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?

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

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

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 + 

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

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?

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

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

Gauge structure of the SM Sin2qw=0.23098±0.00026 Mw=80.451±0.039GeV Mz=90.1876±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

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

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

CKM Matrix Original 2X2 Cabibbo angle CKM 3X3 Matrix

Review of CKM Matrix Review

  

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

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

(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

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

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.

CKM Matrix Measurements |Vud|2 + |Vus|2 + |Vub|2 = 0.9959+-0.0019 = 1 ?? The normality test fails at 2.2 |Vcd|2 + |Vcs|2 + |Vcb|2 = 1.13+-0.33 = 1 ?? The error is too large for a meaningful test!

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