Flavor Delicacies - Cornell University

Transcription

Flavor Delicacies
A Tour Through The Mysteries Of Matter
Matthias Neubert
Cornell University
Flavor Delicacies – p.1/45
High-Energy Physics
God-given units:
~=c=1
∆p · ∆x ∼ 1
⇒
∆E · ∆t ∼ 1
high-energy accelerators are giant microscopes
resolving tiniest distances
create conditions similar to those very shortly
after the birth of the Universe
100 GeV ↔ 10−15 m
1019 GeV ↔ 10−32 m
(where 1 GeV = 109 eV ≈ mass of proton)
Big Accelerators . . .
Collide the Tiniest Particles . . .
. . . as Physicists Watch in Awe
High-Energy Theory
Fundamental laws derived from few, simple guiding
principles:
High-Energy Theory
principles:
symmetries (gauge theories)
High-Energy Theory
principles:
simplicity and beauty
(few parameters, simple equations)
High-Energy Theory
principles:
naturalness (avoid fine-tuning)
High-Energy Theory
principles:
anarchy: everything not forbidden is allowed
High-Energy Theory
principles:
anarchy: everything not forbidden is allowed
Anarchy:
An utopian society of individuals who enjoy
complete freedom without government
These principles have brought us a long way . . .
The “Standard Model”
Grand Picture
Theory of Everything
(strings, branes, M-theory, ... ?)
GUT ?
extra dimensions ?
SUSY ?
extra dimensions ?
Standard Model
electro-weak
strong
electro-magnetic
(gluons)
(photon)
matter:
(3 generations)
Higgs (?)
weak
gravitational
(W,Z bosons)
[ bt bt bt ]
[ ντ ]
[ sc sc sc ]
[ νµ ]
[ du du du]
[ νe ]
quarks
leptons
(gravitons)
τ
µ
why replications ?
hierarchies ?
e
The Puzzle of Flavor
Most of Standard Model parameters are related to the
masses and mixings of fermions (Yukawa couplings)
quark and lepton masses:
mu ≈ 0.004 GeV
md ≈ 0.007 GeV
me ≈ 0.0005 GeV
m νe = ?
mc ≈ 1.3 GeV
ms ≈ 0.2 GeV
mµ ≈ 0.1 GeV
m νµ = ?
mt ≈ 170 GeV
mb ≈ 4.2 GeV
mτ ≈ 1.8 GeV
m ντ = ?
for neutrinos: ∆m2atm ∼ 3 · 10−21 GeV2 , ∆m2sol ∼ 3 · 10−23 GeV2
why so different ?
why families, hierarchical patterns ?
Why Do Light Particles Exist ?
A fundamental theory of elementary particle physics
should describe all phenomena until some high energy
scale Λ (“cutoff”) larger than all experimentally
accessible energies
But:
Relativity + Quantum Mechanics ⇒ Quantum Field Theory
In QFT, particles can aquire mass through interactions
with “nothing” (vacuum):
mass = bare mass + const·Λ
since this is a generic feature of QFT, it seems
that no light elementary particles should exist !?!?
. . . unless
. . . unless there is a symmetry that forbids such
quantum-generated masses
. . . unless there is a symmetry that forbids such
quantum-generated masses
Theorists Love Symmetries
(and the world needs them)
Gauge Symmetries
Photon (carrier of light) is massless as a consequence
of the gauge invariance of Maxwell’s theory of
electromagnetism
gauge transformation:
ψe (x) → eiχ(x) ψe (x) , Aµ (x) → Aµ (x) − ∂µ χ(x)
mass term mγ Aµ (x)Aµ (x) not invariant
⇒
mγ = 0
long-range forces
likewise: mgluon = 0 (strong interactions)
Chiral Symmetries
Physics knows the difference between left and right
gauge group: SUC (3) ⊗ SUL (2) ⊗ UY (1)
weak force (the SUL (2)) acts only on fermions
(spin- 12 particles) with left-handed chirality
mass term mf (f¯L fR + f¯R fL ) not gauge invariant
⇒
mf = 0
massless fermions
So now we know that all particles are massless...
Electroweak Symmetry Breaking
“Mass protection mechanism” only works as long as
symmetries are unbroken
Spontaneous symmetry breaking:
E<v
SUL (2) ⊗ UY (1) → Uem (1)
Higgs mechanism
broken below energy scale v ∼ 100 GeV
E<v
SUL (2) ⊗ UY (1) → Uem (1)
Higgs mechanism
massive gauge bosons:
mW ' 81 GeV, mZ ' 90 GeV ∼ v
√
E<v
SUL (2) ⊗ UY (1) → Uem (1)
Higgs mechanism
√
mW ' 81 GeV, mZ ' 90 GeV ∼ v
massive fermions: mf ∼ 100 GeV ???
E<v
SUL (2) ⊗ UY (1) → Uem (1)
Higgs mechanism
√
mW ' 81 GeV, mZ ' 90 GeV ∼ v
massive fermions: mf ∼ 100 GeV ???
⇒ top quark (mt ' 170 GeV) is only fermion
with a mass of the expected order of magnitude!
Hierarchy Problem
Standard mechanism of electroweak symmetry
breaking requires existence of a scalar particle (Higgs
boson) with mass mH ∼ 100 GeV, but a scalar mass is
not protected by gauge or chiral symmetries
expect mH ∼ Λ ∼ 1016 GeV, unless we are
willing to fine-tune the “bare” Higgs mass against
the mass aquired through quantum effects
(mass = bare mass + const·Λ)
Problem of EWSB: Why is mH Λ ?
The Higgs Story
Higgs desperately needed to achieve electroweak
symmetry breaking
much evidence for a relatively light Higgs from
electroweak precision data (LEP+SLD):
Preliminary
6
10
3
10
mH [GeV]
(5)
0.02761±0.00036
0.02738±0.00020
4
mH [GeV]
∆αhad =
10
2
10
3
2
10
3
41.5
41.6
0
σhad
[nb]
mH [GeV]
0.015
0.02
A0,l
FB
2
80.2
80.4
mW (LEP) [GeV]
Measurement
∆αhad= 0.02761 ± 0.00036
(5)
mH [GeV]
10
10
3
10
Preliminary
2
2
mH [GeV]
10
41.4
Excluded
10
2.5
ΓZ [GeV]
mH [GeV]
∆χ2
2.49
2
0
3
theory uncertainty
10
αs= 0.118 ± 0.002
mt= 174.3 ± 5.1 GeV
2
20.7
20.8
0
Rl
This reasoning has worked before . . .
Top-Quark Mass [GeV]
CDF
176.1 ± 6.6
D∅
172.1 ± 7.1
Average
174.3 ± 5.1
LEP1/SLD/νN/APV
169.0 ± 10.0
LEP1/SLD/νN/APV/mW
180.5 ± 10.0
125
150
175
200
mt [GeV]
. . . however, as soon as the Higgs is found, the
hierarchy problem is born!
Lore:
There must be New Physics at or below the TeV scale!
(1 TeV=1000 GeV)
Our Biggest Problem
Although we firmly believe that New Physics is just
around the corner, we see no trace of it in the data
Standard Model works too well!
Summer 2001
Measurement
1
0.5
(5)
Preliminary
68 % CL
U≡0
2 lept
sin θeff
mW
∆αhad(mZ)
0.02761 ± 0.00036
-.35
mZ [GeV]
91.1875 ± 0.0021
.03
ΓZ [GeV]
0
σhad [nb]
Rl
0,l
Afb
T
Γl
mH
mt
-1
-.48
1.60
20.767 ± 0.025
1.11
0.01714 ± 0.00095
.69
0.1465 ± 0.0033
-.54
0.21646 ± 0.00065
1.12
Rc
0.1719 ± 0.0031
-.12
0,b
0.0990 ± 0.0017
-2.90
Afb
0,c
0.0685 ± 0.0034
-1.71
Ab
0.922 ± 0.020
-.64
Ac
0.670 ± 0.026
.06
0.1513 ± 0.0021
1.47
Afb
-0.5
2.4952 ± 0.0023
41.540 ± 0.037
Rb
Al(Pτ)
0
Al(SLD)
2 lept
-1
-0.5
0
S
0.5
1
Pull
sin θeff (Qfb) 0.2324 ± 0.0012
(LEP)
mW
[GeV] 80.450 ± 0.039
mt [GeV]
(TEV)
mW
174.3 ± 5.1
[GeV] 80.454 ± 0.060
2
sin θW(νN)
0.2255 ± 0.0021
QW(Cs)
-72.50 ± 0.70
meas
fit
meas
(O
−O )/σ
-3 -2 -1 0 1 2 3
.86
1.32
-.30
.93
1.22
.56
-3 -2 -1 0 1 2 3
When will it crack ?
B physics ?
B physics ?
(g − 2)µ ?
B physics ?
(g − 2)µ ?
SUSY partners at LHC, LC ?
B physics ?
(g − 2)µ ?
black holes at LHC ?
B physics ?
(g − 2)µ ?
black holes at LHC ?
... ?
Finding New Physics
Theory
New Physics
No/little experimental guidance
Examples:
general relativity
heavy quarks (Kobayashi–Maskawa)
SUSY, extra dimensions, strings, . . . ?
Finding New Physics
Theory
New Physics
Energy Frontier
Mass production of new particles
Examples:
b quarks at CESR, DORIS
W , Z bosons at LEP
top quarks at Tevatron
Higgs bosons, SUSY (s)particles at LHC, LC ?
Finding New Physics
Theory
New Physics
Energy Frontier
High Luminosity
Precision measurements (effects of virtual particles)
Examples:
charm quark (K–K̄ mixing)
top quark (B–B̄ mixing, EW precision data)
Higgs bosons (EW precision) ?
SUSY (s)particles (g − 2 of muon) ?
Yukawa Couplings
Couplings of Higgs field to fundamental fermions
(quarks and leptons) determines their masses
and
√
flavor-changing interactions (hh0 i = v/ 2 after
EWSB):
LY =
3
X
i,j=1
λij
d
h+ ūiL djR
+
h0 d¯iL djR
+ λij
u
h0∗ ūiL ujR
−
h− d¯iL ujR
+ h.c.
Not all parameters of the complex 3 × 3 matrices λij
d
and λij
u are observable (field redefinitions)
difficulty for model building, since Yukawa
couplings cannot be derived even with perfect
data!
What can be measured are masses and flavor mixings:
Vub Vtd
up down
10
−5
strange
10
−4
10
charm
−3
0.01
Vts
Vcb
Vcd
Vus
bottom
Vtb
Vcs
Vud
top
0.1
1
2 mq
v
Importance of quark flavor mixings (CKM matrix):
only source of flavor-changing interactions in SM
only source of CP-violating interactions in SM
Cabibbo-Kobayashi-Maskawa Matrix
Two strategies:
precision measurements of CKM elements in
weak decays of hadrons (bound states of quarks)
searches for new flavor-changing/CP-violating
interactions
Status of CKM measurements:

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vud: nuclear β decay
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vus: semileptonic K → πeν decay
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vub: semileptonic B → πlν decay
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vcd: charm production off d quarks in DIS
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vcs: semileptonic D → Keν decay
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vcb: semileptonic B → D ∗ lν decay
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vtd : Bd –B̄d mixing
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vts : Bs –B̄s mixing
Two strategies:
interactions

VCKM
 Vud


=
 Vcd


Vtd
Vus
Vub
Vcs
Vcb
Vts
Vtb



0.975

 in magn. 
 ≈  0.221




0.005

0.221
0.003
0.975

0.040 

1
0.040
Vtb : top decay, unitarity
Semileptonic decay:
l
−
ν
Vub W
b
u
π+
B0
d
Mixing:
Vtd*
Vtb
b
B
0
d
W
t
t
W
d
Vtd*
B
0
b
Vtb
theoretical uncertainties from quarks ↔ hadrons
binding effects
Wolfenstein Parameterization
Hierarchy of CKM matrix is made explicit by writing:

VCKM


=

1−
λ2
2
−λ
Aλ3 (1 − ρ̄ − iη̄)
λ
1−
λ2
2
2
−Aλ
Aλ3 (ρ̄ − iη̄)
Aλ2
1



 + O(λ4 )

accurately known: |Vus | and |Vcb|
(λ = 0.224 ± 0.003 and A = 0.82 ± 0.04)
more uncertain: |Vub| and |Vtd | (ρ̄ and η̄)
with standard phase conventions, complex entries
appear in smallest matrix elements (requires ≥ 3
generations) ⇒ CP violation!
Unitarity Triangle
Experimental knowledge about smallest entries can be
summarized by displaying the unitarity relation
Vub∗ Vud + Vcb∗ Vcd + Vtb∗ Vtd = 0
as a triangle in the complex (ρ̄, η̄) plane:
(ρ,η)
α
~Vtd
*
ub
~V
CP Violation
γ
(0,0)
β
(1,0)
CP violation results from a non-vanishing area!
CP Violation
One of the most intriguing aspects of physics, which
links particle physics with cosmology
Microcosmos:
fundamental difference between the interactions
of matter and anti-matter
microscopic violation of time-reversal invariance
(CPT theorem)
Macrocosmos:
baryon asymmetry in the Universe ⇒ our
existence!
What is CP Violation ?
Most interactions in Nature are invariant under parity
...
but the weak force differentiates left from right!
only left-handed fermions and right-handed
anti-fermions take part in the weak interactions
a CP transformation replaces left ↔ right and
matter ↔ anti-matter
If CP were conserved, there would be no way of
explaining to an alien the difference between
matter and anti-matter.
matter and anti-matter. In that case, shaking hand
with an alien could be potentially disastrous!
matter and anti-matter. In that case, shaking hand
with an alien could be potentially disastrous!
Since CP is not conserved, shaking hand with an
alien is a safe endeavor . . .
Short History of CP violation
1964: CP violation in K ↔ K̄ mixing
(tiny effect: ≈ 1.6 · 10−3 )
1999: CP violation in K → ππ decay
(tiny effect: 0 / ≈ 1.7 · 10−3 )
2001: CP violation in B, B̄ → J/ψ KS decay
(large effect: sin 2β = 0.79 ± 0.10)
Pattern of CP violation in mixing and weak decay of
kaons, charm and B mesons is correctly predicted by
the SM and relects the hierarchy of the CKM matrix!
Constraints on the Unitarity Triangle
K from CP violation in K–K̄ mixing:
due to CP violation, the √
long-lived strange meson
|KL i ≈ (|K 0 i − |K̄ 0 i)/ 2 is not exactly a CP
eigenstate and so can decay into two pions
K is sensitive to Im[(Vtd∗ Vts )2 ]
Vtd*
Vts
s
K
0
d
W
t
t
W
d
Vtd*
K
0
s
Vts
|Vub/Vcb | from semileptonic B decays:
ratio can be measured by comparing semileptonic
b → ulν and b → clν decays
l
ν
Vub W
b
B
u
0
−
π+
d
∆md,s from Bd,s –B̄d,s mixing:
B–B̄ mixing amplitudes are dominated by virtual
production of top quarks
∗
∆md,s is sensitive to |Vtd,ts
Vtb |2
Vtd*
Vtb
b
B0
d
W
t
t
W
d
Vtd*
B
0
b
Vtb
Experimental Results (2000)
1
∆md
∆ms/∆md
∆md
η
|εK|
0
|Vub/Vcb|
|εK|
-1
CKM
fitter
-1
0
1
2
ρ
Determination of sin 2β
In B decays into a CP eigenstate fCP , observable CP
asymmetries can arise from the interference of the
amplitudes for B–B̄ mixing and decay:
mixing ~ e -2i β
B0
B0
A
denote: λ = e-2i β A
A
A
fCP
Resulting time-dependent CP asymmetry:
Γ(B̄ 0 (t) → fCP ) − Γ(B 0 (t) → fCP )
ACP (t) =
Γ(B̄ 0 (t) → fCP ) + Γ(B 0 (t) → fCP )
Golden Modes B → J/ψ K
If the decay amplitude itself is real, a theoretically
“clean” measurement of sin 2β can be performed:
B0 → J/ψKS0
B0 → ψ(2S)KS0
B → χc1KS0
0
50
a)
0
B tags
0
b)
−0
50
BaBar (2001)
sin2φ1 . sin(∆md∆t)
ACP (t) = ±sin 2β · sin(∆md t)
(a) Combined
1
0
Belle (2001)
-1
B tags
−
(b) (cc)K
S (ξf = −1)
0
0.5
1/N.dN/d(∆t)
0
-1
B → J/ψKL0
0
d)
(c) J/ψKL (ξf = +1)
0
e)
−0
Asymmetry
0
B tags
0.10
1
0
0.00
-8
-1
B tags
25
q.ξf = −1
0.20
c)
-0.5
25
q.ξf = +1
1
-4
0
∆t (ps)
4
8
(d) Non-CP sample
0
0.5
f)
1
0
-0.5
-1
-5
0
5
∆t (ps)
-8
-4
0
∆t (ps)
4
8
Summary of Constraints (2001)
1
∆md
∆ms/∆md
η
|εK|
sin 2βWA
0
|Vub/Vcb|
|εK|
-1
CKM
fitter
-1
0
1
2
ρ
This has established the existence of a CP-violating
phase in the top sector (Im(Vtd ) 6= 0)
Results at 95% confidence level:
ρ̄ = 0.21 ± 0.12
sin 2β = 0.74 ± 0.15
η̄ = 0.38 ± 0.11
sin 2α = −0.14 ± 0.57
γ = 61◦ ± 16◦
after obtaining a consistent picture of CP
violation in the top sector, the next step must be
to explore the complex phase γ = arg(Vub∗ ) in the
bottom sector
Rare Hadronic B Decays
γ can be probed via the tree–penguin interference in
rare hadronic decays B → πK, ππ, . . .
W
u
b
W
s,d
b
t
u
s,d
g,Z,γ
q
q
B → πK
B → ππ
Tree
Penguin
Ratio
∗
Vub Vus
∼ λ4 e−iγ
Vtb Vts∗ ∼ λ2
|T /P | ∼ 0.2
∗ ∼ λ3 e−iγ
Vub Vud
Vtb Vtd∗ ∼ λ3 eiβ
|P/T | ∼ 0.3
information from CP asymmetries (∼ sin γ) and
CP-averaged branching fractions (∼ cos γ)
The Challenge
QCD, the marvellous theory of the strong interactions, has a split
personality. It explains both “hard” and “soft” phenomena, the
softer ones being the hardest.
(Y. Dokshitzer)
high energies (short distances) ⇔ weak coupling (asymptotic freedom)
low energies (long distances) ⇔ strong coupling (confinement)
Different strategies exist for determining the relevant
hadronic matrix elements:
Hadronic Matrix Elements
General Amplitude Parameterizations:
Isospin and SU(3) Flavor Symmetry
Amplitude Triangles, Quadrangles, ...
Maximal Use of Measurements
QCD-Based Calculations:
QCD Factorization (HQL)
pQCD, QCD Sum Rules, Lattice
Maximal Use of Theory (ambitious!)
various combinations
QCD Factorization
+
Fleischer-Mannel Bound
Neubert-Rosner Bound
Bounds -> Determinations
QCD Factorization
+
Phenom. Penguin Amplitude
Charming Penguins, ...
Two Examples
Measurement of
Γ(B ± → π ± K 0 )
,
R∗ =
±
0
±
2Γ(B → π K )
and of the time-dependent CP asymmetry Sππ in
B → π + π − decays, provide powerful constraints in
the (ρ̄, η̄) plane:
0.6
0.6
1.0
R*=0.8
PSfrag replacements
0.4
0.6
0.2
0.2
0
0
η̄
η̄
0.4
1.2
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6 -0.4 -0.2
PSfrag replacements
0
ρ̄
0.2
0.4
0.6
Sππ : 0
-0.3
-0.6
-0.9
-0.6
-0.6 -0.4 -0.2
0
0.2
0.4
0.6
ρ̄
Rare and Forbidden Decays
Systematic study of rare B decays is richer than
unitarity triangle physics
many clean tests for New Physics possible
processes that are strongly suppressed or
forbidden in the Standard Model offer a farther
reach than the relatively abundant processes used
for CKM physics
γ
b
Example (a “beautiful candle”):
W
s
=
b
s
+ New Physics
t
γ
Rare Decays at Super B-Factories
Selective list of interesting modes:
Decay Mode
Branching
Fractions
B → Xs γ
(3.3 ± 0.3) × 10−4
B → K ∗γ
B → ρ(ω)γ
B → Xs µ+ µ−
B → Xs e+ e−
B → K ∗ µ+ µ−
B → K ∗ e+ e−
B → Xs ν ν̄
B → K ∗ ν̄
B → τν
B → µν
Bd0 → τ + τ −
Bs0 → µ+ µ−
Bd0 → µ+ µ−
B 0 → γγ
5 × 10−5
2 × 10−6
(6.0 ± 1.5) × 10−6
(2 ± 1) × 10−6
e+ e− B-Factories
BaBar
Super-BaBar
Belle
(0.5 ab−1 )
(10 ab−1 )
11K
220K
1.7K
34K
(B tagged) (B tagged)
170
25K
6K
120K
300
6K
3.6K
300
6K
350
7K
60–150 2.2K/4.5K 665/4.2K
120
2.4K
150
3K
8
160
1.5
30
17
350
8
150
Hadron Collider Experiments
CDF
BTeV
ATLAS
D0
LHC-b
CMS
−1
7
(2 fb )
(10 s)
(1 year)
(4.1 ± 0.9) × 10−5
5 × 10−6
5 × 10−5
1.6 × 10−7
10−7
10−9
5/1.5–6
−11
8 × 10
0/0
−8
10
5/11
1/2
9/7
0.7/0.5
0.4
8
Summary
The physics of flavor is the physics of matter
Summary
The puzzles of flavor physics are fundamental
and relate to virtually any open question in
high-energy physics:
Summary
origin of mass ?
Summary
origin of mass ?
origin of families and hierarchies ?
Summary
origin of mass ?
origin of CP violation ?
Summary
origin of mass ?
current and future B-physics program is vital to
answering these questions
Summary
origin of mass ?
current and future B-physics program is vital to
answering these questions
.
.
.
f
f
o
g
n
i
k
a
t
t
s
u
j
s
i
d
l
e
fi
s
i
Th

Flavor Delicacies - Cornell University

Transcription

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