About the scientific life of Harald Fritzsch

About the scientific life of Harald Fritzsch
Peter Minkowski
University of Bern
”Harald Fritzsch Symposium”
6. June , 2008 at the Ludwig-Maximilian University in Munich
1
List of contents
1
’Strong interactions are mediated by a gauge theory’
3
... a few remarks on the pre-history of this idea
2
From our collaboration
19
3
From Caltech becoming a Professor first in Wuppertal 1977 then in Bern 1978
26
4
From Bern to the LMU in Munich 1980 –
27
5
Outlook
31
References
32
2
1
’Strong interactions are mediated by a gauge theory’
... a few remarks on the pre-history of this idea and about QCD
As far as I know from you , Harald , this idea which gave birth to
QCD , was strongly impressed in your mind , when you succeeded
after obtaining the diploma in physics from the University of
Leipzig, to escape through the black sea to Turkey in 1968 .
But how these thoughts developed may be the topic of Murray
Gell-Mann’s contribution and thus I shall only report here about
times long past, starting 1953 with Wolfgang Pauli, and going
backwards to about 1937 to more general ideas of Élie Cartan on
’connections’ .
→
3
Figure 1: ’Many letters, some answers’ ( →
).
4
4
Pauli's Letters
Brief an Oskar Klein, Stockholm, vom 18. 2. 1929
Aber ich verstehe zu wenig von Experimentalphysik um diese Ansicht beweisen zu konnen
und so ist Bohr in der fur ihn angenehmen Lage, unter Ausnutzung meiner allgemeinen
Hilosigkeit bei der Diskussion von Experimenten sich selber und mir unter Berufung auf
Cambridger Autoritaten (ubrigens ohne Literaturangabe) da etwas beliebiges vormachen zu
konnen.
Brief an Oskar Klein, Stockholm, 1929
Ich selbst bin ziemlich sicher (Heisenberg nicht so unbedingt), da -Strahlen die Ursache
des kontinuierlichen Spektrums der -Strahlen sein mussen und da Bohr mit seinen diesbezuglichen Betrachtungen uber eine Verletzung des Energiesatzes auf vollkommen falscher
Fahrte ist. Auch glaube ich, da die warmemessenden Experimentatoren irgendwie dabei
mogeln und die -Strahlen ihnen nur infolge ihrer Ungeschicklichkeit bisher entgangen sind.
Brief an die Gruppe der \Radioaktiven" 1930
Physikalisches Institut
der Eidg. Technischen Hochschule
Zurich
Zurich, 4. Dez. 1930
Liebe Radioaktive Damen und Herren!
Wie der U berbringer dieser Zeilen, den ich huldvollst anzuhoren bitte, Ihnen des naheren auseinandersetzen wird, bin ich angesichts der falschen Statistik der N- und Li 6-Kerne, sowie des
kontinuierlichen -Spektrums auf einen verzweifelten Ausweg verfallen, um den Wechselsatz
der Statistik1 und den Energiesatz zu retten. Namlich die Moglichkeit, es konnten elektrisch
neutrale Teilchen, die ich Neutronen2 nennen will, in den Kernen existieren, welche den Spin
1/2 haben und das Ausschlieungsprinzip befolgen und sich von Lichtquanten auerdem noch
dadurch unterscheiden, da sie nicht mit Lichtgeschwindigkeit laufen. | Das kontinuierliche
-Spektrum ware dann verstandlich unter der Annahme, da beim -Zerfall mit dem Elektron
jeweils noch ein Neutron emittiert wird, derart, da die Summe der Energien von Neutron
und Elektron konstant ist.
Nun handelt es sich weiter darum, welche Krafte auf die Neutronen wirken. Das wahrscheinlichste Modell fur das Neutron scheint mir aus wellenmechanischen Grunden dieses
zu sein, da das ruhende Neutron ein magnetischer Dipol von einem gewissen Moment ist. Die Experimente verlangen wohl, da die ionisierende Wirkung eines solchen Neutrons
nicht groer sein kann als die eines -Strahls, und dann darf wohl nicht groer sein als
e (10?13 cm). Ich traue mich vorlaug aber nicht, etwas uber diese Idee zu publizieren, und
wende mich erst vertrauensvoll an Euch, liebe Radioaktive, mit der Frage, wie es um den
experimentellen Nachweis eines solchen Neutrons stande, wenn dieses ein ebensolches oder
etwa 10mal groeres Durchdringungsvermogen besitzen wurde wie ein -Strahl. : : :
Also, liebe Radioaktive, prufet, und richtet.|Leider kann ich nicht personlich in Tubingen
erscheinen, da ich infolge eines in der Nacht vom 6. zum 7. Dez. in Zurich stattndenden
Balles hier unabkommlich bin. : : : Euer untertanigster Diener
W. Pauli
1
2
Heute Pauli'sches Ausschlieungsprinzip
Heute Neutrinos
Here three letters in conjunction
with the neutrino hypothesis
are shown , from
Rudolf Mössbauer, Proc. of
’Neutrino Astrophysics’ Ringberg Castle
Tegernsee 20.-24. Oct. 1997 , ed. by
M.Altmann, W. Hillebrandt, H.-T. Janka and
G. Raffelt, TU München 1998 [1a] .
(→ )
5
But the strong interactions gauging a nonabelian local SU2 group
are subject of another letter , and concerning the association of the
gauge group with isospin ( G = SU 2 ) we have to say with Pauli :
’ganz falsch’ , yet ... . The following letter from Wolfgang Pauli to
Abraham Pais, 25. July 1953, is from
K. Meyenn, ’Wolfgang Pauli, Wissenschaftlicher Briefwechsel’,
Band IV, Teil II, Springer Verlag 1999 [2a] .
6
From the five derivation pages
only two shall be shown
→
7
M 6 = M 1+3 × S 2 →
8
The equation number is eight →
9
This first in time excursion , shall put into perspective your own
ideas, Harald , and leave open the eventual existence of other
similar ones .
In fact it would be incomplete, not to mention here Élie Cartan. The
interest of the latter in general relativity is documented by a book :
Élie Cartan - Albert Einstein: Letters on Absolute Parallelism,
1929-1932, Robert Debever Editor, Princeton Univ. Press. 1979 [3a] .
The next picture shows Élie Cartan returning from a turbulent ship excursion during an International
Mathematics Conference in Oslo , 1936 – from the photo album of George Pólya [4a] .
→
10
He tried to understand general relativity
but found general group-valued connections,
which include the specific SU2-valued one
derived by Wolfgang Pauli, around 1937 .
→
11
The ’Überbau’ structure of fibre bundles, mathematically elaborated
later, is fine , but so enormously generalised, that the jewels
relevant for quantized gauge field theories are difficult to recognize.
a
The next figure shall serve to put Wolfgang Pauli and Arnold Sommerfeld in perspective with your
University, the LMU in Munich. It is taken from the exposition at the ETH library at the occasion of the
centenary of W. P., URL http://www.ethbib.ethz.ch/exhibit/pauli/index.html/ [5a] .
a
I am grateful to Raymond Stora for pointing out to me two later indirect accounts of this work , by
a) Charles Ehresmann, ’Les connexions différentiables dans un fibré différentiable’, Colloque de Topologie (Espaces fibrés), Centre Belge de Recherches Mathématiques, Bruxelles, 5.-8. Juin 1950 [6a] , and
b) mimeographed notes of lectures by Shiing-Shen Chern, Institute for Advanced Study, Princeton
∼ 1951 [7a] .
12
Wolfgang Pauli as high school student in Vienna , his student card at the LMU and
Arnold Sommerfeld and Wolfgang Pauli during a conference on metals in Geneva 1934 →
13
Varna, Bulgaria the starting point of your escape with Stefan, 1968 .
→
14
Igneada, Turkey – the ’road to freedom’, 1968 [8a] .
→
15
”Forces between quarks ( and antiquarks ) are mediated by gauge bosons ...” this was your conviction
maybe related to your studies of general relativity . This brings you into the group of physicists and
mathematicians, which I mentioned in the introduction to your scientific life .
It brought you – a well conceived plan – to Aspen and later in 1970 to the Stanford Linear Accelerator
Center in order to discuss with Murray Gell-Mann and try to initiate your collaboration
Three accounts shall be cited here :
[1] William A. Bardeen, H. Fritzsch, Murray Gell-Mann , CERN-TH-1538, May 1972, ’Light cone current
algebra, π 0 decay, and e + e− annihilation’ , William A. Bardeen, H. Fritzsch and Murray
Gell-Mann . CERN-TH-1538, May 1972, presented at Topical Meeting on the Outlook for Broken
Conformal Symmetry in Elementary Particle Physics, 4-5 May 1972, Frascati, Italy, hep-ph/0211388.
[2] Harald Fritzsch and Murray Gell-Mann (CERN) ’Current algebra: Quarks and what else?’,
Proceedings of 16th International Conference on High-Energy Physics, Batavia, Illinois, 6-13 Sep
1972, published in eConf C720906V2 (1972) 135-165, also in Physics, Proceedings of the XVI
International Conference on High Chicago 1972 p.135 (J. D. Jackson, A. Roberts, eds.),
hep-ph/0208010 .
[3] H. Fritzsch, Murray Gell-Mann and H. Leutwyler (Caltech) , ’Advantages of the Color Octet Gluon
Picture’, CALT-68-409, 1973, Phys.Lett.B47 (1973) 365-368.
This shall acknowledge your original and seminal contribution to the conception of QCD .
16
Let me also show
’ The road to freedom (at short distances) ’
quoting four references
[4] I. B. Khriplovich, ’Greens functions in theories with a non-abelian gauge group’ , Yad. Fiz. 10 (1969)
409 , engl. transl. Sov. J. Nucl. Phys. 10 (1970) 235 .
[5] G. ’t Hooft, Remarks at the Colloquium on renormalization of Yang-Mills fields and applications to
particle physics, Marseille 1972 .
[6] D. J. Gross and F. Wilczek, ’Ultraviolet behaviour of nonabelian gauge theories’ , Phys. Rev. Lett. 30
(1973) 1343 .
[7] D. Politzer, ’Reliable results for strong interactions ?’ , Phys. Rev. Lett. 30 (1973) 1346 .
g2
µ d / d µ log
“
3/2
Z3
/Z1
”
= −b1
+ O
16 π 2
`
g4
´
12 − 1
(1)
C2 (G) −
b1 =
4
3
T2 (DG)
3
C 2 ( SU N ) = N ; tr T
a
(D)T
b
( D ) = T 2 ( D ) δ ab
→
17
... this shows the delight in your collaboration →
18
2
From our collaboration
In fall 1971 you and Murray Gell-Mann arrived for a stay of one year at CERN . Soon later we met and
started to collaborate , first on problems related to deep inelastic scattering and the short distance
expansion of products of local currents .
But let me move to fall 1973 , whence I had followed an offer to become a research fellow at Caltech and
we resumed there a wider collaboration . First lets turn to a paper on unified gauge-interactions, which
took more than a year to be completed :
[8] Harald Fritzsch and Peter Minkowski (Caltech), ’Unified Interactions of Leptons and Hadrons’,
CALT-68-467, (Received Dec 1974), Annals Phys.93 (1975) 193-266 .
It is not that you, Harald, were working slowly that this took so long, to the contrary, but many things
developed alongside.
First on the experimental side
a) in September 1973 the neutral current interaction was found in the reactions
(2)
ν µ ( ν µ ) N → ν µ ( ν µ ) + hadrons
in the Gargamelle bubble chamber [9] filled with freon , refining inconclusive earlier searches.
→
19
[9] F.J. Hasert et al., Gargamelle Neutrino Collaboration, ’Observation of Neutrino Like Interactions
Without Muon Or Electron in the Gargamelle Neutrino Experiment’, Phys.Lett.B46 (1973) 138-140 .
b) in November 1974 the joint efforts of Samuel Ting et al. at Brookhaven ,
[10] J.J. Aubert et al., E598 Collaboration, ’Experimental Observation of a Heavy Particle J’,
COO-3069-271, 1974, Phys.Rev.Lett.33 (1974) 1404-1406 ,
and Burton Richter et al. at SLAC ,
[11] J.E. Augustin et al., SLAC-SP-017 Collaboration, ’Discovery of a Narrow Resonance in e+ eAnnihilation’, SLAC-PUB-1504, Nov 1974, Phys.Rev.Lett.33 (1974) 1406-1408 ,
led to the discovery of (closed) charm in the form of the vector meson resonance J/ψ in the
reactions
(3)
p + Be → J/ψ + X → e + e − + X
8
< hadrons
e + e − → J/ψ →
: µ+µ−
[10]
[11]
Furthermore the resonance was almost immediately after first announcements confirmed jointly
by three experimental groups extending the energy range at the Adone facility at Frascati .
→
20
On the theoretical side – without detailed quotations nor attempt of completeness here – (some) seminal
insights and results, beyond what I have already mentioned, were
1967 [12] L.D. Faddeev, V.N. Popov (Steklov Math. Inst., St. Petersburg) , 1967, ’Feynman Diagrams for
the Yang-Mills Field’ , Phys.Lett.B25 (1967) 29-30 , with references therein to Chen-Ning Yang and
Robert Mills, Ryoyu Utiyama, Sheldon Glashow and Murray Gell-Mann, Bryce de Witt and
Richard Feynman .
1971 a spontaneously broken SU 2 w gauge theory with one doublet of (pseudo-) scalars was proven
to be renormalizable (to 2 loops) by Gerardus ’t Hooft after a long preparation-phase in
collaboration with Martinus Veltman .
1973 Abdus Salam and Jogesh Pati formulated a ’Unified Lepton-Hadron Symmetry and a Gauge
Theory of the Basic Interactions’, noting the implication of baryon-number instability in such a
framework .
1974 Howard Georgi and Sheldon Glashow presented a unified gauge theory based on the group SU 5,
’Unity of All Elementary Particle Forces’ .
a
→
a
I thank Nevena Ilieva for her thoughtful insisting on considering all contributions in particular
those due to Ludwig Faddeev .
20a
with Abdus Salam →
21
1974 Claudio Becchi, Alain Rouet and Raymond Stora formulated the algebraic anticommuting
structure at ’first ghost level’ of what became known as the BRST formalism , T for
Igor Tyutin ( and Efim Fradkin & ) .
back to our paper : [8] ’Unified Interactions of Leptons and Hadrons’ .
One aspect , which shall be singled out here, concerned the (eventual) role of the
gauge group SO10 ( its covering group D 5 or spin10 ) a .
SO10 did not fall into a seemingly infinite chain of possible gauge groups SOn ; n ≥ 10 , in order to
avoid mirror fermion families , but revealed itself as the largest possible group within such orthogonal
chains . This leaves unanswered – to this day – the question why ( not to speak of if)
there exist 3 families of 16-flavor spin 1/2 families b .
a
[13] H. Georgi (Harvard U.), 1975, ’Unified Gauge Theories’ , in *Coral Gables 1975, Proceedings,
Theories and Experiments In High Energy Physics*, New York 1975, 329-339.
b
Maybe here is a good place to remember : [14] F. Gürsey, Pierre Ramond (Yale U.),
P. Sikivie (Maryland U.), ’A Universal Gauge Theory Model Based on E6’, YALE-3075-118, Sep 1975,
Phys.Lett.B60 (1976) 177.
22
Let me mention 2 more papers from the time at Caltech :
[15] Harald Fritzsch, Peter Minkowski (Caltech) , ’Psi Resonances, Gluons and the Zweig Rule’,
CALT-68-492, Mar 1975, Nuovo Cim.A30 (1975) 393.
[16] ’Vector-Like Weak Currents, Massive Neutrinos, and Neutrino Beam Oscillations’, CALT-68-525,
(Received Nov 1975), Phys.Lett.B62 (1976) 72.
In [15] a hypothesis is layed out, that the gauge-boson degrees of freedom in QCD also materialize in
resonances , with clear simplifying dynamics , to be revealed, allowing a classification and
phenomenological identification . This expectations have – as yet – not been met , excepting very
definite results obtained in lattice simulations without (anti-)quarks , or with the latter all beeing very
heavy, with masses comparable to the one pertaining to the bottom quark .
In [16] the theme of neutrino flavors – light and heavy – and (anti-)neutrino oscillations is taken up and
embedded within a vectorlike form of chiral gauge interactions . You, Harald, were also very active in
communicating these results to Bruno Pontecorvo and beyond to convince first Felix Böhm, Peter Vogel
and collaborators at Caltech and then Robert Mössbauer, then director of the Institut Laue Langevin in
Grenoble, to perform a search for the oscillations, entailing a demanding precision of a possible detector
not too near to a reactor source.
The letter never arrived (according to Samoil Bilenky) and the first oscillation experiments yielded
null-results but
→
23
’Geduld bringt Rosen’ ( ’Patience brings roses’ )
from [17] S. Abe et al., KamLAND Collaboration, ’Precision Measurement of
Neutrino Oscillation Parameters with KamLAND’, Feb 2008, arXiv:0801.4589 [hep-ex]
24
3
From Caltech becoming a Professor first in Wuppertal 1977 then in Bern 1978
Time is (probably) getting short . Thus I select several papers from the above time with only short
comments possible .
[18] H. Fritzsch (Wuppertal U. & CERN) , 1978, ’Chromodynamics’, Talk in *Singapore 1978,
Proceedings, 1978 International Meeting On Frontier Of Physics, Vol.2*, Singapore 1978,
1005-1042.
[19] H. Fritzsch (CERN & Wuppertal U.) , ’Weak Interaction Mixing in the Six - Quark Theory’,
CERN-TH-2433, Dec 1977, Phys.Lett.B73 (1978) 317-322.
[20] Harald Fritzsch (Bern U.) , ’How to discover the b flavored baryons’, Print-79-0922 (BERN),
(Received Nov 1979), Phys.Lett.B90 (1980) 167.
In this paper you discuss the transition on the quark level b
→ c c s inside
Λ b = ( bud ) → J/ψ ( c c ) K p X , an ingenious inclusive decay channel .
25
4
From Bern to the LMU in Munich 1980 –
In 1980 you accepted an offer to the prestigious ’chair’ in theoretical physics at the Ludwig-Maximilian
University , a chair which had been occupied (shortly) by Ludwig Boltzmann and during the decisive
years of the discovery and development of quantum mechanics by Arnold Sommerfeld . This position
was accompanied by a participation within the Max Planck Institute for Physics ( Werner Heisenberg
Institute ) .
In assuming all these functions , you did not only publish 167 papers, as given in the e-archives, but
launched as promotor and key organizer several conferences and series :
a) International Conferences on Quantum Chromo Dynamics, in Montpellier, France, beginning 1985,
chaired by Stephan Narison.
b) Symposia in Oberwölz, Styria, Austria, jointly with W. Plessas and W. Schweiger, University of Graz ,
1998, 2003, 2006 .
c) International Conferences on Flavor Physics beginning 2001 every two years, 2007 at the Kavli
Institute for Theoretical Physics China, the Institute of Theoretical Physics (ITP), Chinese
Academy of Sciences, in Beijing, China .
d) Workshops on Flavor, 2005 in Chamonix, France and 2007 in Albufeira, Portugal – in the Hapimag
resorts .
26
So I shall select two areas of research , which mark – but in no way exhaust – your important
contributions until the present
i) maximal CP violating phase in quark flavor mixing ( the CKM matrix ) , with implications also for the
lepton sector . This idea you exposed in an original paper in 1979 .
[21] Harald Fritzsch (Munich U.) , Zhi-zhong Xing (Beijing, Inst. High Energy Phys.), ’Lepton mass
hierarchy and neutrino mixing’, Jan 2006, Phys.Lett.B634 (2006) 514-519, hep-ph/0601104 .
[22] Harald Fritzsch, Zhi-zhong Xing (Munich U.), ’Mass and flavor mixing schemes of quarks and
leptons’, LMU-99-16, Dec 1999, Prog.Part.Nucl.Phys.45 (2000) 1-81, hep-ph/9912358 .
→
ii) are natural constants really constant ?
[23] Harald Fritzsch (Munich U.), ’The Fundamental Constants in Physics and their Time Dependence’,
LMU-ASC-03-08, Feb 2008, arXiv:0802.0099 [hep-ph] . ( Only the most recent of a sries of papers is
cited here. )
For this work, for your ’oeuvre integral’ – as well as for your contributions to the construction of
QCD – you were awarded the ’Dirac Silver Medal for the Advancement of Theoretical Physics’ by
the University of New South Wales, Sydney, Australia, 15. April 2008 .
27
A comment to i) above :
You point out a particular way to parametrize the CKM (also neutrino-) mass matrix, restricting the
electroweak symmetry breaking to one (or two) doublet(s) of Higgs-scalar(s)
0
V CKM
−s u
cu
B
B
B su
@
0
=
(4)
=
C
C
0 C
A
1
cu
0
,
V
which is congruent with
0
0
1 0
C
C
−s C
A
c
c
s
cd
B
B
B sd
@
0
RJ (−iϕ)Rx(ϑ)
−s d
cd
0
0
1
C
C
0 C
A
1
Rz (ϑd)
s = sin ϑ
and to compare with the ( (u α ) d )
`
e
−iϕ
B
B
B 0
@
0
Rz (ϑu )
s u,d = sin ϑ u,d
(5)
0
1 0
∗
cd V cb
× ( (u α ) b ) ∗ unitary triangle or any other pair-triangle
´ −1 `
V ud V
∗
ub
+ V
∗
cd V cb
+
∗
V td V tb
´
= 0
→
28
from [24] E. Barberio et al., Heavy Flavor Averaging Group, ’Averages of b-hadron properties
at the end of 2006’, arXiv:0704.3575v1 [hep-ex]
(6)
PDG :
α ≡ φ2 =
“
99
+ 13
−8
”◦
↔
α ∼ ϕ = 90 ◦
Your derivation based on a particular texture with respect to the mass hierarchies and maximal CP
violation is not only remarkably correct but also shows an element of choice or even trial and errror
definitely outside the realm of a renormalizable field theory in flat 4-d space-time.
c1
5
Outlook
We hope that your creative mind, in scientific life and beyond will continue to bloom – in good health and
untouched by the professional change imposed by your retirement .
Thank you
r1
References
[1a] Rudolf Mössbauer, Proc. of ’Neutrino Astrophysics’ , Ringberg
Castle, Tegernsee 20.-24. Oct. 1997 , ed. by M.Altmann,
W. Hillebrandt, H.-T. Janka and G. Raffelt, TU München 1998 .
[2a] K. Meyenn, ’Wolfgang Pauli, Wissenschaftlicher Briefwechsel’,
Band IV, Brief [1614] und Anlage zum Brief, Teil II, Springer
Verlag 1999 .
[3a] Élie Cartan - Albert Einstein: Letters on Absolute Parallelism,
1929-1932, Robert Debever Editor, Princeton Univ. Press 1979.
[4a] George Pólya, ’The Pólya picture album : encounters of a
mathematician’ , G. L. Alexanderson ed., Birkhäuser Verlag.
Boston - Basel, 1987 .
r2
References
[5a] ’Wolfgang Pauli and Modern Physics’, Exhibition of the
ETH-Bibliothek at the occasion of the 100th birthday of
Wolfgang Pauli, April 6 to May 6, 2000 in the entrance hall of
the ETH Zurich, August 17 to September 26, 2000 at the CERN
in Geneva, May 25 to July 27, 2001 at the University Linz,
Virtual Exhibition, Rudolf Mumenthaler, Miriam Helvig ,
http://www.ethbib.ethz.ch/exhibit/pauli/index.html/ .
[6a] Charles Ehresmann, ’Les connexions différentiables dans un
fibré différentiable’, Colloque de Topologie (Espaces fibrés),
Centre Belge de Recherches Mathématiques, Bruxelles, 5.-8.
Juin 1950 .
r3
References
[7a] Shiing-Shen Chern, mimeographed lecture notes , Institute for
Advanced Study, Princeton ∼ 1951 ( unpublished ) .
[8a] H. Fritzsch, ’Flucht aus Leipzig’, Piper Verlag München - Zürich
1990 .
[1]
William A. Bardeen, H. Fritzsch and Murray Gell-Mann, ’Light
cone current algebra, π 0 decay, and e + e− annihilation’ ,
CERN-TH-1538, May 1972, presented at Topical Meeting on the
Outlook for Broken Conformal Symmetry in Elementary
Particle Physics, 4-5 May 1972, Frascati, Italy, hep-ph/0211388 .
r4
References
[2]
Harald Fritzsch and Murray Gell-Mann (CERN) ’Current
algebra: Quarks and what else?’, Proceedings of 16th
International Conference on High-Energy Physics, Batavia,
Illinois, 6-13 Sep 1972, published in eConf C720906V2 (1972)
135-165, also in Physics, Proceedings of the XVI International
Conference on High Chicago 1972 p.135
(J. D. Jackson, A. Roberts, eds.), hep-ph/0208010 .
[3]
H. Fritzsch, Murray Gell-Mann and H. Leutwyler (Caltech) ,
’Advantages of the Color Octet Gluon Picture’, CALT-68-409,
1973, Phys.Lett.B47 (1973) 365-368 .
r5
References
[4]
I. B. Khriplovich, ’Greens functions in theories with a
non-abelian gauge group’ , Yad. Fiz. 10 (1969) 409 , engl.
transl. Sov. J. Nucl. Phys. 10 (1970) 235 .
[5]
G. ’t Hooft, Remarks at the Colloquium on renormalization of
Yang-Mills fields and applications to particle physics, Marseille
1972 .
[6]
D. J. Gross and F. Wilczek, ’Ultraviolet behaviour of nonabelian
gauge theories’ , Phys. Rev. Lett. 30 (1973) 1343 .
[7]
D. Politzer, ’Reliable results for strong interactions ?’ ,
Phys. Rev. Lett. 30 (1973) 1346 .
r6
References
[8]
Harald Fritzsch and Peter Minkowski (Caltech), ’Unified
Interactions of Leptons and Hadrons’, CALT-68-467, (Received
Dec 1974), Annals Phys.93 (1975) 193-266 .
[9]
F.J. Hasert et al., Gargamelle Neutrino Collaboration,
’Observation of Neutrino Like Interactions Without Muon Or
Electron in the Gargamelle Neutrino Experiment’,
Phys.Lett.B46 (1973) 138-140 .
[10] J.J. Aubert et al., E598 Collaboration, ’Experimental
Observation of a Heavy Particle J’, COO-3069-271, 1974,
Phys.Rev.Lett.33 (1974) 1404-1406 .
r7
References
[11] J.E. Augustin et al., SLAC-SP-017 Collaboration, ’Discovery of
a Narrow Resonance in e+ e- Annihilation’, SLAC-PUB-1504,
Nov 1974, Phys.Rev.Lett.33 (1974) 1406-1408 .
[12] L.D. Faddeev, V.N. Popov (Steklov Math. Inst., St. Petersburg) ,
1967, ’Feynman Diagrams for the Yang-Mills Field’ ,
Phys.Lett.B25 (1967) 29-30 .
[13] H. Georgi (Harvard U.), 1975, ’Unified Gauge Theories’ , in
*Coral Gables 1975, Proceedings, Theories and Experiments In
High Energy Physics*, New York 1975, 329-339.
[14] F. Gürsey, Pierre Ramond (Yale U.) , P. Sikivie (Maryland U.) ,
’A Universal Gauge Theory Model Based on E6’,
YALE-3075-118, Sep 1975, Phys.Lett.B60 (1976) 177.
r8
References
[15] Harald Fritzsch, Peter Minkowski (Caltech) , ’Psi Resonances,
Gluons and the Zweig Rule’, CALT-68-492, Mar 1975, Nuovo
Cim.A30 (1975) 393.
[16] Harald Fritzsch, Peter Minkowski (Caltech) , ’Vector-Like Weak
Currents, Massive Neutrinos, and Neutrino Beam Oscillations’,
CALT-68-525, (Received Nov 1975), Phys.Lett.B62 (1976) 72.
[17] S. Abe et al., KamLAND Collaboration, ’Precision
Measurement of Neutrino Oscillation Parameters with
KamLAND’, Feb 2008, arXiv:0801.4589 [hep-ex] .
r9
References
[18] H. Fritzsch (Wuppertal U. & CERN) , 1978, ’Chromodynamics’,
Talk in *Singapore 1978, Proceedings, 1978 International
Meeting On Frontier Of Physics, Vol.2*, Singapore 1978,
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