thus there may be an argument
at, a value more like 10”
-1
Ta.hle
decay
for choosing
M
Gev.
2 - Limits
on Neut,rino
Mass
..:
.;.:::.-
‘.
Because
Yukawa
the SO(10)
interaction
has such a large munber
and its Higgs potential
However,
most analyses’
followiilg
qualitative
1.
model
The neutrinos
there are no definitive
that fit t,he quark and charged
conclusions
of parameters
concerning
lepton
.,,
in its
to those of the other
together)
m(v,)
ii=1
: m(vJ
analogy
: m(r+)
= d(U)
: d(c)
: d(t)
with
interactions
flavor
the quark
expressed
eigenstates
mixing
are mixt.ures
described
in mass eigenstates
of the mass eigenstates
by Eqs.
(14).
As a result
the limit
assumptions
(31)
or 2.
2. The neut.rino
in
detected
it is possible
preceding
the main
of neutrinos
resenting
mixing
mixing
angles
of the neutrinos
in Ue are all small
(f7= - 0.2) with particularly
The most direct
between
on Neutrino
way to study neutrino
mass from the kinematics
to that
of the order
small mixing
4. Limits
missing
relative
of the KM
of the charged
of the Cabibbo
the first and lhird
a non-zero
confirmed
by other
mass of v, arolmd
experiments.
30 ev, hut
It is unlikely
that
this
Present
mass experiments
an earlier
of the
which
limits
lifetime
Detailed
which
supernova
is m(ve)
supernova
produces
5 15ev, similar
with
to
more neutrinos
burst
(a pulse of V.
of neutrinos)
it is possible that analysis
maSses can also be obtained
the observed
time when the universe
density
t, of the universe
as a function
by the Hubble
10’ times
and other evidence.
of
the number
of
and thus determine
It is then possible
of the neutrino
Ho.
Assuming
Ho > 50 km se,-’
a density
have a mass of several ev they
down.
constant
arguis a relic
The same the-
all space with
is about
of the universe
is slowing
cosmological
background
and denser.
filling
Thus if the neutrinos
expansion
specified
This number
from
microwave
was hotter
also be relic neutrinos
the energy
the universal
from radiochemical
-132-
and
could detect a large range of V~ or vT masses
reviews
are found in Ref. 10.
SN
and IMB
analysis
all flavors
Mpc-’
the rate
at
to calculate
mass and the present rate
If the neutrino
large the value t, will turn out too small to be consistent
can be
the supernova
statistical
of the neutronization
emission
cosmology
in the universe.
of expansion
has not, been
any of these limits
a study
110 cmm3 for each generation.
baryous
has persist.ently
result
reduced by more than a factor of three in the foreseeable future.
of neutrino
ory says there should
masses is by the determination
are shown in Table 2. In t,he case of 3H decay one experiment
indicated
from
The
dominate
neutrinos.
on neutrino
In the standard
leptons.
generation.
con&&u
down to 2 ev or less. Furthermore
rep-
Masses
of decays involving
that
from
(19 in Kamiokande
on t.he particular
3H decay. i;br a future
from a future
Limits
angle
depends
thermal
matrix,
mixing
interval
of neutrinos
100 ev and 100 kev.
ments.
analogue
limits
from
time
of neutrinos
used. I believe a reasonable
could provide
the weak
have the form
and U’ is the lepton
in a short
obtained
obtained
(32)
~j = (z+,v~,I/~)
arriving
the limit
between
where
energies
19S7a. Because of the small number
fermioils
with
on the mass of V, can be obtained I1 from the observation
A limit
of different
analogous
::.
-
predictions.
masses yield the
neutrinos:
have a mass hierarchy
__,.)
..::.
-..:
mass is t.oo
wit.11 t,imes determined
..‘...
.:
I>,
‘-.
-. ::
-,
t, > 10 109 y7-s
A beam that
is originally
1 u(t) >=
rn(V,) +m(v,)
This limit
does not bold if neutrinos
an earlier
time
in tile history
decay mechanism
constraints.
that
satisfies
+ m(v,)
decay rapidly
will annihilate
(33)
enough
of the universe.
It is hard
cosmological,
astrophysical,
In the GR model the limit
into nmssless nlajorons
of the order of the neutrino
< 80ev.
and so disappear
m(v,)
which
of the universe
in Table
m(vw)
2. If we further
< 1 ev, and m(l/c)
requires
neutrino
<<
oscillation
energy
needed to satisfy
conditions
on m(v,,)
demity
of Eq. (31) then m(v,)
of the universe;
that
limits
to probe small neutrino
< VP 1 v(t)
The prohabilit,y
such small nmsses
Ppe =I<
25 and 50 ev could provide
is, provide
:
The basic idea of neutrino
v&, may be written
<< p’.
v, because of the change in the relative
projection
>=
the dark
masses using neutriiio
of neutrino
oscillations
oscillatioiis
is not too small.
of an oscillation
vp (u(t)
its mixtures
of t.lle mass eigenstates
(38)
into vp is then given by
>12= 2sin2%~os2%x[1-Cos2(_2__1
m2- m2
2p
)t] = sin’ Z%sin’(nz/!)
(39)
oscillation
length
c = c, = -aL
m;-m;
pro-
is given by
= 2.5 meters
~(Mea)
Am2(ev2)
to express
the oscillation
.
(40)
These
It is convenient
using just two gen-
The flavor eigenstates
on the state V~ given by
matter
masses.
can be illustrated
to three is straightforward.
phase
- sin 89cos %e--IELt + cm 9 sin %emiEzt.
Formulation
mass diITerence and t.be mixing
are met in most theories
the extension
(37)
= (m; - mf)
< 80 ev,
the time evolution
erations;
An?
and has a non-zero
where the characteristic
Oscillations
._ : _
-.:..:.:
.
and
R = 1.
vided there is a signilirant.
(36)
The state (35) is 110 longer purely
than the direct
1 ev. The only way to explore
5. Neutrirro
It is possible
more stringent
~nass between
(35)
EZ - E, Y cm; - 7$)/2P
studies.
We note in passing that a neutrino
the critical
(33) we have a constraint
accept the hierarchy
>
is
the kij are not too small.
is many orders of magnitude
sin % 1 *
assuming
and experimental
when the temperature
result
eCElt cos 9 1 y > +eCEzt
to find a theoretical
of its two compomnts
If we accept the cosmology
of time
where
at
(33) can be evaded because the neutrinos
nmss provided
ve becomes as a function
vp components.
for what
follows
of a two-component
vector
in flavor
pheimn~enoii
space v(t)
with
as
I+ and
Then
v, and
vy and *
(41)
The 2 x 2 matrix
h4’ is given by
M;”
(34)
-133-
= $L’
- Am2 cos 2%“)
(42~)
_
._
_.
‘_Z.
:.
:
:..
..
M;,
= ;(P’
is easy to see that
(42b)
-t Am2 cos 2%,,)
iIm
since substituting
where %, is the mixing
Pauli notation
angle (subscript
this matrix
v is for vacuum)
and $
= no: + mi.
(45)
this into (43) gives exp[-Ncrz/2]
tion of the amplitude
In
p(n - 1) = iNa/
due to the absorption
which
cross section
represents
V.
the deple-
Combining
(44)
and (45) one obtains
has the form
CT= 4iThf(O)/p
(46)
M2 ~~21+Am2(-cos2%,~,+sin2%,a,).
which is found in many books.
of the iudex of refraction.
Neglecting
the unit matrix
precession
of a spin -4
axis. Neutrino
To probe
must
magnet
oscillations
the same folm
in a magnetic
oscillations
from Eqs.
passing through
cases one must
take into consideration
to the material
medium.
the phases of the flavor
as a precession
over very large distances.
of neutrinos
in flavor
space.
In practice
adding
the sum of the forward
mitted
wave; a succinct
assumption
about
the target
atoms.
of the oscillations
neutrinos
effective
due
and cme source
- l)s] .
wave packet;
oplical
scat.tering
theorem
of the neutrino
to the spacing
are limitations
in applications
Physics.‘3
nor does it make any
related
of
to the
these limitations
are
current
both
n and f(0) must
be considered
model f(0) is diagonal
(W boson exchange)
in flavor.
as matrices
in flavor
If we consider
the weak
cme f~ids for V, scattering
from electrons
= -xh’Gp/2n
is given by the opt,ical theorem
PC" - I) = --di~N,
of scatterers
amplit~ude.
per unit
I1 is customary
volume
and f( 0) is t.he roberent.
at. this point. t.0 note that
can be found in any book on quant~um mechanics.
this is not the case. A number
(47)
(44)
where
forward
notes on Nuclear
of targets
effect there
to the trans-
(43)
P(” - 1)= 257W(O)lP
where N is the number
a lattice
of the neu-
by coherently
important.
f(0)
The index of refraction
the absorpl.ion
waves from all the targets
is given in Fermi’s
Like any coherent
in the real part
(44) may be derived
the ratio of the wave-length
space. In the standard
charged
e+p[ip(n
derivation
does not require
For our example
term
Equation
scattered
size of the neutrino
not generally
have to do with
negligible.
the result
leads to
of the propagating
this
is completely
Note that
here, however,
For the prol~lenis of interest
trinos
the earth or the sun. In such
point is that oscillations
of change in phase is the index of refraction
of the
(39) and (40) t,hat one
the modification
The essential
components
as the problem
field at an angle 28, to the spin
may be considered
small values of AILS it follows
look for oscillations
studying
this is exactly
We are interested
of books give t.he imaginary
the
current;
Unfort,unately
part of Eel. (44).
N, is number
reve&ed.
muons.
It
however,
-134-
of elect,rons
per unit, volume.
Of course, I,,, do not scatler
lhey
scalter
elastically
There is also scattering
iron,
elasl ically
muons
For ce 1.he sign must
from electrons
but normal
of u, and v,, via the neutral
media
be
via I he charged
do not contain
current
this is the same for all flavors aud so only adds an overall
(Z exchange);
phase (not a
relative
phase) to the propagating
factor
r/(t).
We cau uow take account
(43) by using Eq. (41) but replacing
Mze = ;(p’
Note that iu obtaiuiug
(37) the ueutriuos
of the phase
- Am2cos20,)
the eigeustates
+ 2hGN,y.
(48)
esseutially
with
the velocity
replaced
by
e,,
value
of N,,
oscillations
are described
of the suu) the upper
the resouauce
where
deusity
of light.
by Eq.
(39) with
0,e
the upper
the upper
= siu20,/(cos20,
-
state
which
Iu this case
1. At large densit,y
is primarily
v, (&,
by the mixing
term
vP. If the density
cau be used, which
As a result
is now primarily
M$.
variation
meaus that
the original
At
the levels
Finally
at zero
is not too rapid
no transitiou
v, remains
vP. The probability
(such
near 900).
the two levels come close together;
state is primarily
the eigenstates.
state,
to zero density.
that
takes
primarily
ve is still I+ is
Pee = cos’ 0, cos2 B,, + sin2 0, sin2 fIti = i( 1 + cos 20, cos 20,)
e,, = c,p
2(e,/e,)
-
k-0= 27r/diGNe
co5 ze,
+
= (1.6 x 107/p,) meters
where 0, is the original
(51)
not included
where pe is the electron
number
value C, defines a characteristic
order
of the earth’s
&, >> 6, oscillations
which
radius.
density
length
in units
in matter;
For e,, <<
are highly
C,, and e, are ~~~~prable.
6,
suppressed;
of Avogadro’s
for uormal
matter
effects
of particular
In particular,
(54)
(50)
(ev/eo)2]-f
nun~ber.
matter
The
interest
rapidly
it is of the
can be ignored;
meam
oscillating
Pe, that
(Note
that
a complete
conversion
in deriving
are three important
(54) we have
siuce this is a
For 8, uear n/2 aud 8, small we
of v, to v+. l?or values of 0, too small (this
(B,, = 45O) and the adiabatic
the adiabatic
Eq.
the ~1 and vs components
term and averages to zero.)
go beyoud
There
(52)
between
is small by Eq. (42~) ) tl ie mass eigenstat.es
M$
the resonance
for
value of B,,.
any interference
have almost
for
in the case iu
e, = e,cos20,
in
given by
(49)
ev/e,)
= 4Y
f&
approximat.ion
place between
etn
tal128,
corresponds
chauge as showu in Figure
as the center
the adiabat,ic
For a fixed
in matter
would cross but they are “held apart”
Eq. (45) we have set z = t, since with the approximaliou
are moving
45“ down to 0,” = 8, which
through
Eq. (42a) by
get too close together
approximation
approximation
cases in which
fails.
Formulas
at
for
are given in Refs. 14 and 15.
matter
effects play an important
role:
8,, becon~s
45O. The importance
of ibis case was discovered
Sniirnov
who refer to it as the resonant
matter.
For the case of Y., G@ the sign of the right-hand
reversed,
effectively
be satisfied
chauging
for v, if m(v,)
amplification
the sign of C,. Thus
< m(vP)
1XI t not for 4.
by Miklraeyev
of neutriuo
side of Eq.
the resonance
and
oscillations
(1) Neutrinos
by
rays and passing
in t.he atmosphere
a major
condition
(2) Neutrinos
cau
For small values of 0, Rq.
(3) Neutrinos
For most applications
= 6.S x 10~Am2(euz).
the value of N, varies.
as the density
decreases,
8,
passing
(53)
Of particular
decreases
from
interest
a value
as a result of collisions
of the earth
of cosmic
before being detected.
originating
uear the ceuter of the sun aud traversing
is the
near
a radius
of the sun.
through
originating
90°
-135-
iu the core of a collapsing
star (supernova)
and
the dense out,er layers.
6. Ned-ino
case in which,
portion
(47) is
(52) gives
E,(Meu)p,
originat.ing
through
We first
summarize
tory neutrino
oscilld.ion
briefly
Oscrllations
our preseut
experiments.
:
Erpe~iments
knowledge
We distinguish
obtained
from
labora-
two types of experiments.
Appearance
experiment~s
new flavor
(like
Uisup~ewawx
measure
quantities
v,~) a.ppears in a beam
experiments
measure
like PPe of Eq.
originally
quantities
(39) in which
a different
flavor
like Pee of Eg.
(like
a
v.).
(54) in which
.
one measures
the flux of a given flavor
some distance
from
the source.
In the
.. ..‘-:
case of only two flavors
Pp. + Pee = 1.
However,
in general,
the original
lation
flavor
experiments
disappearance
experiments
to any new flavor.
probabilities
only a correlated
amples for which most information
oscillations.
Our prejudices
t.o note that
production
this important
v,, disappearance
+Ne
iment
it also provides
result
was simply
at CERN.17
limits
and 8, so that
these quantities.
The exand V, -v,,
may he very small;
is summarized
in Figure
For the larger
experiment
The lower branch
experiment
(39) the oscil-
An?
are vP - V, oscillations
two experiments.
an emulsion
by neutrinos.
between
is available
Eq.
from
are the most diffGzult to probe experimentally.
shown come from
E531,
limit
on both
of vP - v,. oscillations
Our present, knowledge
Ihey come from
x depend
suggest that. I+ - I+ oscillations
in any case ye - r+ oscillations
The results
are sensit.ive t.o oscillations
As can be seen from
at a given distance
provide
at Fermilab.”
a byproduct
2.
values of Am2
It is interesting
of a study
of charm
of the curve comes from the CDHS
Since this was a disappearance
on 9 - V, oscillations;
however,
better
experlimits
are
r-
Figure
1
of electron
Eigenvalues
density
N,
of
of the M2 matrix
or distance
I
the sun
as
from
a function
the center
available
in that
case. If we assume I3 in this case equals or is greater
Cabibbo
angle (indicated
(assrmihg
m.(v,)
<<
constraint
on m(q).
by t.he dashed
m(vT)).
As we have noted
be of enormous
int.erest
involving
J+ are certainly
worthwhile.
There
by Koshiba.
is also shown
a value of m(v,)
2 a dashed
Further
cross that
data on atmospheric
ward and downward
neutrinos
be required.
so it is necessary
than the
m(q)
< lev
if sin’ 28 < 10e2 there is no
If the effect were as large as indicated
vu and ve or vP and V, would
-136-
then we conclude
had
for cosmology.
in Figure
of the preliminary
line)
On tl le other
ev would
interpret&xi
.
-:
between
efforts
large mixing
The effect
on oscillations
represents
neutrinos
appears
25 and 50
a possible
presented
here
angles between
for both
to assume a vacuum
up
oscillation
‘_
-_
.;
.:
.I
length
short
negligible
enough
with
There
is a mwb
best present
the solid
greater
laboratory
body
limits
line in Fig.
disappearance
apply
to affect the downward
neutrinos.
3.
of knowledge
on Am2
For large
on vP - V~ oscillations.
mixing
angles the best limits
t.0 L,~- V, oscillations.
These disappearance
experiments
to values of sin’ 20 less than 0.1. The remaining
of V, in vP beams at the CERN
occasional
with
experiments
the acquisit.ion
Reference
Our theoretical
3 that very little
I
data.
prejudices
by
: ./: .. :
come from
of course also
are not sensitive
come from looking
PS and the Brookhaven
For a review
they
for the
AGS. While
have disappeared
of accelerator
experiment.s
discussed
from
above suggest m( vP) < lev with
with sin’ 20 of the order IO-‘.
of this paramet.er
laboratory
abstracted
discussed
Am2 < lev’
3 are indications
by future
i
limits
have seen signs of oscillations
of better
The
see
19.
much less so that
Fig.
effects are
and sin’ 28 are shown schematically
using iie from reactors. l8 These limits,
experiments
appearance
Thus matter
this solution.
range has been explored.
of discovery
possibilities
or limits
experiments
of the type
already
various
by Koshiba)
conference
but there is no assurance
that
Fig.
The dashed lines in
that
could be achieved
done.
These have been
and proposals
reports’8~2”
m( ve)
We see from
(including
those
the experiments
will
be
done in the near future.
To go further
0.5
1.0
sources
sin*20
using
listed
one needs to go to still
at the end of Section
atmospheric
Ii t tie da&dot
neut,rinos
large
Hz0
with
those
coming
would
Cerenkov
from
above.
be a large enhancement
Future
neutrinos.
gone different
distances
distances
through
and we turn
has already
the earth;
comparing
For neutrino
this is shown
of neutrino
vw and V, arriving
energies
oscillat,ions
to the
been obtained
around
by the
group
using
from
below
300 Mev there
inside t.he e&h
because
satisfied.
large det,ectors
In principle
larger
One result
3. The resrdt 2’ comes from the IMB
detector
Eq. (53) is approximately
-137-
passing
curve in Figure
their
5.
can further
because
explore
neutrinos
and t,hrough
the oscillations
coming
different
ill different
amounts
of earth
of at.mospheric
directions
have
these experi-
.’
,..’
_
I
.
IO
nieuts
cau explore
uncertainties
Figure
I
a wide range of parameters.
in the incident
3 is a schematic
lo-’
flux as well as by statistics.
indication
of the possible
smaller
by exploiting
earth
Super Kamiokande
mixing
10”
;’ \
. \
Since the matter
\
way around)
\
ampliftcation.
detecting
The dotted
values that would
nuclear
by
curve in
be explored
..._.*37Ci - - -4:; - - -c:“_.-..-.
.-. a....
7
\
\
\
_--- -l ---\\
c\
\
\
12
\
\
\
7’G\a\,
\
16'
\
\
should
Icy3
I
1o-2
of the energy
a way of probing
be able to dist.inguish
in the form
.
.\
\
\
3 with
flux comes from
the weak pp reaction
the calculated
\
neutrino
This
relative
that
the resultant
the other
to solar neutrinos.
The
in the sun give off
The study
of these neutrinos
reactions
fluxes.
over distances
yielding
While
makes them
larger
neutrinos
are
the predominant
is the first step in nuclear
difficult
a very low flux but the high energy of these neutrinos
introduction
be
nnrons.
burning
to detect.
of t.he very rare PI’111 chain of reactions
For the standard
to the
can practically
energy
oscillations
of these neutrinos
sI3 is t.he product
easier to detect.
\
:.
of what goes on in the solar interior
The three major
shown in Table
produces
\
of neutrinos.
a way of exploring
the size of the earth.
In contrast
_
.’
:‘-:“
.::.
n+ from p-.
we must turn
for providing
our understanding
iu the suu, the lower energy
\
exists”
from Eq. (53) applied
up to 10 Gev.
and then detecting
are responsible
provides
than
and so
make them much
to these reactions
see Reference
23.
\
\
I
that
a portion
and also provides
/
//
\
the possibility
effect holds only for V~ (and not i?p or conceivably
the detector
reactions
In principle
However,
neutrinos
To go to values of Am.’ below 10w4ev2
Am2 16"
lCiE
is limited
angles for values of Am2 of the order 10m2 to 10-3ev2
the resonant
this requires
detector.
done only by using rock as the target
lci5
sensitivity
‘..
by the proposed
to explore
16"
Their
\I
I
10-l
1
I
Table
3
-
Sources
Maior
ENERGY
of
SPECTRUM
Solar
Neutrinos
RELATIVE
FLUX
:
SIN2 28
Figure
future
3
Existing
experiments
limits
on vu-ve
1
~
and possible
oscillations
The hrst (aud for more than 15 years only) attempt
was carried
-138-
out by Ray Davis
using
37C1 as the target
to detect solar neutrinos
mat.erial.
The 37C1 is
.
converted
to 37A by the reaction
time dependence.
sunspots,
~e+~~Cl-+e-+~~A.
The experiment
produced
requires
per month.
detecting
the production
Very elegant radiochemical
for this purpose.
The threshold
ppv and ahnost
too high for ‘Bev.
given in SNU (solar neutrino
37C1 detector
units,
In contrast
of which
(SSM).
etc.)
varied
In Figure
for the
Am2
experiment
carried
are taken
the present
from laboratory
of the opacity
dances.
Fundamental
The calculations
from the
out from
radius,
the boundary
luminosity,
measurements
due to complex
of nuclear
atoms,
dance with
calculations
their
uncertainties.
(special
understood.
The major
(such
might
be wrong.
temperature
as neglect
the input
Excluding
exotic
question
of diffusion
approximatelyz4
would
not support
Iaws of physics
mixing
sensitive
it.
However,
the experiment
at the Baltimore
APS meeting
with
oscillations
the high-energy
ergy neulrinos
unlikely
cannot
are well
iu its infinite
a new source of support
in 1987 and the result
for that
is 5 + 1 SNU. Davis believes
Davis,
now at
part
be
in the sin’ &,
a factor
by the neutrino
effect).
hypothesis
the SSM. One is a study
Neutrino
in general
traversed
the oscillation
with
of two or
solar neutrino
values of 0” is due to the en-
medium
oscillations
the spectrum
flux.
of the
is modified
For example,
is depleted
from
are an energy-
of ‘Bv
This is because the resonance
if
for Am2
-
but the lower en-
condition
of Eq. (53)
unchanged.
differeut
in flux.
to distinguish
if the threshold
electrons
from
even for a fixed v, energy.
t,hat detects
electrons
that
consists
of a distorted
sB spectnun
in the Am2 - sin’ 26 space that give the
It is possiblez6
because the detected
detector
The delection
regions
like Kamiokande
for t.he Gran Sasso Tunuel
-139-
of about
of the ‘B spectrum
There are at least two proposals
this could be a real
it cannot
and less ‘B exists in the sun the total flux is reduced
elecCronic
.h
:
for low values of E, even near the center of the sun. In con-
remains
energy spectrum
year reported
is wrong
neutrinos.
Thus
._
_,
away from
but the spectrum
dilIi;rult
wisdom,
however,
is
trast if the SSM is wrong
same reduction
on solar neutrinos.
small
are the cause of a reduced
would also distinguish
central
be a reduction
of detecting
get through.
be satisfied
1120 Jet,ector
euded in 1985 because Brookhaven,
Penn, continued
phenomenon.
10-4ev2
in accor-
deviations
3’CZ encloses the region
by the material
something
The result
the SSM prediction.
would
of the ‘B
neutrino
in the solar interior)
reported
that
above 10 Mev.
uncertainty,
we at leas.1 two way of distinguish;ng
from
approximations
to the calculated
there
here by
out using the Kamiokande
and three standard
the center of the sun (MSW
spectrum
dependent
with
with
As discussed
flux of I+ in the Davis or the Kamiokande
abun-
as TJ*.
In the last year there have been t,wo new results
The Davis experiulent
involving
some reasonable
or convective
The sB flux is ext,remely
T,, varying
possibilities
the relewwt
is whether
energy
rates, calculations
were varied
onIy to ‘Bv
and theoretical
The possibility
the assumpt,ion
parameters
all the values obtained
parameters
There
radius,
of solar element
has been carried
is sensitive
of the oscillations
as it emerges from
the sun
(initial
Input
reaction
and observation
kinds 25 of WIMPS)
new particles
made
in which
to describe
conditions
etc. are fit.
The range of values given above includes
one thousand
plane for which
experiments.
are based on the standard
laws of physics are applied
for this is known.
3 the dashed curve labeled
more in the detected
small amounts
detection
to disagree
0.9 to 1.3 SNU for ‘Be Y, and 5.3 to
hancement
of 4.5 x 10’ years with
until
This experiment
(This includes
of the Davis
How serious is this discrepancy?
solar model
detector.
said definitively
19’70 to 1985 was 2.1 f 0.3 SNU.
over the period
the first electronic
zero. Given the experimental
the
neutrinos
is irrelevant)
Koshiba
explanation
equal to 0.45 times the SSM prediction
have been developed
ratez4 of detected
the definition
the result
30 argon atoms
(55) is too high to detect
The calculated
is 3.9 to 8.4 SNU for ‘Bv,
cycle).
of less than
methods
of the reaction
10.5 SNU for the sum over all neutrinos.
CNO
(55)
His data for the last ten years show an anti-correlation
but no reasonable
different
can be reduced;
spectra
however,
in an
it is
v, + F --t v, + e have a continuous
It. would
from
be much Iwtter
inverse
aim at this.
of a large liquid
beta react.ions
One called ICARUS
argon detector.27
to have an
like (55).
planned
The other
- .,
. . ..
L:
:
is a large Da0
”
d&ector
planned
The second possibi1it.y
nos oscillate.
electrons
In principle
in detectors
for scattering
from
on nucleons
from
via their
However,
current.)
via the charged
which
One possibility
the disintegration
only
current).
with
is the DzO detector
Detailed
A more difficult
found
cur-
if one can detect the
Of great importance
is the detection
uses “Ga
Gran
out in the early
tions
indicate
GO tons in the Soviet
1990’s.
that
It should
(26%)
sin’ 8, that would
detected
be emphasized
(-
nz(r+)
<<
in greater
conclusion
for exploring
m(v,)).
Resulls
that
should
the theoretical
in the
be coming
thau a factor
The major
of two reduction
between
This range is of great interest
to nexuses M in t.he see-saw formula
lo-’
(with
emerging
the supernova
from 10 *l to lOI
(> IO9 gq’cc
the outer
portion
of t,he neutrino
equal mixture
neutrino
layers of
to those of the sun.
oscillations
coming
flux
of all flavors
of
have no effect.
from the supernova
only Ver the neutronization
and 0 were within
burst.
Since the
the region labeled 3’C1
burst would explore
neutrinosphere
). Indeed
pass through
as seeu from
small values of 0 is almost
Fig.
impossible
onre agaiu the great impor(.ance
of detectors
for seeing t,he ueulrinos
from the very limit.ed
tion burst,
at their
is
much larger
very small values of 8) up to 1000 eu2 or more since the V,
the first. event observed
provide
can be
experhents
to those *B v hxxn the suu, most of these would
In spite of a huge number
and 10m4 ev (assuming
since it corresponds
from
a variety
in the V. flu
experiinents
the major
that the very first neutrinos
if the values of Am’
This emphasizes
at Fig. 3 is that. for reasonable
angle, solar neutrino
values of m(vl,)
however,
are similar
of an approximately
Thus in the first, approximation
10-4eu2 with
other
regions
3 t.he region
to explore
of establishing
of very high
of Am’
above
in any other way.
a progranl
with
from the next supernova.
of papers on the subject
observations
no conclusions
can be
of SN 1987a. It, is quite possible
in t.he Kamiokande
br:t those who draw statist.ical
detect,or
inferences
came from
from
that
the neutroniza-
a single event do so
own peril.
7. CmcllLsion
roughly
Gev. Of course, the solar
Neutrinos
-140-
,. ‘.. ;...
effect could also take
and passing through
t.!lis is that
consists
values of Am2
drawn
to be reached by staring
from a supernova
of a short pulse ccmtaining
density
calcula-
in 71C:a are due to ppv so
15%) in the prediction.
of V, to v,, or uT due to the MSW
in detecting
a supernova
be transfornxd3z
detector.
values 0, of the order of the C!abibbo
the possibility
Union.
30 tons of gallium
effect for solar neutrinos
for solar neut.rino
in Fig. 3. In fact a study of this neutronization
for this purpose
is the ‘Be V. We also show in Fig. 3 the values of Am2 and
result
in the gallium
The major
with
only 54% of the events expected
that. there is still scmle uncertainty
contribution
experiment
of the MSW
of 1mxpert.s
energies of t,hese ye are similar
of the pp,pvsince their flux can he calcu-
in place of 37C!1 It is being planned
Sasso and with
for this purpose.
Thus we
may be massless.
:
-: .:. I.,
The problem
It is expected,
A radiochemical
and 10m4 ev can also be explored.
star where the densi1.y conditions
from
We
that lllost
Gev.
the exploding
consist
lated to a high degree of accuracy.
A discussion
place for V, emerging
using
reaction
has also been proposedz9
lo-’
thoUgl1
Even
it is possible
Ref. 31.
in
neutrinos.
using “B
30.
The transformation
flux
v+d--tv+n+p.
A special detector
between
Ye and V, to be smaller
results of calcula(iolls
in Ref.
given
for all flavors.
the flux of V, nwasured
are also sensit,ive to ue - VT oscillations.
angle betwren
cm get. close to values of M of lOI
0.15
give the total
the mixing
of the range of nz(v,)
from
about
experiments
expect
the neutri-
be via neutral
flux in this way should
ncut,rino
this cross section
have the same cross section
to be compared
Ontario.
scattering
is
of det~ecting vP or V, would
of t.he neutrino
of oscillations
or ICARUS.
(due to the neutral
also scatters
inverse beta reactions.
neutron
be detected
method
Thus a measurement
independent
of the vP or V, into which
uw or V, could
electrons
more dist.inctive
reut. interactions
is the de&lion
like Kamiokande
t,inws that. of V, (which
but
to be placed in a mine in Sudbwy,
Nevertheless
the search for a non-zero
mass is
_’
..:
exciting
for many reasons.
would
be new physics
might
he explored
The most reasonal~le explanation
at a large mass scale M. Values
in this way. A mass of the heaviest
of 25 to 50 ev would
mean that
close the universe.
Neutrino
from
theories
grand
unified
observation
and prediction
Arguments
from
our attention
angles.
could
explain
combined
enough
consisten1
an apparelit
of the solar neutrino
cosmology
neutrino,
provide
nmsses and mixings
on relatively
From this point
interesting
relic neutrinos
experiments.
be carried
dark matter
to
4. D. Dearborn
Phys.
et al, Phys.
L&t.,
In particular,
large
accessil&
the light.est neutrino
effect)
provide
in no other
to do experiments
focus
way.
Nieuwenheieen
Proc.
over longer
and reactors
et al, Nut.
there ~a.11lx a large enlrancement
due to the effect of the solar maberial.
neutrino
experiment
calculated
flux.
Only a concerted
yield some definite
gallium
conclusions.
experiment,
possibilities
must lx qlmlified
is abollt
of possible
effort using a variety
KEK
At least one new experiment.,
to get ul~derway
(1986),
numlm
Workshop
1566 (1979);
Phys.
and R. Slansky,
in North
Rev., m,
in Supergravit,y
Holland
(1979),
1694
(eds. P. van
317; T. Yanagida
(eds. A. Sawada and A. Sugimoto),
Phys.
KEK
(1979),
185 (1981) and references
Reports,“Z,
et al, Phys.
Neutrinos
in
p. 95.
therein.
Rev., E,
2597 (1988) and references
86 (eds. 0. Fackler
and J. J. Van) Editions
therein.
Front&es
(MSW
any one solar
12. J. Bernstein
in the
and J. N. Bahcall,
Phys.
L&t.,
Bx,
366 (1988)
E,
39 (1981).
and
therein.
13. E. Fermi,
and G. Feinlerg,
Nuclear
Physics,
Phys.
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of Chicago
(1950),
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p. 201.
detect~ors can
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of other
exciting
of Energy
Phys.
Rev.
S. J. Parke,
Phys.
Rev. Let.t., 57, 1275 (1986).
15. S. T. Petcov,
in part. by the 1J.S. Departments
5,
pp. 441-584.
references
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and a number
et al,
L. M. Krause
297 (1981).
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P. Ramond,
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if v, is
rmcertail&s
of different
Rev.
and D. Freedman)
9. M. Gronau
have been proposed
This work was supported
contract
lwcanse
from
M. Fukugita
a large
I,ecause
of the oscillation
Conclusions
5G, 26 (1986);
Rev. DZ6, 1840 (1982);
Phys., m,
Phys.
8. P. Langacker,
neutrinos.
to study
is possil&
411 (1981).
will
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oppoxtunity
This
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mixing
oscillation
solar, or supernova
a unique
Lett.,
Phys.
Lett.
(1980).
of (.he range of
by neutrino
values of Am2 ~UWII I,y a factor
solar mutrims
radlge of values
e,
Phys.
Rev.
42, 1522 (1982),
5. II. Georgi
between
theory
very
at accelerat.ors
one must use af~mosplmic,
et al, Phys.
Rev. L&t.,
10. Massive
To go much fimther
and M. Roncadelli,
expectations
ideas from part,icle
the range it is necessary
out to explore
3. G. B. Gelulitli
6. S. Weinberg,
of view we find that only a small portion
To extend
L+,
with
masses a.nd llot
and we hope t,llat new experiments
presumal~ly
disagreement
values of Am2 and sin’ 28 have been explored
distarlces
mass
flux.
with
mm11 wutrino
of a non-zero
of M up to 1Ol5 Gev
16. N. Ushida
under
DE-AC02-76ER03066.
17. F. Dydak
Phys.
Lett.,
et al, Phys.
et al, Phys.
z,
373 (1988) and references
Rev. Lett.,
47, 1694 (1981).
L&t.,
34 (1984).
c,
therein
,.
rtrfe7.P71(.E9
18.
1. S. M. 13ilenky and S. 7’. P c t COY, Hcv. Mod.
2. K. Fujikawa
I-eferwces
and R. E. Shmck,
I’hys.
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F’llys.. “,
liTI (19%‘).
Lett.,
42, 963 (1980)
Scientific
and
F. Boelm~,
(1986),
148.176.
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Kitagaki
au(l II. Yuta.
eds.)
World
p. 135.
19. M. Shaevitz
therein.
in Neutrino
in Reference
10, p. 259 or Neutrino
86 (Reference
18); pp.
1
20.
hoc.
National
BNL
Neutrino
Laboratory
Workshop
21. J. Lo Secco et al, Phys.
L&t.,
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et al., Pllys.
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660
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1. Introduction
The
Collider
tracking
Detector
and
proton-antiproton
derived
overview
run
at
of the
density
and
the
CDF
Detector
CDF
apparatus
here
coordinates
only
) as the
the
polar
the
and
beam.
over
and
the
great
detail
during
After
I will
inclusive
..
..
,I :
j:..
the
a brief
present
results
charged
particle
of the
coil,
calorimeters
are
a set
R-s
reconstruction
tracking
are divided
and
segmentation
plates,
region
into
the
and
into
a larger
uses plastic
region,
outer
between
and
regions
time
be
CTC
projection
particles
is complemented
based
17 I <l.O,
part,
to
the
quality.
tower
by
geometry.
on very
the
natural
plug
with
as sampling
is
part,
with
steel
absorbers.
medium,
,:.
region
In all cases there
electromagnetic
hadronic
scintillator
wires
is of order
of charged
2.2< Iv I <4.0.
an inner
sense
is measured
of 8 vertex
region,
solenoid
wire
on a projective
three
for
of
per
measurement
central
the forward
layers
position
based
angle
is a cylindrical
Lying
pipe
the
l.O< lvl<2.2,
I~l<l.
vertex
polar
substitute
7 II 4.0 for 8=2’.
resolution
and
provide
calorimetry
constraints:
86
I
q=-ln(tan(B/2)).
volume
resolution
momentum
event
to
by
2, and
use spherical
superconducting
magnetic
with
Ref.
B as the
, and
a 1.5 Tesla
(CTC),
of the
4s sampling
axis,
7, given
the
in
1. We
is convenient
of 1.2 m. The
beam
which
on Fig.
r) N 1 for b’=40°
transverse
a measurement
central
set,
..1:;:-
of
on resuIts
collected
and
polar
It
around
Within
a mechanical
The
as the
for ~~22.0 GeV/c
beryllium
absorbing
line
chamber
(VTPC)
geometric
based
a radius
5 0.002~~
Outside
The
the
tracking
almost
in
overview
comparisons:
with
the
magnetic
products
here
Collider.
data
“pseudo-rapidity”
is built
modules
1987
physics,
the
I report
of 30 nb-’
coordinate.
detector
distributed
and
1.8 TeV.
is described
the beam
angle
200 pm,
the
purpose
study
Tevatron
jet
azimuthal
Some convenient
bp,/p,
and
a brief
with
and
central
=
to
spectra.
The
coaxial
6
luminosity
production,
2. The
The
is a general
designed
Fermilab
detector
boson
present
at
an integrated
data
on vector
Fermilab
device
collisions
from
1987
at
calorimetric
lead
and
is
-416-
:’
: .-
segmented
into
electromagnetic
resolution
uE/E
absorption
=
regions
and
Muon
system
size
the
deep
use
A#=150
and
has a depth
and
central
has
hadronic
o,.E
gas proportional
Av~0.1.
of 20 radiation
=
central
and
a
data
is
5
written
compartment
70%/a.
sampling
The
with
thresholds
The
lengths
plug
a tower
size
in the
behind
the
is essentially
regions
scintillation
100%
on
magnetized
central
hadron
region
consists
calorimeters
efficient
for
both
sides
are
toroids
with
drift
of 4 layers
in the
muons
muon
region
over
3 GeV/c.
spectrometers
chamber
of
and
4.
of
sets
forward
counters
are mounted
calorimeters
electromagnetic
“beam-beam”
counters
(BBC)
in the
are used for
on the
region
front
TeV.
3.2<lt71<5.9.
luminosity
neutlinos3
The
Data
Fermilab
These
based
measurement
in the
on
instantaneous
logged
luminosities
several
kinds
The
“Level
energies.
Collider
momentum
physics
supplied
from
of order
of data
10”
by
to
cm-‘s.r
depending
sets,
1 Buffet”
selected
colliding
February
data
the
set
beams
May
were
on
contains
following
high
calorimetric
the
beam
to
>20-45
GeV
Electron:
1 tower
in EM
CMU:
Central
muon
FMU:
Track
in towers
calorimeter
stub
candidate
matched
with
1.0 GeV
with
Et
in forward
muon
Level
combination
counters
1 triggers
with
during
the
consisted
of
the
presence
a 15 nsec window
of hits
any
of
on both
centered
sides
on the beam
The
of
a
counters
in
events
were
recorded
of 9,400
events
was
recorded
decays
into
at CDF
other
Drell-Yan
leptons
with
of isolated
set of 25.3
converge
detector
the
nb-”
malfunctions.
on
and
analyses,one
associated
but
cross-check
the
identification
data
detector
systematics,
a powerful
via
charged
in two parallel
on the
a common
gross
different
Et
analysis
of
the
Et
ring
Et
-417-
passed
on
culled
The
two
the
same
performance
and
these
energy
beam
and
opposite
of Etmiss
by
of the
occur
with
leading
comparing
required
required
as
over
all
events
to
was applied
to
have
a jet
Igl less than
region
Etmias signal.
that
outside
Mismeasured
the
Etmiss
energy
algorithm
are
in the
by requiring
of any jet
defined
1.0.’
cuts.
deposition
crossing.
absence
3.6 and
clustering
events
GeV
2. We
transverse
less than
on the quality
hadronic
the
A jet
15.0
are suppressed
+ cone of 180°*300
significance
array,
than
in Fig.
of
ITI
25.0 GeV.
greater
selected
the
sum
in the region
splashes
at the
is outlined
vector
of 1614 events
by requiring
in
beam-beam
crossing.
very
from
free
tower
with
the central
of the
beam-beam
with
56,000
energy
the
start
calorimeter
the
main
conditions
have
towers
We next
GeV.
track.
road.
above
are
missing
‘centered
Valid
paths
that
than
A total
or more.
>(7.0-12.0)
to a trigger
were
collected
in pp collisions
their
transverse
and
Etmias greater
cluster
CEt
set was
in the
sample
were studied
missing
magnitude
have
tracking
triggers:
Jet:
by
\V bosom
providing
calorimeter
transverse
and
data
of hits
are produced
identified
neutrino,
Both
The
CDF
and
delivered
efficiencies.
Average
achieved.
triggers
a constant
70 nb-’
Production
then
runs
sample,
of protons
1987.
to maintain
of the
Approximately
a smaller
W bosons
the
approaches
period
coincidence
crossing.
addition,
unreconstructed
and
Set
Tevatron
antiprotons
only
The
electrons.
1987
bias”
Boson
and
from
S. The
or “minimum
beam
In
Vector
of the
triggering.
and
the
process
of scintillation
bias
requiring
Intermediate
triggering
counters.
Two
luminosity
30 nb-’
the
consisting
planes
with
Approximately
at 4% = 0.63 TeV.
The
In
adjusted
rate.
low
with
at I.8
drift
1~1<0.7.
roughly
to tape.
trigger
of
time
coverage
were
acquisition
Another
and
Aq=O.l.
chambers
forward
of
14%/a;
lengths
forward
A4=50
large
towers
compartment
Et
QCD
dijets
than
it to the
rays
3.0
of a 20 nsec
greater
cluster.
Cosmic
less than
Finally,
size of the
were
and
GeV
of
window
suppressed
5.0 GeV
in the
we evaluate
overall
the
random
: ..,.
.,.
.:’
I_._ ;;:.
-,-...
E Analysis
-Missing -T“Good”
error
from
bias
events,
width
4
Runs
where
1.0 v
in the
x lo5 events
calorimeter
and
of
After
Missing
1614
E,
p such
events
@T- > 25GeV
Cl
> 15GeV
typical
projection
of
the
calorimeter
out of time
dijet cut (E,
$,/K
events
> 2.8
J
11 track with
trk
EC’ / p < 2.0
The
W boson
analysis
on missing
Et.
-418-
top
with
energy
to
have
a
: .: ,.,
:
GeV
vs.
in Figs.
Most
kinds
two
at large
passes
events
the
is consistent
dijet
is
cut;
the
the
with
the signature
based
on electrons,
4b,
Et
for
we see one
stiff
electromagnetic
in
the
the
and
the
tower
in
electron
shows
the
and
a clear
non-electron
backgrounds
Etmias in Fig.
R-(
LEG0
event.
for
events
other
the
a cursor
unoccupied
of missing
the
we see that
4a and
of
and
CTC,
EtmiaS significance
electron
3, where
rectangle
in an otherwise
of momentum
of the
plot,
loose
such
page,
In the
LEG0
samples.
which
the
were
rather
track
Fig.
a tower
(The
the
These
the
contained
of
to
GeV.
In
to
in
is beneath.
to be the
tri-jet,
described
4b is a mismeasured
contains
a narrow
W + 7~ followed
by
hadronic
hadronic
decay.
The
W analysis
selection
of events
central
region
cluster
has the
calorimeter
based
the
found
One of the
cluster;
2
required
a matched
is shown
is displayed
test
the
containing
l~l<l.O
with
ratio
Ehad/Eem
beam
data.
in a cone of radius
Fig.
minimum
transverse
remained.
events
between
above.
tau
Electron Cluster
Eem, Etot
> 0.85
39.0
events
were
and
were
events
with
pointing
of Etmi*’
sample
jet
GeV
program.)
distribution
separation
> 5 GeV, qS -+ 150”)
at
calorimeter
28.3
recording
non-electron
in
to be Gaussian
of the
according
along
event
is
has Et em=27.2
The
E, < 3GeV
=
115
cuts,
Twenty-two
CTC
display
actually
115
measured
sum
Events
clusters
such
of the
pt
interactive
I& OualitY
quality
Etot/p<2.0.
A
with
scalar
calorimeters.
of Eem/Eto’>0.85
that
representation
I
is the
electron-like
signatures.
track
< 1.0
;,:1,
plug
Etmis*
for
requirements
EtPC
is well
of Etmisa is found
Etmias/~>2.8.
these
searched
This
distribution
where
central
significance
i. = 25.3 nb-’
fluctuations.
the
“isolation”
outlined
an isolated
cluster
Et>15
1ess than
in Fig.
electromagnetic
GeV.
0.05,
An
a value
5, begins
cluster
with
the
in
the
“electromagnetic”
determined
from
If we let Etcone be the total transverse
energy
R =[Av’+A# 2] l/Z =0.4, centered
on the electromagnetic
is defined to be:
ccJne
clus
I I %
- Et
E clus
t
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m
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c
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4
Runs
We
required
cuts.
In
momentum
second
were
452 I
Cluster
Of
the
cluster
remaining
described
the
above.
electron
show
events
We
take
The
2M EM Cluster
in
in these
electron
22
Fig.
in
be about
identified
result
G =
electrons.
-420-
with
9a;
And
have
a
..:
: :. .,_.,
--
these
in Fig.
Etmiaa
the
smooth
in Figs.
7a,b,c
of
and
apparently
happily,
Et
as
distributions
ALL
of these
analysis.
analysis
as our
anticipated
of transverse
[zE”,E”,(~
loose
cut
distributions
most
pt has the
=
relatively
anti-dijet
The
the missing
the
distribution
for
the
beam-beam
cracks,
were
30%.
for the
this
and
and
final
Jacobian
W
form,
msss
- COSA~~J~~*
curve
is
the
ISAJET
cross
the
the
first
result
for
with
The
from
various
effect
of the
were
studied
data.
The
net
from
jets
were
estimated
sequential
background
decay
via
the
measured
corrections
Monte
rapidity
Carlo;
efficiency
all other
is estimated
from
jet
data
W + 7 * Y was estimated
contribution
is less than
for
cuts,
1 event.
to
and
from
We
section:
error
is displayed
1.8 TeV.516
and
the
from
total
is derived
counters
backgrounds.
Backgrounds
The
process
thresholds
derived
from
Carlo;
agreement
on isolated
from
the
the
are presented
via
of electron
section
the background
where
based
of
Eclua/p
is depicted
demanded
characteristics,
events
acceptance,
efficiencies
< 0.5
events
requirements.
8. The
cross
calorimeter
> 3GeV
we then
found.
o.B
analysis
pair;
the
event
that
GeV/c’.’
efficiency,
Ehod/Eem < 0.05
W boson
cluster
for
were
the
is shown
find
The
mass
candidates
distribution
as seen in Fig.
Monte
5
to
Twenty-one
in the sample
sample.
The
Fig.
found
One such
both
track
6 were
and
clean
were
M,=83.0
I(R=0.4)
and a large
Z” study.
pass
and
GeV
by the selection
luminosity
@T > 25GeV
dijet cut
events,
which
a charged
cluster,
Et misa>25.0
Mt
ET
events
that
of
variables
rather
unbiased
Ec’/ptrk < 2.0
ET
4521
electromagnetic
169 events
signature
> 1 CTC track with
Missing
found
demanded
175 passing
to a separate
Et
events
/
to the
the
electromagnetic
In
< 0.10
175
2.0.
and
6.
events
Ehod/Eem<
0.05
Track Match
0.10
we further
p extrapolate
removed
missing
I(R=0.4)
than
events,
be less than
2 = 25.3 nd’
EM
I less
these
is statistical
along
the
= 2.6 f 0.6 f 0.4 nb
with
theoretically
and
previous
_.
the
second
is systematic.
results
in Fig.
Sb, and
calculated
increase
of W
Our
shows
good
production
for
”
(P.0
> a)
UorlQlosI
-.
01lQtl
,s.,
,‘.
W3/PQH
‘.
,,
>.
:-:, -_
.,. : ,:
r
W Electron
z
Et
ISAJET
5.36
(63
GeV)
_
6-
40
Fig.
9a
60
80
Transverse Mass (GeVh?)
Transverse
mass
distribution
for
100
W sample.
40
Et (GeV)
:_
::
Fig.
8
Electron
p, in the
LO
210
E,,(TeV)
W sample.
Fig.
9b
W production
cross section.
..-‘.
.,
5. Jet
Production
At
6
=
triggers
to
parton
1.8
TeV,
scatterings
event
is shown
a.
Jet
The
array
we
expect
be dominated
and
by
associated
in Fig.
kinematics
the jet
direction
is measured
by the
total
cluster
The
pions
by
of the jet
central
and
associates
electrons.
has
anticipated
absolute
various
unavoidable
effects
energy.
The
measured
using
tracking
and
cracks.
from
After
resolution
the
cross
A typical
two-jet
which
of
energy
tracks
net
energy
jets
due
of about
are
balance
distribution
u=9.0
Jet
effect
the
The
measured
energies
CTC.
was
Charged
of fragmentation
effect
varies
from
error
and
studied
of leakage
from
40
on
33%
GeV
this
to
to
the
correction
interval.
we
in
of opposite
measure
two-jet
jet
the
intrinsic
events.8 For
momenta
jet
a jet
Et
Et=50
has a Gaussian
GeV.
Cross
differential
measured
luminosities
section
was derived
cross section,
GeV.
same
applied,
momentum
the
goes
through
in the
study
great
of 50
lasers,
have
low
the
effects
energy
250
the
to
and
We
at
in
to these
as that
forward
errors
reconstructed
correction
with
beams
to
response
used
pursued
2%.
contribute
of calorimeter
corrections
apparent
clusters:
in test
about
used to study
Inclusive
the jet
of flashers
also
the
calorimeter
and
is tracked
was
with
the
into
been
a variety
were
we find
apparent
and
accuracy
12% to 4% over
distribution
has
calibration
sources
isolated
cluster
all
scale
Carlo
the
The
LEt
parton-
to
has been calibrated
Carlo
via
b.
high
hard
energy
centroid,
Monte
measured
varies
applying
deposited
Monte
The
of the
GeV,
Cs13’
nonlinearity
fluctuations;
by
cluster
energy
The
internal
highest
our
from
bremsstrahlung.
locally
the
calorimeter
movable
20%
from
energy.7
validation
industry.
and
gluon
are reconstructed
which
an
states
resulting
10.
an algorithm
GeV
final
jets
Reconstruction
jet
The
the
hadronic
Section
cross section,
and
the
number
by deconvoluting
a procedure
whose
du/dEt,
of jets
the jet
uncertainty
can be computed
at each
Et
Et.
resolution
is estimated
from
The
from
true
the
Fig.
to vary
-423-
10
A generic
two-jet
event.
from
25%
to 5% over
11 we show
fiducial
this
central
have
a good
have
good
insure
Et
vertex
timing
greater
the
luminosity
error
ranges
250 GeV
Also
QCD
EE,
the
70%
in Fig.
with
CDF
12.”
cross
missing
in
the
Et
above.
The
section
over
,_ :.: :_ ..
)
To
jet
with
include
the
uncertainties
in
full
:I.
. . .
,- :.
-::
and
analysis.
bin
from
analysis
center,
a central
each
the
section
as the jet
best
current
limit
that
progress
this
will
the
c. Jet
400
this
In this
advantage
Angular
Normdication
EHLQlQ’=2E:
systematic
the
,lO Cc\’
the
graphs,
of curves
as momentum
all
lowest
to
D+02Q2=2~
transfer
EHLQ2Q*=fEf
order
evolved
arises
from
CDF Prei.
the
scale.g
The
show
good
calculations
well
to large
this
Et,
known
contact
Et
experiments
the
experiments,
on about
confirmed
limit
out
case, the
by
to about
advantage
of a factor
of increased
Ts
of possible
constituent
an enhancement
compositeness
UA
in
of quark
predicts
based
energies
is a probe
parameterization
the
other
as a result
distribution
interaction
approaches
GeV,
Et
at
scale
which
find
that
In
Fig.
600 nb-‘.‘O
in
A*.ii
The
A*
is
13 we
the
CDF
data;
analysis
in
700
GeV,
based
only
30
of higher
energy
of 20 in integrated
on
of the
jet
two and t,hnx-jet
subprocesses
with
center
events.
of quark-quark
the
characteristic
of mass
is seen to far
Et (GeV)
luminosity.
scattering
In lhc live-jet
and
has
been
Fig.
cabs, the l)rcdomin~mt.
gluon-gluon
Rutherford
angle
scattering
Uncerta;ntJ
D+O2Q’=f@
Distributions
distribution
to occur
from
2 + 2 tree
family
errors
with
jet
is obviously
n~ei~surctl in both
the
sensitivity
is from
move
of data.”
outweigh
and
highest
The
about
uses
as. The
Within
as a 4-fermion
than
of predictions
calculation
is compared
cross
expected
discussed
Fig.
over
data.
increased
At
substructure.
t-channel
detector
required
errors
. In
used in this
contributions
of the
running
function
the
The
scattering
The
34%
absolute.
result
is apparent.
nb-’
The
11 is a range
This
and
is
agreement
show
threshold.
to
in the
GeV
averaged
of the
we also
corrections
of structure
greater
described
acceptance,
and
from
normalization
quark
60 cm
as systematic
functions
The
within
sense
to 250
section
171 < 0.7. Events
as well
calculation.
structure
Fig.
the
40 GeV
cross
interval.
shown
choice
located
in the
than
interval
0.1 <
understood
error
Et
differential
eta interval
a well
statistical
the jet
corrected
are
form:
-424-
11
The
inclusive
jet
cross section.
1
:
-
A UAl--
T/F= 630&V
+ UA2 - - fi
t
10’
= 630GeV
MS--&=63GeV
-----
10'
QCD (Duke-Owens
z
p
D
100
5
c
zlo-'
w
4
D
10-a
lo-
9’1
I
Et
0
100
200
300
200
100
0
(GaV)
300
Et (GeV)
Fig.
Fig.
12
Jet
spectra
in colliding
hadron
experiments.
13
compositeness
-425-
Inclusive
jet
cross
section
at scale A* = 400 GeV.
with
modification
for
quark
..:::,
.‘I. :.
, _- :
: :.1 ... .
-.
.
.I
E* is the
where
momentum
result
of gluon
have
the
Rutherford
cuts
jet
opposite
the
the jets
angular
Et
leading
t
jet
interval
and
beam
axis.
effect
of limited
0.51~~
- y,I,
To study
the effect
of this
cut,
0.7,
1.2.
acceptance
Carlo,
and
jet
jet
subprocess
is usually
is expected
The
are small
for
the
the
events
6*
to
the
again
y,
into
to be the
the
angle
of
by
cutting
jet
rapidities.
the three
were
and
180°i300
acceptance
corrections
cut
of
of
ys are the
we examined
first
the
boosted
taken
and
satisfied
requirement
interval
were
was
detector
where
which
additional
azimuthal
passing
frame,
=
1.0,
t is the
a sample
and
in the
The
to the
the
y*
using
analysis
10 GeV
jet.
respect
We controlled
the
distributions
center-of-mass
with
and
B* of the leading
inclusive
with
longitudinal
angle
case, since the third
form.
jet
of the
a second
scattering
In the three-jet
bremsstrahlung,
We studied
quality
center-of-mass
transfer.
requirements
determined
of order
I y* I <
via
20%
for
on
Fig.
Monte
the
cut.
Three
The
angle
distribut,ion
8*
dN/dcos@*
Fig.
14a, along
that
the
the
discussion
the
There
of the
most three-jet,
supplemented
and
good
care
the
initial
data
sets
our
good
for
QCD
di-jets.
Jet
Angular
Distrtbution
et
in
Note
Et
trigger
of 114,
agreement
140,
with
acceptances.
events.
regarding
the
theory
as the
state
with
show
calculation
between
calculation.
thresholds
dN/dcos6*
The
sets is displayed
QCD
mass
14b we show
or final
data
acceptance
required
QCD
agreement
cos0*=tanh(y*).
order
invariant
of different
events can be described
with
a first
has been done for lhrcc-jet
case. In Fig.
jet,
relation
angular
three
additional
in this
is, again,
All
in spite
analysis
leading
finite
the
in the two-jet
from
two-jet
respectively.
of the
acceptance
for
the three
effective
prediction,
A similar
from
the curve
produces
164 GeV
QCD
for
with
combination
thresholds
and
is obtained
14a
third
gluon
13 for
detector
distribution
from
and
result
See Ref.
uniform
the
data,
a
dN/dcos6*
previous
plot.
indicating
that
of a 2 + 2 subprocess
bremsstrahlung.
Fig.
-426-
14b
dN/dco&*
for
QCD
tri-jets.
6
=
1 .3
l’ev
d.
Jet
The
CDF
Fragmentation
excellent
central
track
finding
tracking
fragmentation
in hadronically
for
are
this
study
inclusive
measurements
estimated
the
pt
dense jet
those
in
overlayed
tracking
inferred
jets.
Sec.
with
efficiency
the
from
events,
rapidity
the
y of the jet
calorimeter
cluster
that
with
“rapidity
plateau”
number
of tracks
core
to the
pt
cutoff
Fig.
Hadronically
15b,
multiplicity
e+e‘
results
jet
along
produced
core
in the
The
jets
which
at much
on
track
and
an
85%
in
tracking
respect
jet
Note
jet
energy.
(400
results
MeV/c)
high
from
energies
with
binned
and
other
used
,
Y
L,’
3
2
=
4
s
particles
in
6
5-Ln(E+PL/‘E-PL)
the
Fig.
a small
158
measured
the
effect
of
of di-jet
mass
is
with
dN/dy
for
respect
to the jet
charged
jets.
Rapidity
y
is
axis.
experiments.r5
are seen to have
a smooth
.t,...I.‘..l,.
0
of
as a measure
eliminates
as a function
jet
the
suggestion
We
axis
cut
the
sample,
the
to the jet
to
15a shows
a mean
extrapolation
from
energies.
Bias
Physics
One of the
most
familiar
plateau
in
defined
a large
rapidity
multiplicity
at very
Minimum
rapidity
real
provided
Figure
masses.
respect
is consistent
lower
f or
The
with
with
increasing
y 1 2 with
multiplicity.
event.
tracks
centroid.
dN/dy
broadens
having
charged
underlying
the
section
which
events
invariant
6.
the
in jet
distribution
in
in
the
particle
requirements
in
Carlo
sets of dijet
shown
quality
briefly
Monte
corrected
due
Track
by
charged
of 90%
to three
the
afforded
the
Studies
6.
according
bias
of
discussed
efficiency
of the jet
resolution
study
core.‘”
We measured
axis
to
spectra
were
average
and
allows
produced
similar
charged
efficiency
chamber
results
charged
from
high
particle
energy
production.
hadron
The
collisions
is
rapidity
is
as
:.
_
For
which
light
particles
we define
this
as the
is approximately
a function
of polar
angle
:
..~-..
alone,
“pseudo-rapidity”:
Fig.
y 2 7 = -In(tan(6/2)).
15b
to the jet
-427-
Jet
axis.
total
charged
“multiplicity”
with
y 2 2 with
respect
-.
-._
:.
..
.,
At
CDF,
the
charged
VTPC
particles
uncorrected
sample
chambers
with
good
distribution
is shown
data
shows
The
effects
of
in Fig.
a plateau
measure
the
efficiencies
dN/dq
vs.
16, along
with
out
to
the
polar
between
7 for
the
results
limits
angle
distribution
rapidities
UA5.‘s
acceptance
of
t3.0.
minimum
from
of our
of
The
bias
data
The
CDF
at
7 =
2.8.
7-
of reconstruction
interactions
are under
correction
will
understood
dN/dy
study;
be less
in terms
is flat.
efficiency,
The
630
GeV
result
1800
GeV
result
10%.
conversions,
results
The
difference
central
the
preliminary
than
of the
The
decays,
slight
dip
between
densities
indicate
at
y and
are measured
that
the
. CDF
1.8 TeV
total
7 can
6.
be
7; the distribution
l
CDF 0.63 TeV
of
to be:
=
dN/dq)t=O
= 3.98 t 0.4 at 1800 GeV
lies
secondary
small
dN/d~),,=c
is in good
and
2.95 e 0.3 at 630 GeV
agreement
above
the
with
best
results
In(s)
fit
from
to
the
UA5,
lower
but
energy
data.17
The
inclusive
minimum
Tracks
with
certain
quality
(ITI
samples
down
requirements,
and
l.O),
in R-l
sample
transverse
was
momenta
less than
vertex
this
charged
bias
and
was
momentum
measured
in
to 400 MeV/c
including
an
to within
estimated
the
were
the
extrapolation
to
several
included
within
track
methods
in
tracking
traversal
5 cm in s. The
via
distribution
central
if they
passed
of all
CTC
layers
5.0~
of the
event
finding
to
the
system.
be
efficiency
00.
0.4
0.6
1.2
1.6
2.
2.4
2.6
r)
in
approximately
99%.=’
The
observed
decays,
and
uncertainty
due
momentum
section
particles
Our
0.63
pt
spectrum
conversions,
to
from
are assumed
result
TeV
were
the
1.8
pt
found
to
spectrum
for
decay
in flight,
correction
larger
and
distortion
the
be negligible.
and
the
The
measured
than
neutral
5%.
due
to
invariant
The
Fig.
finite
cross
luminosities.
in Fig.
TeV.
The
17 for
the
smooth
two
center-of-mass
curves
are
a
All
energies
fit
to
18
experiments.
to be pions.
is shown
and
corrected
no
misreconstruction
resolution
follows
was
with
the
parameterization:
-428-
dN/dq
for
the
CDF
minimum
bias
samples
and
other
d3,
E----c---“.
AP ”
d3p
Our
lo-24y
results,
and
a comparison
A18
0
I
CDF 1800 GeV
CDF 630 GeV
We find
above.
off.
to
0.63
are as follows:
TeV
0.55
TeV
(UAl)
1.3 GeV/c
1.3 GeV/c
1.3 GeV/c
n
8.28t.02
8.89t.06
9.14*.02
A
0.45i.01
0.33*.01
0.46k.01
that
p0 and
fit
our
flatten
n are highly
result
result
result;lg
TeV
to UAl
PO
The
Our
(Pt+Po)
was found
at 0.63
TeV
correlated,
and
to be independent
is in reasonable
result
at 1.8 TeV
shows
that
with
increasing
c.m.
energy
simply
fix
of the
lower
agreement
the
p,
with
value
pt
cut-
the
UAl
pt
distribution
continues
as
observed
in
other
experiments.”
7.
Conclusion
Analysis
1 o-3o
results
of a small
on
W boson,
establishing
1 O-3’
the
at fi=1.8
run
1 o-32
0
2
4
6
8
in
luminosity
10
P, (GeV/c)
for the
17
the minimum
The
bias
inclusive
charged
transverse
momentum
spectrum
for
work
and
hard
the
staffs
of
construction
samples.
Nazionale
and
-429-
work
our
of
one
not
of
the
Nucleare
and
has
for
produced
significant
production,
for
the
1988/1989
picobarn,
as well
reconstructing
next
Tevatron
foresee
and
an
CDF
as
physics
Collider
integrated
stands
poised
to the Top.
been
possible
Accelerator
detector.
of Japan,
detector
inverse
have
of the
Energy,
di Fisica
Education
than
set
particle
expectations
Winter
institutions
of the
Department
CDF
to go right
would
data
inclusive
of the
and
of more
skill,
and
Realistic
Fall
opportunity
This
Fig.
power
TeV.
the
preliminary
jet,
Division
for
their
many
This
work
was
National
of Italy,
the
Alfred
without
dedication,
We
contributions
supported
Science
the
the
of Fermilab.
Ministry
P. Sloan
by
Foundation,
of Science,
Foundation.
thank
to
the
the
U.S.
Istituto
Culture
‘: 1:::-: :
c. .‘: “- :: :
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Laboratory
(1988).
-._
-1..
on ProtonAccelerator
-430-
:.
:
I
1988 SLAC SUMMER INSTITUTE LIST OF PARTICIPANTS
Iris Abt
SLAC
Mail Bin 96
P.O. Box 4349
Stanford, CA 94309
Bimet: ABTQSLACVM
Gerard D. Agnew
Brunel University
Rm. F67, GEC Mirst Research
East Lane, Wernbley
Middx., HA9 7PP, England
Bitnet: [email protected]
:AanCgim
Ahn
MailBin
P.O. Box 4349
Stanford, CA 94309
Bimet: AHNQSLACVM
Roy Aleksan
SLAC
MaiI Bin 78
P.O. Box 4349
Stanford, CA 94309
Bimet: ROYQSLACVM
JamesAlexander
SLAC
Mail Bin 61
P.O. Box 4349
Stanford, CA 94309
Bimet: JIMAGSLACVM
Max J. Allen
University of Victoria
Dept. of Physics
P.O. Box 1700
Victoria, BC, Canada V8W 2Y2
Bimet: MAXQSLACVM
Dante Amidei
University of Chicago
Enrico Fermi Institute
5640 Ellis Avenue
Chicago, IL 60637
Bimet: DAN@FNAL
Giuseppe Ballocchi
University of Rochester
Dept. of Physics’& Astronomy
Rochester, NY 14627
Bimet: BEAR@FNAL
Farhang Amiri
Weber State College
Physics Dept.
Ogden, UT 84408
Carlos G. Arroyo
Columbia University
Dept. of Physics
New York, NY 10027
Bimet: ARROYO@SLACVM
Timothy L. Barklow
SLAC
Mail Bin 61
P.O. Box 4349
Stanford, CA 94309
Bimet: TIMBQSLACVM
David Aston
SLAC
Mail Bin 62
P.O. Box 4349
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Bimec DYAEB@SLACVM
John E. Bartelt
SIAC
Mail Bin 78
P.O. Box 4349
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Bitnet: BARTELTBSLACVM
William B. Atwood
SLAC
Mail Bin 96
P.O. Box 4349
Stanford, CA 94309
Bitnet: ATWOOD@SLACVM
Doris A. Averill
Indiana University
Dept. of Physics
Bloomington, IN 47405
Bimet: DORJS@SLACVM
Mark D. Baker
M.I.T.
Dept. of Physics
Cambridge, MA 02139
Bimet: MBAKER@FNAL
JosephBaIlam
SIAC
Mail Bin 78
P.O. Box 4349
Stanford, CA 94309
Bimet: JBALLAMBSLACVM
Richard S. Benson
University of Minnesota
School of Physics & Astronomy
Minneapolis, MN 55455
Bitnet: BENSON@FNAL
Karl Berkelman
Cornell University
Newman Lab
Ithaca, NY 14853
Bitnet: KB@CRNLNS
Gabriel Bassompierre
Lab de Phys. des Particules
Ch. de Bellevue, B.P. 909
F-74019 Annecy-le-Vieux
CEDEX, France
Timothy L. Bienz
SLAC
Mail Bin 62
P.O. Box 4349
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Bimet: BIENZ@SLACVM
Roberto Battiston
Perugia University
Dipartimento di Fisica
Via Pascoli
I-06100 Perugia, Italy
Bimet: RBN@SLACVM
Ikaros Bigi
SLAC
Mail Bin 81
P.O. Box 4349
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Bimet: BIGI@UNDHEP
Andrew Bazarko
Columbia University
Pupin Hall
New York, NY 10027
Bimet: BAZARKC@SLACVM
Gian Mario Bilei
Perugia University
Dipartimento di Fisica
Via Paccoli
I-06100 Perugia, Italy
Bimet: GMB@SLACVM
Alice L. Bean
University of California
Dept. of Physics
Santa Barbara, CA 93106
Bitnet: BEANQUCSB
-431-
Andrew T. Belk
Imperial Coil. Sci. Tech.
Blackett Lab
Prince Consort Road
London, SW7 2AZ, England
Bimet: BELK@CERNVM
Uwe Binder
CERN- EP Division
CH-1211 Geneva 23
Switzerland
Bimet: BINDER@CERNVM
_:
’
_- .:.,
,-
:
.:
:
P. Fred Bird
SLAC
Mail Bin 62
P.O. Box 4349
Stanford, CA 94309
Bimet: BIREQSIACVM
Richard Blankenbecler
SLAC
Mail Bin 81
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Stanford, CA 94309
Bimet: RZBTH@SLACVM
Ellioa Bloom
SLAC
Mail Bin 98
P.O. Box 4349
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Bimet: BLLIOTIQSLACVM
Gerard R. Bonneaud
LPNHE Cole Polytechnique
Routede Saclay _
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F-91128, Palaiseau, France
Bimet: BONNEAUDQCERNVM
Kirk 0. Bunnell
SLAC
Mail Bin 65
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Bimet: KIRKQSLACVM
Mail Bin 96
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Bimet: GRBQSLACVM
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SLAC
Mail Bin 95
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Bimet: PAT@SLACVM
Bennet B. Brabson
Indiana Universitv
Dept. of Physics ’
Bloomington, IN 47405
Bimer: BBRABSON@SLACVM
David L. Burke
SLAC
Mail Bin 61
P.O. Box 4349
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Bimet: DAVEBQSLACVM
Alan M. Breakstone
University of Hawaii
Dept. of Physics
Honolulu, HI 96822
Bimet: ALANBQSLACVM
Giovanni Bonvicini
University of Michigan
Dept. of Physics
Ann Arbor,-MI 48109
Bimet: GIOVANNIQSLACVM
Jean-ClaudeBrient
SLAC
Mail Bin 65
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Bimet: JCBRIENTBSLACVM
HaraId P. Bomer
Oxford University
Nuclear Physics Lab
1 Keble Road
Oxford OX1 3RH, England
Dave I. Britton
TRIUMF
4004, Wesbrook Mall
Vancouver, BC, Canada
V6T 2A3
Bimet: BRITPIENU@TRIUMFCL
Fabio Bossi
Laboratori Naz. Di Frascati
INFN
P.O. Box I3
I-00044 Frascati, Italy
Bitnet: BOSSI@VAXLNF
Charles Brown
Fermilab
MS 122
P.O. Box 500
Batavia. IL 60510
StephenE. Bougerolle
University of Victoria
Dept. of Physics
P.O. Box 1700
Victoria, BC, Canada VSW 2Y2
Bimet: STEVEB@SLACSLD
Thompson H. Burnett
University of Washington
Dept. of Physics, FM-15
Seattle, WA 98195
Bimet: ‘IHB@SLACVM
Jerome K. Busenitz
University of Notre Dame
Dept. of Physics
Notre Dame, IN 46556
Bitnet: BUSENITZQFNAL
Blas Cabrera
Stanford University
Dept. of Physics
Stanford, CA 94305
Roger K. Brooks
SLAC
Mail Bin 8 1
P.O. Box 4349
Stanford, CA 94309
Bimet: RBROOKSQSLACVM
-432-
Shen-Ou D. Cai
Northwestern University
Dept. of Physics
Evanston, IL 60208
Alessandro Calcaterra
Lab. NazionaIi di Frascati
Via E. Fermi. 40
C.P. 13
I-0044, Frascati, Italy
Bimet: ACAL@SLACVM
Barbara Camanzi
Istituto Naz. Fiz. Nucleare
via Paradiso I2
I-44100 Ferrara, Italy
Massimo Carpinelli
INFN-Pisa
Via Livomese 582/A
I-56010 San Piero a Grado
I&Y
Bitnet: CARPINELL@IPIVAXIN
Andrea Castio
Istituto Naz. Fiz. Nucleare
via Marzolo 8
I-35100 Padova, Italy
Bitnet: [email protected]
George B. Chadwick
SLAC
Mail Bin 94
P.O. Box 4349
Stanford, CA 94309
Bimet: GBCQSLACVM
Swati Chakravarty
Carleton University
Dept. of Physics
Ottawa, ON, Canada KlS 5B6
Bitnet: SWATIQNRCHEP
Vladimir Chaloupka
University of Washington
Dept. of Physics, FM-15
Seattle, WA 98195
Bitnet: CHALOUPK@UWAPHAST
Lee Chang
Tsinghua University
Dept. of Physics
Beijing loo084
People’s Republic of China
Maurice P. Chapellier
Conun. a 1’EnergieAtomique
B.P. No. 511
F-75 Paris 15, France
Bimet: CHAP@FRSOLll
Harry W.K. Cheung
University of Colorado
Physics Department
Campus Box 390
Boulder, CO. 80309
Bimet: H CHEUNG@COLOPHYS
Mokhtar Chmeissani
University of Michigan
Dept. of Physics
Ann Arbor, MI 48109
Bimet: CHMEISSANI@UMIPHYS
Hing T. Cho
University of Oklahoma
Dept. of Physics & Astronomy
440 West Brooks, Room 131
Norman, OK 73019
Jong Bum Choi
SLAC
MaiIBin81
P.O. Box 4349
Stanford, CA 94309
Bimet: CHOI@SLACVM
Sergio Conetti
McGill University
Physics Dept.
3600 University Ave.
Montreal, PQ, Canada H3A 2T8
Bitnet: SERGIO@FNAL
Adrian R. Cooper
SLAC
Mail Bin 8 1
P.O. Box 4349
Stanford, CA 94309
Bimet: ADRlAN@SLACVM
Dieter Cords
SLAC
Mail Bin 78
P.O. Box 4349
Stanford, CA 94309
Bimet: CORDS@SLACVM
Mail Bin 78
P.O. Box 4349
Stanford, CA 94309
Bimet: DAI@SLACVM
Bemd Dehning
Max Planck Inst. fur Phys.
Fohringer Weg 2
Postfach 40 12 12
D-8000 Munich 40, West Gemrany
Bitnet: DEHNING@CERNVM
Mourad Daoudi
University of California
Physics Dept.
Riverside, CA 92521
Bimet: DAOUDI@SLACVM
Stefano Dell’Uomo
1st. Naz. di Fis. Nucleare, Rome
P.le A. Moro 2
I-00185 Rome, Italy
Bimet: [email protected]
Sridhara Dasu
SLAC
Mail Bin 62
P.O. Box 4349
Stanford, CA 94309
Bimet: DASU@SLACVM
Patrixia DeSimone
Lab. Nazionale di Frascati
Via Enrico Fermi 8
I-00044 Frascati, Roma
Italy
Bimet: PATRIZIA@SLACVM
Correa, Albert0 DosReis
Ferrnilab
MS 122
P. 0. Box 500
Batavia. IL 60510
Michel Davier
University Paris Sud
Lab de I’Accelerateur Lineaim
Batiment 200
F-91405 Orsay, CEDEX, France
Bimet: DAVIER@FRLALSl
David P. Coupal
SLAC
Mail Bin 95
P.O. Box 4349
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Bimet: DPC@SLACVM
Andrew J. Davies
University of Melbourne
School of Physics
Parkville, Vict. 3052
Australia
Wim deBoer
SLAC
Mail Bin 61
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Bimer WDB@SLACVM
David H. Coward
SLAC
Mail Bin 65
P.O. Box 4349
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Bimet: DHC@SLACVM
PascalDebu
DPhPE - CEA Cen Saclay
B.P. no. 2
F-91 191 Gif-stir-Yvette
France
Bitnet: DEBLJ@FRSAC12
Paschal A. Coyle
University of California
SCIPP
Santa CI-UZ,CA 95064
Bimet: PASCHAI@SLACVM
-433-
Robert DiRosario
University of Illinois
Dept. of Physics
1110 West Green Street
Urbana, IL 61801
Bimet: ROBERT@SLACVM
Lance Dixon
SLAC
Mail Bin 81
P.O. Box 4349
Stanford, CA 94309
Bitnet: STUBBINS@SLACVM
Brian L. Dougherty
Lawrence Berkeley Lab
Bldg. 50A, Room 6141
University of California
Berkeley, CA. 94720
Marvin H. Douglas
U.C. San Diego
Dept. of Physics
B-019
La Jolla, CA 92093
Bitnet: [email protected]
Frederik C. Eme
NIKHEF - H
P. 0. Box 41882
1009 DB Amsterdam
The Netherlands
Bitnet: UOOO42@HASARAS
Sidney Drell
SLAC
Mail Bin 80
P.O. Box 4349
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Bitnet: DRELL@SLACVM
Rahim Esmailzadeh
SLAC
Mail Bin 81
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Bitnet: RAHIM@SLACVM
Richard J. Dubois
TRIUMF, University of Victoria
Dept. of Physics
P.O. Box 1700
Victoria, BC, Canada V8W 2Y2
Bimet: RICHARD@SLACVM
Gary Feldman
SLAC
Mail Bin 78
P.O. Box 4349
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Bimet: GARYQSLACVM
Luca Fiorani
SLAC
Mail Bin 96
P.O. Box 4349
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Jean E. Duboscq
University of California
Dept. of Physics
Santa Barbara, CA 93106
Bitnet: DUBOSCQ@SBHEP
David N. Femandes
SLAC
Mail Bin 61
P.O. Box 4349
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Bimet: DAVEF@SLACVM
Carrie S. Fordham
SIAC
Mail Bin 9.5
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Bitnet: CARRIE@SLACVM
Michael J. Fero
M.I.T.
Dept. of Physics
Cambridge, MA 02139
Bitnet: MFEROQSLACVM
Raymond E. Frey
University of Michigan
Dept. of Physics
Ann Arbor, MI 48109
Bitnet: RAYFREY@SLACVM
R. Clive Field
SLAC
Mail Bin 78
P.O. Box 4349
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Bimet: SARGON@SLACVM
Dieter Freytag
SLAC
Mail Bin 57
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DRFQSLACVM
Bard Dunietz
SLAC
Mail Bin 8 1
P.O. Box 4349
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yJ;rn
Dunwoodie
Mail Bin 62
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Bimet: WMD@SLACVM
JamesEastman
Lawrence Berkeley Lab
MS 50-137
Berkeley, CA 94720
Bimet: [email protected]
Giuseppe Fiiccchiaro
SLAC
Mail Bin 43
P.O. Box 4349
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Bitnet: SLD::FINOCCHIARO,
VAXRONFINOCCHIARO
Faust0 Fiorani
University di Panna
Dipartimento di Fisica
Viale delle Scienze
I-43100 Parma, Italy
Bimet: [email protected]
Carlos E. Figueroa
University of California
SCIPP
Santa Cruz, CA 95064
Bitnet: CARLOS@SLACSLD
Alfred Fridman
SLAC, Bin 98
P.O. Box 4349
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Bimet: FRIDMANQSLACVM
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Joshua Frieman
SLAC
MailBin
P.O. Box 4349
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John R. Fry
University of Livemoo
Dept. of Physics
P.G. Box 147
Liverpool L69 3BX, England
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David Fryberger
SLAC
Mail Bin 20
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Michele Gallinaro
Lab. Nazionali, Frascati
via E. Fermi, 8
C.P. 13
I-o0044 Frascati, Rome
Italy
Bimet: MICHGALLQIRMLNF
Kock-Kiam Gan
SLAC
Mail Bin 61
P.O. Box 4349
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Bimet: KKGQSLACVM
Arthur F. Gartinkel
Purdue University
Dept. of Physics
Lafayette, IN 47907
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Earl Gero
University of Michigan
Dept. of Physics
Ann Arbor, MI 48109
Bitnet: GERO@SLACVM
..::..
‘.:
.. ,-:
Duncan B. Gibaut
Carnegie Mellon University
Dept. of Physics
Pittsburgh, PA 15213
Bitnet: GIBAUTQFNAL
Xin L. Gong
University of Hawaii
Dept. of Physics
Honolulu, HI 96822
Bimet: XIN@SLACVM
Lawrence J. Hall
University of California
Dept. of Physics
Berkeley, CA 94720
Bimet: HALL LJ@LBL
Despina Hatzifotiadou
CERN- EP Division
CH-1211 Geneva 23
Switzerland
Bimet: DESPINABCERNVM
Valerie Gibson
CERN - EP Division
CH-1211 Geneva 23
Switzerland
Bimet: GIBSON@CERNVM
t%&oph Grab
Mail Bin 65
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Bimet: GRAB@SLACVM
Gail G. Hanson
sL4c
Mail Bin 78
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Bimet: GAIL@SLACVM
Christopher Hawkins
SLAC
Mail Bin 61
P.O. Box 4349
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Bimet: HAWKINS@SLACVM
Giorgio Gratta
University of California
Nat. Sci. II
SCIPP
Santa Ctuz, CA 95064
Bimet: GRATTAQSLACVM
Haim Harari
Weizmann Inst. of Science
Dept. of Nuclear Physics
P.O. Box 26
76100 Rehovoth, Israel
Bimet: FHHARARI@WEIZMANN
John L. Hearns
Glasgow University
Dept. of Physics & Astronomy
z;zf;z
(3128QQ
Paul Griffin
SLAC
Mail Bin 8 1
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Bimet: PAG@SLACVM
Robert F. Han
Lawrence Berkeley Lab
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Bimet: HARR@SLACVM
Christopher Hearty
Lawrence Berkeley Lab
University of California
Berkeley, CA 94720
Bimet: HEARTYQSLACVM
Frederik A. Harris
University of Hawaii
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Thomas M. Himel
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Mail Bin 95
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Fred J. Gilman
SLAC
Mail Bin 81
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Gary Gladding
University of Illinois
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Thomas Glanzman
SLAC
Mail Bin 78
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Paul Grosse-Wiesmann
SLAC
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fSi~y~L. Godfrey
Mail Bin 98
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Bitnet: GLGCB@SLACVM
Paolo Gomes
University of California
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Physics Board of Study
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Francoise Guerin
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David J. Hadden
SLAC
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Paul F. Harrison
Liverpool University
Dept. of Physics
P.O. Box 147
Liverpool L69 3BX, England
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Keith W. Hartman
Pennsylvania State University
Dept. of Physics
104 Davey Lab.
University Park, PA 16802
Bimet: HARTMAN@FNAL
Bimet: ALO3@GWIA
Chili Ho
University of California
Physics Dept.
Riverside, CA 92521
Sven Olof Holmgren
Stockholm Universitv
Inst. of Physics
’
Vanadisvagen9
S-l 1346 Stockholm, Sweden
Bitnet: HOLMGRENQSLACVM
:.;
.::
s.
.. ..
::
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i.
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Paul Hong
Northwestern University
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Carl J. Im
SLAC
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Lewis P. Keller
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Walter Innes
SLAC
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Tina M. Kaarsberg
State University of New York
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Stony Brook, NY 11794
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Steohane A. Keller
Iowa State University
171-H University Village
Ames, IO 50010
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George Irwin
Stanford University
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Marek Karliner
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Peter Chong-Ho Kim
SLAC
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Nobu Katayama
State University of New York
Dept. of Physics
Albany, NY 12222
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Mary King
University of California
SCIPP
Physics Board of Study
Santa Cruz, CA. 95064
Bimet: MARYK@SLACVM
Jung
i
Seong J. Hong
University of Michigan
Dept. of Physics
Ann Arbor, MI 48109
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Alan K. Honma
University of Victoria
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Columbia University
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SLAC
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University oishizuoka
Lab. Comp. Science
Yada 395, Shizuoka 422
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John A. Jaros
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SLAC
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Anthony Johnson
Boston University
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Boston, MA 02215
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James E. Hylen
Johns Hopkins University
Dept. of Physics
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William T. Kirk
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Igor Klebanov
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Matthew Jones
University of Victoria
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_,:
..
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SpencerKlein
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Maii Bin 95
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:
,’
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Dale S. Koetke
SLAC
Mail Bin 61
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Frederic J. Kral
Lawrence Berkeley Lab
MS 50A-2160
University of California
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Andrew Lankford
SLAC
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Juergen Krueger
DESY
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D-2000 Hamburg 52
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Jan A. Lauber
University of Colorado
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University Of California
Dept. of Physics
Knudsen Hall 4-140
Los Angeles, CA 90024
Bitnet: KONIGSBE@BNLVMA
Masatoshi Koshiba
CERN - EP Division
CH-1211 Geneva 23
Switzerland
Wayne Koska
University of Michigan
Dept. of Physics
Ann Arbor, MI 48109
Bitnet: KOSKA@SLACVM
Lee Anne Kowalski
SLAC
Mail Bin 61
P.O. Box 4349
Stanford, CA 94309
Bimet: ANNE@SLACVM
gt$l
Kozanecki
Mail Bin 95
P.O. Box 4349
Stanford, CA 94309
Bimet: WJTOLD@SLACVM
Michael P. Kuhlen
California Inst. Tech.
Dept. of Physics
Mail 356-48
Pasadena,CA 91125
Bitnet: KUHLENQSLACVM
Lap Y. Lee
California Inst. Tech.
Lauritsen Lab 35648
Pasadena,CA 91125
Bimet: [email protected]
David W.C.S. Leith
SLAC
Mail Bin 62
P.O. Box 4349
Stanford, CA 94309
Bimet: LElTH@SLACVM
Paul F. Kunz
SLAC
Mail Bin 62
P.O. Box 4349
Stanford, CA 94309
Bimet: PFKEB@SLACVM
David C. Lewellen
SLAC
Mail Bin 8 1
P.O. Box 4349
Stanford, CA 94309
Bitnet: DCL@SLACVM
Masahiro Kuze
University of Tokyo
Dept. of Physics .
7-3-l Hongo, Bunkyo-ku
Tokyo 113, Japan
Bitnet: KUZE@JPNKEKVX
Steven C. Lin
Columbia University
Dept. of Physics
New York, NY 10027
Bitnet: LIN@SLACVM
Jonathan Labs
SLAC
Mail Bin 65
P.O. Box 4349
Stanford, CA 94309
Bimet: JONLABSQSLACVM
Willis T. Lin
Universitv of California
Physics dept.
Riverside, CA 92521
Bitnet: WXLPO9@SLACPHYS
Armando Lanaro
University of Rochester
Dept. of Physics & Astronomy
Rochester, NY 14627
Bimet: LANARC@FNAL
-437-
Christopher B. Liiakis
Northeastern University
Dept. of Physics
Boston, MA 0211.5
Bitnet: LIRAKIS@FNAL”
Wi!liarn S. Lockman
l$;~ty
of California
Santa Cruz, CA 95064
Bimet: BILLY@SLACVM
Kenneth R. Long
Rutherford and Appleton Labs
Chilton
Didcot, Oxon. OX2 7NR, England
Bitnet: LONG@UKACRL
John LoSecco
University of Non-e Dame
Dept. of Physics
Notre Dame, IN 46556
LOSECCC@JNDHEP
Xing-Min Lu
Columbia University
Pupin Hall, Box 105
New York, NY 10027
Bimet: XLU@SLACVM
Vera G. Luth
SLAC
Mail Bin 95
P.O. Box 4349
Stanford, CA 94309
Bimet: VGL@SLACVM
David B. MacFarlane
McGill Universitv
Physics Dept. 3600 University Ave.
Montreal PQ
Canada H3A 2T8
Bimet:
[email protected]
.‘s:,
.-
.A
:, .::1..,_
..
- ..
-:-:. :.
:,..
Leon Madansky
Johns Hopkins University
Dept. of Physics
34th and Charles St.
Baltimore. MD 21218
Lisa Mathis
Lawrence Berkeley Lab
University of California
Berkeley, CA 94720
Bitnet: LGMF@[email protected]
Walid Majid
University of Illinois
Dept. of Physics
1110 W. Green St.
Urbana, IL 61801
Bimet: WALIDQSLACVM
Laurent Mathys
SLAC
Mail Bin 62
P.O. Box 4349
Stanford, CA 94309
Bimet: MATHYSQSLACVM
David J. Mellor
University of Illinois
Dept. of Physics
1110 W. Green St.
Urbana, IL 61801
Bimet: DJM@SLACVM
Robert Lee Messner
SLAC
Bin 94
P.O. Box 4349
Stanford, CA. 94309
Bimet: ROMQSLACVM
Eric J. Mannel
University of Notre Dame
Dept. of Physics
Notre Dame, IN 46556
Bimet: MANNEI@FNAL
John A.J. Matthews
Johns Hopkins University
Physics Dept.
Baltimore, MD 21218
Bimet: JYM@SLACVM
Giancarlo Mantovani
University of Perugia
Dipartimento di Fisica
I-06100 Perugia
Italy
Bimet: GIANCARLQIPGUNIV
Tom Mattison
SLAC
Mail Bin 95
P.O. Box 4349
Stanford, CA 94309
Bimet: MATTISON@SLACVM
E. Cas Mimer
Los Alamos National Lab
MS H846, P.O. Box 1663
Los Alamos, NM 87545
Bimet: MILNER@LAMPF
Thomas Markiewicz
sL4c
Mail Bin 96
P.O. Box 4349
Stanford, CA 94309
Bitnet: TWMARKBSLACVM
John McGowan
Universitv of Illinois
Dept. of Physics
1110 W. Green St.
Urbana, IL 61801
Bitnet: JFM@SLACVM
JussaraM. de Miranda
Fennilab
MS 122
P.O. Box 500
Batavia, IL 60510
Bimet: J MIRANDA@FNAL
JoseL. Martinez
University of Cincinnati
Dept. of Physics
Cincinnati, OH 45221
Bimet: JLMQSLACVM
Brian T. Meadows
University of Cincinnati
Dept. of Physics
Cincinnati, OH 45221
Bimet: BRIANQSLACVM
Michiko Miyamoto
Kobe College
11-2, I-chome
Yamate, Nakasuji
Takarazuka City
Hyogo Prefecture
Japan 665
Hiroaki Masuda
SLAC
Mail Bin 96
P.O. Box 4349
Stanford, CA 94309
Bimet: MASUDA@SLACVM
Joao R.T. de Mello-Neto
Fetmilab
M.S. 122, E769
P.O. Box 500
Batavia, IL 60510
Bimet: J MELLO@FNAL
Douglas G. Michael
Harvard University
Dept. of Physics
Cambridge, MA 02138
Bimet: MICHAEL@FNAL
Kenneth C. Moffeit
SLAC
Mail Bin 78
P.O. Box 4349
Stanford, CA 94309
Bimet: MOFFEIT@SLACVM
-43a-
RoIIin Morrison
University of California
Dept. of Physics
Santa Barbara, CA 93106
William M. Morse
Brookhaven National Lab
Physics Dept., Bldg. 510A
Upton, L.I., NY 11973-5000
Bitnet: JNET%“MORSE@BNLCLl”
Benoit Mom
Lab de Phys. des Particules
Ch. de Bellevue, B.P. 909
F-74019 Annecy-le-Vieux
CEDEX, France
Bimet: MOURS@CERNVM
Steve Mrenna
Johns Hopkins Universitv
Dept. of Physics & Astronomy
Homewood Campus
Baltimore, MD 21218
Bimet: INS CSM@JUHVMS
George Mundy
SLAC
Mail Bin 96
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Bitnet: MUNDYQSLACVM
Charles T. Munger
SLAC
Mail Bin 61
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Bimet: CHARLESQSLACVM
William Murray
Indiana University
Dept. of Physics
Bloomington, IN 47405
Bimet: MURRAYQSLACVM
.T
Tadashi Nagamine
Kyoto University
Dept. of Physics
Yoshida-honmachi, sakyo-ku
Kyoto-shi 606, Japan
Bimet: NAGAMINE@FNAL
Jordan A. Nash
SLAC
Mail Bin 95
P.O. Box 4349
Stanford, CA 94309
Bimet: JAN@SLACVM
p$lichael
Nelson
Mail Bin 26
P.O. Box 4349
Stanford, CA 94309
Bimet: ENFLSON@SIACVM
Ai G. Nguyen
Michigan State University
Dept. of Physics
East Lansing, MI 48824
Bitnet: AINGUYEN@FNAL
Harold 0. Ogren
Indiana University
Dept. of Physics
Bloomington, IN 47405
Bimet: OGREN@SLACVM
Heungmin Oh
University of California
Physics Dept.
Riverside, CA 92521
Bimet: OH@SLACTWGM
Tsunehiko Omori
Nat. Lab. for High Energy Physics
KEK
Oho, Tsukuba-shi
Ibaraki-ken 30.5,Japan
Bitnet: OMORI@JPNKEKVM
Mirko M. Nussbaum
University of Cincinnati
Dept. of Physics
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Bitnet: MMN@SLACVM
Kathryn O’Shaughnessy
SLAC
Mail Bin 78
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Bitnet: KATHYO@SLACVM
Dale Pitman
SLAC
Mail Bin 65
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Bimet: PITMAN@SLACVM
M&n L. Per1
SLAC
Mail Bin 61
P.O. Box 4349
Stanford, CA 94309
Bimet: MARTIN@SLACVM
Rainer Pitthan
SLAC
Mail Bin 96
P.O. Box 4349
Stanford, CA 94309
Bimet: RAINERQSLACVM
Ida M. Peruzzi
Laboratori Naz. di Frascati
via E. Fermi, 40
C.P. 13
I-00046 Frascati (Rome)
Eric J. Prebys
University of Rochester
Dept. of Physics &Astronomy
Rochester, NY 14627
Bimet: PREBYS@FNAL
IdY
Jeffrey S. Orszak
Boston University
Dept. of Physics
590 Commonwealth Ave.
Boston, MA 02215
Bitnet: JEFFO@SLACVM
Bimet: lMP@SLACVM
Michael Peskin
SAC
Mail Bin 81
P.O. Box 4349
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Bimet: MPESKIN@SLACVM
%%&ang K.H. Panofsky
H. Pierre Noyes
SLAC
Mail Bin 81
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Bimet: NOYES@SLACVM
Michele Pauluzzi
Perugia University
Dipartimento di Fisica
Via Pascoli
I-06100 Pemgia, Italy
Bimet: PAULUZI@SLACVM
Mail Bin 76
P.O. Box 4349
Stanford, CA 94309
Sherwood Parker
University of Hawaii
Dept. of Physics
Honolulu, HI 96822
Bimet: SHERQSLACVM
Larry Parrish
University of Washington
Dept. of Physics
Seattle, WA 98195
-439-
Charles Prescott
SLAC
Mail Bin 80
P.O. Box 4349
Stanford, CA 94309
Bimet: PRESCOTT@SLACVM
Bernard Peyaud
DPhPE - CEA Cen Saclav
B.P. no. 2
F-91 191 Gif-sur-Yvette, France
Nading Qi
Academia Sinica
Inst. of High Energy Physics
P. 0. Box 918
Beijing
The People’s Republic of China
Marcello Piccolo
Laboratori Nazionali, Frascati
via E. Fermi, 40
C.P. 13
I-00044 Frascati, Rome, Italy
Bimet: MXP@SLACVM
Helen Quinn
SLAC
Mail Bin 8 1
P.O. Box 4349
Stanford, CA 94309
Bimet: QUINN@SLACVM
Livio Piemontese
lstituto Naz. Fiz. Nucleate
via Paradise 12
I-44100 Ferrara, Italy
Bitnet: LlVICt@SLACVM
Pauicia Rankin
SLAC
Mail Bin 78
P.O. Box 4349
Stanford, CA 94309
Bimet: TRlClA@SLACVM
Blair N. Ratcliff
SLAC
Mail Bin 62
P.O. Box 4349
Stanford, CA 94309
Bimet: BLAIR@SLACVM
Paul Rensing
SLAC
Mail Bin 62
P.O. Box 4349
Stanford, CA 94309
Bitnet: RENSING@SLACVM
Maria P. Roco
University of Iowa
Dept. of Physics & Astronomy
Iowa City, IA 52242
Bimet: ROCO@SLACVM
Jeffrey D. Richman
University of California
Dept. of Physics
Santa Barbara, CA 93106
Bimet: RICHMAN@SLACVM
Natalie A. Roe
SLAC
Mail Bin 61
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Bitnet: NATALIE@SLACVM
John Keith Riles
SLAC
Mail Bin 95
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Bimet: KEITHRQSLACVM
E. Michael Riordan
SLAC
Mail Bin 80
P.O. Box 4349
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Bitnet: EMR@SLACVM
Heidi M. Schellman
University of Chicago
Dept. of Physics
Chicago, IL 60637
Bimet: SCHELLMAQFNAL
Leon S. Rochester
SLAC
Mail Bin 96
P.O. Box 4349
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Bimet: LSREAQSLACVM
Patrick G. Reutens
SLAC
Mail Bin 96
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Bitnet: REUTENSQSLACVM
Burton Richter
SLAC
Mail Bin 80
P.O. Box 4349
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Bimet: KATHY@SLACVM
Markus W. Schaad
Lawrence Berkeley Lab
University of Cahfornia
Berkeley, CA 94720
Bimet: SCHAAD@SLACVM
Jack L. Ritchie
SLAC
Mail Bin 63
P.O. Box 4349
Stanford, CA 94309
Bimet: RITCHIEQSLACVM
Rafe H. Schindler
sL4c
Mail Bin 65
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Bimet: RAFFQSLACVM
Daniel V. Schroeder
sL4c
Mail Bin 8 1
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Bimet: DVS@SLACVM
David C. Schultz
SLAC
Mail Bin 62
P.O. Box 4349
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Bimet: DCS@SLACVM
Matt Sands
University of California
SCIPP
Santa CNZ, CA 94064
Bimet: SANDS@SLACVM
Alan J. Schwartz
Stanford University
High Energy Physics Lab
Stanford, CA 943054080
Bimet: SCHWARTZ@HARVHEP
Jack Sandweiss
Yale University
Dept. of Physics
P.O. Box 6666
New Haven. CT 065 11
Felix Sefkow
DESY
NotkeStrasse85
D-2000 Hamburg 52
West Germany
Bitnet: FlSSEFQDHHDESY3
Attilio Santocchia
Perugia University
Dipartimento di Fisicd
Via Pascoli
I-06100 Perugia, Italy
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-440-
Stephen L. Shapiro
SLAC
Mail Bin 62
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Bimet: SHAPlRO@SLACVM
Vivek A. Sharma
Syracuse University
Dept. of Physics
Syracuse, NY 13244
Bimet: VS@CRNLNS
?:“c””
Sharpe
Mail Bin 81
P.O. Box 4349
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Bimet: SHARF’E@SLACVM
Junpei Shirai
Nat. Lab. for High Energy Physics
KEK
Oho, Tsukuba-shi
Ibaraki-ken 305, Japan
Bimet: SHIRAIQJPNKEKVM
Ian M. Silvester
Oxford Universitv
Nuclear Physics Lab
Keble Road
Oxford OX1 3RH, England
Bitnet: [email protected]
Armand Simon
Max Planck Inst. fur Kemphysik
Postfach 103 980
D-6900 Heidelberg, West Germany
Bimet: ASC@CERNVM
Constantine Simopoulos
sL.Ac
Mail Bin 62
P.O. Box 4349
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Bimet: CONSIMQSLACVM
Robert L. Singleton
SLAC
Mail Bin 81
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Bitnet: BOBSQSLACVM
Ian E. Stockdale
University of Illinois
Dept. of Physics
1110 W. Green St.
Urbana, IL 61801
Bitnet: lES@SLACVM
Nobukazu Toge
SLAC
Mail Bin 62
P.O. Box 4349
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Bitnet: TOGE@SLACVM
Chukwuma Kenneth Uzo
SLAC
Mail Bin 98
P.O. Box 4349
Stanford, CA 94309
Bitnet: KENUZO@SLACVM
Stewart A.J. Smith
Princeton University
Dept. of Physics
P.O. Box 708
Princeton, NJ 08544
Bitnet: SMITH@PUPHEP
Calvin Stubbins
SLAC
Mail Bin 81
P.O. Box 4349
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Bitnet: STUBBINS@SLACVM
Walter H. Toki
SLAC
Mail Bin 65
P.O. Box 4349
Stanford, CA 94309
Bitnet: TOKI@SLACVM
Jaroslav Va’Vra
SLAC
Mail Bin 62
P.O. Box 4349
Stanford, CA 94309
Bitnet: JJVQSLACVM
Fumihiko Suekane
Nat. Lab. for High Energy Physics
KEK
Oho, Tsukuba-shi
Ibaraki-ken 305, Japan
Yung-Su (Paul) Tsai
SLAC
Mail Bin 81
P.O. Box 4349
Stanford, CA 94309
Bitnet: YSTIH@SLACVM
Richard J. VanKooten
SLAC
Mail Bin 95
P.O. Box 4349
Stanford, CA 94309
Bitnet: RICKV@SLACVM
Andre S. Turcot
University of Victoria
Dept. of Physics
P.G. Box 1700
Victoria, BC, Canada VRW 2Y2
Bitnet: TURCOT@UVVM
Cristina Vannini
INFN-Pisa
Via Livornese 582/A
I-56010 San Piero a Grade
Italy
Bitnet: CVN@SLACVM
VANNINI@IPIINFN
Arthur E. Snyder
Indiana University
Dept. of Physics
Bloomington, IN 47405
Randy J. Sobie
Universitv of British Columbia
Physics Dept.
Vancouver, BC, V6T 2A3
Canada
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Jacob Sonnenschein
SLAC
Mail Bin 81
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Kevin Sparks
University of California
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Davis, CA 95616
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Thomas Steele
SLAC
Mail Bin 9.5
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Morris Swartz
SLAC
Mail Bin 78
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Anthony Szumilo
University of Washington
Dept. of Physics
Seattle, WA 98 195
Bitnet: SZUMlLO@SLACSLD
Marc Turcotte
TRlUMF
University of British Columbia
Dept. of Physics
Vancouver, BC, Canada V6T 1W5
Bitnet: MARCQSLACVM
Lucas Taylor
Imnerial Coil. Sci. Tech
Blacken Ldb
Prince Consort Road
London, SW7 2AZ, England
Bitnet: TAYLORWCERNVM
Georg Tysarczyk
Universitv of Heidelberr
Physikalisches Inst. ”
Philosophenweg 12
D-6900 Heidelberg, West Germany
Bitnet: GEORG@DHDlHEPl
Richard E. Taylor
SLAC, Bin 96
P.O. Box 4349
Stanford, CA 94309
Bimet: RETAYLORQSLACVM
Tracy Usher
University of California
Dept. of Physics
Irvine, CA 92717
Bitnet: TUSHER@UCIVMSA
-441-
Geert J. VanOldenborgh
NIKHEF
P. 0. Box 41882
1009 DB Amsterdam
The Netherlands
Bitnet: T19QNIKHEFH.HEP.NL
Piero Giorgio Verdini
INFN-Pisa
Via Livornese 582/A
I-56010 San Piero a Grade
Italy
Bitnet: PGV@SLACVM
VERDINI@IPIINFN
._
_, ;
1:.
::
? .-:.
Purushotham Voruganti
SLAC
Mail Bin 78
P.O. Box 4349
Stanford, CA 94309
Bitnet: PURU@SLACVM
Steven R. Wasserbaech
SLAC
Mail Bin 65
P.O. Box 4349
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Bimet: SRW@SLACVM
Michael F. Wade
Durham University
Dem. of Phvsics
South Road
Durham DHl 3LE, England
Bitnet: [email protected]
Achim W. Weidemann
University of Tennessee
Dept. of Physics
Knoxville, TN 37996
Bitnet: ACHlM@SL4CVM
Tony Waite
University of Victoria
Dept. of Physics
P.O. Box 1700
Victoria, BC, Canada V8W 2Y2
Bitnet: APW@SLACVM
Mark Walton
SLAC
Mail Bin 81
P.O. Box 4349
Stanford, CA 94309
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Ning Wang
University of California
Dept. of Physics
Berkeley, CA 94720
Zi Wang
Utah State University
Dept. of Physics
Logan, UT 84322
Bennie F.L. Ward
University of Tennessee
Dept. of Physics
401 Nielsen Physics Bldg.
Knoxville, TN 37996-1200
Bitnet: BFLWQSLACVM
Judd O’Hara Wilcox
University of California
Dept. of Physics
Davis, CA 95616
Bimet: WILCOXQUCDHEP
Raymond Willey
University of Pittsburgh
Dept. of Physics
Pittsburgh, PA 15260
Bitnet: WILLEY@PlTTVMS
David A. Williams
University of California
SCIPP
Santa Crux, CA 95064
Bitnet: WlLLIAMSQSLACTBF
Andreas Weigend
SLAC
Mail Bin 95
P.O. Box- 4349
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Michael S. Witherell
University of California
Dept. of Physics
Santa Barbara, CA 93106
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Alan Weinstein
SLAC
Mail Bin 65
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Stanford, CA 94309
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Lincoln Wolfenstein
Carnegie Mellon University
Dept. of Physics
Pittsburgh, PA 15213
Marvin Weinstein
SAC
MailBin
P.O. Box 4349
Stanford, CA 94309
Bitnet: NNQSLACVM
John W. Womersley
University of Florida
Dept. of Physics
Gainesville, FL 32611
Bitnet: WOMERSLEY@FNAL
Christopher Wendt
SLAC
Mail Bin 8 1
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Gwo-Guang Wong
University of California
Physics Dept.
Riverside, CA 92521
Michael Woods
SLAC, Bin 78
P.O. Box 4349
Stanford, CA 94309
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Norbert Wermes
CERN
CH-1211 Geneva 23
Switzerland
Bitnet: NNW@CERNVM
-442-
Guy Wormser
SLAC
Mail Bin 95
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Jeffery L. Wyss
1st. Naz. Fiz. Nucleare
via Marx0108
I-35100 Padua, Italy
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Chiaki Yanagisawa
State University of New York
Dept. of Physics
Stony Brook, NY 11794
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George P. Yost
University of California
Dept. of Physics
Berkeley, CA 94720
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Charles C. Young
SLAC
Mail Bin 96
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Michael Vincent Yurko
Indiana University
Dept. of Physics
Bloomington, IN 47405
Bitnet: MYURKC@SLACVM
Carla Zaccanielli
University of California
SCIPP
Nat. Sci. II
Santa CNZ, CA 95064
Bimet: ZACCCARDE@SLACVM
._ ._ :-1
._.
Geordie H. Zapalac
SLAC
Mail Bin 98
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Stanford, CA 94309
Bimet: GEORDIEQSLACVM
Richard W. Zdarko
SLAC
Mail Bin 36
P.O. Box 4349
Stanford, CA 94309
Bimet: RWZl%@JSLACMAC
Guenter Z.ech
University of Siegen
Fachbereich fur Phvsik
Postfach 101240 .
D-5900 Siegen, West Germany
Tianchi Zhao
University of Washington
Dept. of Physics
Seattle, WA 98 195
Bitnet: TCZ@FNAL
._.
-443-
-446
THE
SLAC SUMMER
INSTITUTES
ON PARTICLE
PHYSICS
1973 - 1967
1973
DEEP
INELASTIC
“Hadton Production
in Deep Inelastic Processes”
“Hadron Production
in the Collision of Virtual
Photons with Nucleons - an Experimental
Review”
“Phenomenological
Analysis”
“Asymptotic
Behavior and Short Distance
Singularities”
WEAK
1976
ELECTROPRODUCTION
CURRENTS
AND
J. D. Bjorken
M. Per1
“Weak Interaction
Theory and Neutral
“Weak Interactions
at High Energy”
“$ Spectroscopy”
“A New Lepton?”
“Lectures on the New Particles”
“New Particle Production”
F. J. Gilman
Y. Frishman
1977
Notes of Lectures on Current
and PCAC”
“Experimental
Phenomenology”
Algebra
“Gauge-Theories
of Weak and Electromagnetic
Interaction”
“How to Transform
Current Quarks to Constituent
Quarks and Try to Predict Hadron Decays”
THE
STRONG
S. Drell
DEEP HADRONIC
STRUCTURE
THE NEW PARTICLES
J. Primack
M. Kugler
1978
D.W.G.S. Leith
M. Davier
J.
S.
G.
G.
J.
D.
D. Bjorken
G. Wojcicki
J. Feldman
J. Feldman
D. Jackson
Hitlin
H.
S.
F.
M.
Harari
D. Drell
J. Gilman
L. Per1
AND
WEAK INTERACTIONS
AND FUTURE
R.J. Cashmore
F. J. Gilman
1979
D. Sivers
R. Blankenbecler
H.D.I. Abarbanel
QUANTUM
J. D. Bjorken
M. Davier
H. Harari
G. H. Trilling
-445-
D.
J.
H.
S.
H. Perkins
Ellis
Quinn
Wojcicki
CHROMODYNAMICS
“Lepton Nucleon Scattering”
“Massive Lepton Pair Production”
“QCD Phenomenology
of the Large Pr Processes”
“Perturbative
Quantum Chromodynamics”
“Elements of Quantum Chromodynamics”
F. J. Gilman
E. D. Bloom
K. C. Myffeit
- PRESENT
“Accelerator
Neutrino Experiments”
“Weak Interactions
at High Energies”
“Gauge Theories of the Weak Interactions”
“Weak Decays”
AND
“Leptons as a Probe of Hadronic Structure”
“Lepton Scattering as a Probe of
Hadron Structure”
“High pl Dynamics”
“Hadronic
Collision and Hadronic Structure
(An Experimental
Review)”
“The New Spectroscopy”
“The New Spectroscopy
(An Experimental
Review)”
QUARK SPECTROSCOPY
HADRON
DYNAMICS
“Quarks and Leptons”
“Quark Confinement”
“Hadron Spectroscopy”
“Lectures on the Quark Model, Ordinary
Mesons,
Charmed Mesons, and Heavy Leptons”
“Quarks and Particle Production”
M. Schwartz
S. Wojcicki
T. Appelquist
INTERACTIONS
“Diffractive
Processes”
“Amplitude
Structure in Two- and
Quasi-Two-Body
Processes”
“Resonances:
Experimental
Review”
“Resonances:
A Quark View of Hadron Spectroscopy
and Transitions”
“Lectures on Inclusive Hadronic Processes”
“Large Momentum
Transfer Processes”
“Hadron Dynamics”
1975
Currents”
AND
INTERACTIONS
“Raw
1974
WEAK INTERACTIONS
AT HIGH ENERGY
THE PRODUCTION
OF NEW PARTICLES
W. G. Atwood
R. Stroynowski
R. Stroynowski
S. J. Brodsky
J. D. Bjorken
1980
THE
WEAK
19S3
INTERACTIONS
“Gauge Theories of Weak Interactions”
“Neutrinos
and Neutrino Interactions”
“Weak Decays of Strange and Heavy Quarks”
“From the Standard Model to Composite Quarks
and Leptons”
“Physics of Particle Detectors”
1981
THE
STRONG
M.
F.
D.
H.
J. Veltman
J. Sciulli
Hitlin
Harari
AT
S. Ellis
R. Hollebeek
R. F. Schwitters
M. E. Peskin
M. G. D. Gilchriese
J. Ellis
A. H. Walenta
“Jets in QCD: A Theorist’s Perspective”
“Jets in e+e- Annihilation”
“Jet Production
in High Energy Hadron Collisions”
“Aspects of the Dynamics of Heavy-Quark
Systems”
“Heavy Particle Spectroscopy
and Dynamics B’s to Z’s”
“
And for Our Next Spectroscopy?”
“Review of the Physics and Technology of Charged
Particle Detectors”
“A Review of the Physics and Technology of
High-Energy
Calorimeter
Devices”
D. M. Ritson
J. Jaros
J. Marx
H. A. Gordon
R. S. Gilmore
W. B. Atwood
1954
PHYSICS
SPECTROSCOPY
:..:.:::::.:,..i:,.;-
P. M. Mockett
INTERACTIONS
“Quark-Antiquark
Bound State Spectroscopy
and &CD”
“Meson Spectroscopy:
Quark States and Glueballs”
“Quantum
Chromodynamics
and Hadronic Interactions
at Short Distances”
“Untangling
Jets from Hadronic Final States”
“Heavy Flavor Production
from Photons and Hadrons”
“Design Constraints
and Limitations
in e+e- Storage Rings”
“Linear Colliders:
A Preview”
1982
DYNAMICS
AND
HIGH ENERGY
AT VERY
HIGH
E. D. Bloom
M. S. Chanowitz
S. J. Brodsky
G.
C.
J.
H.
THE
SIXTH
QUARK
“The
Last Hurrah for Quarkonium
Physics:
The Top System”
“Developments
in Solid State Vertex Detectors”
“Experimental
Methods of Heavy Quark Detection”
“Production
and Uses of Heavy Quarks”
“Weak Interactions
of Quarks and Leptons:
Experimental
Status”
“The Experimental
Method of Rine-Imaging
Cherenkov (RICH) Counters”
“Weak Interactions
of Quarks and Leptons (Theory)”
Fox
A. Heusch
LeDuff
Wiedemann
E. Eichten
C.
T.
G.
S.
J. S. Damerell
Himel
L. Kane
Wojcicki
T. Ekelaf
II. Harari
ENERGIES
PIEF-FEST
LLExpectations for Old and New Physics at
High Energy Colliders”
“Beyond the Standard Model in Lepton Scattering
and Beta Decay”
“Grand Unification,
Proton Decay, and
Neutrino Oscillations”
“e+e- Interactions
at Very High Energy:
Searchine Beyond the Standard Model”
“The Gauge Hierachy Problem, Technicolor,
Supersymmetry,
and All That”
“Composite
Models for Quarks and Leptons”
“Electron-Proton
Colliding Beams:
The Physics Programme and the Machine”
R. N. Cahn
“Pief’
“Accelerator
Physics”
“High Energy Theory”
“Science and Technology Policies for the 1980s”
“Inclusive
Lepton-Hadron
Experiments”
“Forty-Five
Years of e+e- Annihilation
Physics:
1956 to 2001”
“We Need More Piefs”
M. Strovink
H. H. Williams
J. Dorfan
L. Susskind
S.
R.
T.
F.
J.
B.
Drell
R. Wilson
D. Lee
Press
Steinberger
Richter
J. Wiesner
:::
H. Harari
B. H. Wiik
-446-
“_
I
1985
SUPERSYMMETRY
“Introduction
to Supersymmetry”
“Signatures
of Supersymmetry
in e+e- Collisions”
“Properties
of Supersymmetric
Particles & Processes”
“Supersymmetry:
Experimental
Signatures at
Hadron Colliders”
“Superworld/Hyperworlds”
“Very High Energy Colliders”
“Some Issues Involved in DesiRning a 1 TeV (cm.)
e* Linear Collider Using ?on;entional
T&h&logy”
“Wake Field Accelerators”
“Plasma Accelerators”
“Collider Scaling and Cost Estimation”
1986
PROBING
THE
STANDARD
LOOKING
BEYOND
Polchinski
Burke
M. Barnett
Darriulat
M. E. Peskin
B. Richter
G. A. Loew
P. B. Wilson
R. D. Ruth & P. Chen
R. B. Palmer
MODEL
“Electroweak
Interactions
-Standard
and Beyond”
“CP and Other Experimental
Probes of Electroweak
Phenomena”
“Pertubative
QCD: K-Factors”
“Experimental
Tests of Quantum Chromodynamics”
“Phenomenology
of Heavy Quark Systems”
“Heavy Quark Spectroscopy
and Decay”
“Some Aspects of Computing
in High Energy Physics”
“Data Acquisition
for High Energy Physics Experiments”
1987
J.
D.
R.
P.
H. Harari
B. Winstein
R. Field
J. Dorfan
F. Gilman
R. Schindler
P. Kunz
M. Breidenbach
THE Z
“Theory of e+e- Collisions at Very High Energy”
“Prospects
for Physics at, e+e- Linear Colliders”
“Physics with Polarized Electron Beams”
“Electron-Proton
Physics at HERA”
“Hadron Colliders Beyond the Z””
“Physics at Hadron Colliders (Experimental
View)”
“The Dialogue Between Particle Physics and Cosmology”
M. E. Peskin
G. J. Feldman
M. L. Swartz
G. Wolf
C. Quigg
J. L. Siegrist
B. Sadoulet
-447-
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