1. CKM Matrix If Universe is the Answer, What is the Question?
Matter-Antimatter Asymmetry
in the Laboratory
and in the Universe
If Universe is the Answer, What is the Question?

2. The Question is … “What happened to all the anti-matter?”
Outline
Symmetry in Physics
CKM
B physics at BaBar and Belle
B physics at Fermilab

3. Examples of Symmetry Operations
Symmetry in Physics
Symmetry is the most crucial concepts in Physics.
Symmetry principles dictate the basic laws of Physics, and define the fundamental forces of Nature.
Symmetries are closely linked to the particular dynamics of the system:
E.g., strong and EM interactions conserve C, P, and T. But, weak interactions violate all of them.
Different kinds of symmetries:
Continuous or Discrete
Global or Local
Dynamical
Internal
Examples of Symmetry Operations
Translation in Space
Translation in Time
Rotation in Space
Lorentz Transformation
Reflection of Space (P)
Charge Conjugation (C)
Reversal of Time (T)
Interchange of Identical
Particles
Change of Q.M. Phase
Gauge Transformations

4. Three Important Discrete Symmetries
Parity, P
Parity reflects a system through the origin. Converts right-handed coordinate systems to left-handed ones.
Vectors change sign but axial vectors remain unchanged
x  -x L  L
Charge Conjugation, C
Charge conjugation turns a particle into its anti-particle
e+  e- K-  K+ g  g
Time Reversal, T
Changes the direction of motion of particles in time
t  -t
CPT theorem
One of the most important and generally valid theorems in quantum field theory.
All interactions are invariant under combined C, P and T transformations.
Implies particle and anti-particle have equal masses and lifetimes + 

5. C, P, T violation? C is violated P is violated T is violated
Intuitively…
C is violated
P is violated
T is violated
Since early universe…
“Alice effect”
Boltzmann and S=klnW

6. We can test this in 1st generation meson system: Pions
C and P violation! CP
We can test this in 1st generation meson system: Pions
Experiments show that only circled ones exist in Nature C and P are both maximally violated!
But, CP and T seems to be conserved, or is it?

7. CP and T violation! For 37 years, CP violation involve Kaons only!
K0  p+ p-
We can test this in 2nd generation meson system: Kaons
For 37 years, CP violation involve Kaons only!
Is CP violation a general property of the SM or is it simply an accident to the Kaons only?
Need 3rd generation system: B-mesons and B-factories

8. The Standard Model (SM)
Electroweak physics as SU(2) x U(1) gauge theory
Gauge representations of quarks and leptons
Three generations of “ordinary” matter
Inward Bound

9. Gauge structure of the SM
Sin2qw= ±
Mw=80.451±0.039GeV
Mz= ±0.0021GeV
Gauge structure was verified in 1990s at …
LEP (ALEPH, DELPHI, L3, OPAL)
SLAC (SLD)
Fermilab (CDF, D0)
SM Prediction:
1-(Mw/Mz)2
= Sin2qw

10. Flavor structure of the SM
The SM interaction can change the flavor of quarks and leptons
- Leptons only change in the same generation  Lepton flavor conservation
- Quarks can change into a quark of any generation  Quark mixing e- W- ne e- W- nm b W- c b W- u
V = CKM matrix V V

11. CP Violation in the Standard Model
The CKM matrix is a 33 complex unitary matrix
Requires 4 independent parameters to describe it:
3 real numbers
1 complex phase
The existence of a complex phase is what gives rise to CP violation
If there were only 2 quark generations, the corresponding 22 matrix would be all real  No CP violation
Some implications:
Because we want to see effects due to complex phase, CP violating observables are the result of interference between different amplitudes
All three quark generations must be involved in the process
All CP violating observables are dependent upon one complex phase
CP violation is built in to the SM with 3 generations

12. CKM Matrix
Original 2X2 Cabibbo angle
CKM 3X3 Matrix

18. Review of CKM Matrix
Review

19.   

21. Unitary Triangle
Unitarity of V implies e.g., VudV*ub + VcdV*cb + VtdV*tb =0
 this relationship can be depicted as a triangle in the complex plane
Non-zero CKM angles  CP violation
All CKM angles can be
measured from B decays
Nomenclature
BaBar: a, b, g
Belle: f2, f1, f3

22. CKM Matrix
V can be written as 3 real parameters A, l, r and one complex phase h.
The 4 parameters are given by:

24. (r,h) constraints: Pre-BaBarian times
B factories
measure
CKM angles
Bd mixing  Dmd
B rln  Vub , D*ln  Vcb
Bs mixing  Dms / Dmd
Kaon mixing & decays  eK
Blue blobs, 95% CL
estimates of a set of
theoretical models

29. The CKM Matrix mass eigenstates weak eigenstates
The parameters of the Standard Electroweak Model are:
The 4 quark mixing parameters
reside in CKM matrix
& fermion masses and mixings
mass eigenstates
weak
eigenstates
In SM , A, ,  are fundamental parameters
Does the CKM fully explain quark mixing? CP Violation?
To detect new physics in flavor changing sector must know CKM well
Must overdetermine the magnitude and phase of each element

30. 1 1 CKM Matrix Status eig eib Vud/Vud 0.1% Vus/Vus =1% Vub/Vub 25%l e l
eig B n n n K n p p 
Free/bound
Vcd/Vcd 7%
Vcs/Vcs =15%
Vcb/Vcb 5% l l D n B n l D D n K p
Vtd/Vtd =36%
Vts/Vts 39%
Vtb/Vtb 29%
eib 1 Bd Bd Bs Bs
Vud, Vus and Vcb are the best determined due to flavor symmetries: I, SU(3), HQS. Charm (Vcd & Vcs) and rest of the beauty sector (Vub, Vtd, Vts) are poorly determined. Theoretical errors on hadronic matrix elements dominate.

31. CKM Matrix Measurements
|Vud|2 + |Vus|2 + |Vub|2 = = 1 ??
The normality test fails at 2.2
|Vcd|2 + |Vcs|2 + |Vcb|2 = = 1 ??
The error is too large for a meaningful test!

32. References
Transparencies from:
Dr. S.W. Yang
Prof. Tom Browders …