CKM Matrix

1. CKM Matrix 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. Symmetryis 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 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 Symmetry in Physics Examples of Symmetry Operations

4. +  Three Important Discrete Symmetries • Parity, P • Parity reflects a system through the origin. Convertsright-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? Intuitively… • C is violated • P is violated • T is violated Since early universe… “Alice effect” Boltzmann and S=klnW

6. C and P violation! • 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 We can test this in 1st generation meson system: Pions

7. CP and T violation! CP violation T violation K0 p+p- • 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? We can test this in 2nd generation meson system: Kaons Need 3rd generation system: B-mesons and B-factories

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

9. Gauge structure of the SM Gauge structure was verifiedin 1990s at … • LEP (ALEPH, DELPHI, L3, OPAL) • SLAC (SLD) • Fermilab (CDF, D0) Sin2qw=0.23098±0.00026 Mz=90.1876±0.0021GeV Mw=80.451±0.039GeV SM Prediction: 1-(Mw/Mz)2 = Sin2qw

10. W- W- W- W- b e- b e- u c ne nm 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 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 as3 real parametersA, l, randone complex phaseh. The 4 parameters are given by:

24. (r,h)constraints: Pre-BaBarian times b 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 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. CKM Matrix Status Vud/Vud 0.1% Vus/Vus =1% Vub/Vub 25% l 1 l e eig B n n n K n p p  Free/bound Vcd/Vcd 7% Vcs/Vcs =15% Vcb/Vcb 5% l l B D n n l D D n K p Vtd/Vtd =36% Vtb/Vtb 29% Vts/Vts 39% 1 eib 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 = 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!

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