1. CERN, October 2008PDG Collaboration Meeting1 The CKM Quark-Mixing Matrix Revised February 2008 A. Ceccucci (CERN), Z. Ligeti (LBNL) and Y. Sakai (KEK)

2. CERN, October 2008PDG Collaboration Meeting2 Definitions The charged current W ± interaction couples to the physical left- handed quarks as The CKM matrix can be parameterized by three mixing angles (s 12,s 23,s 13 ) angle and one CP-violating phase (  ) The hierarchical structure makes convenient to define: These relations ensure that the CKM matrix written in terms of A,,  and  is unitary to all orders in and that (  +i  )=-(V ud V ub *)/(V cd V cb *) is phase-convention independent

3. CERN, October 2008PDG Collaboration Meeting3 Magnitude of the CKM elements (I) |V ud | –From: Superallowed 0 +  0 + Nuclear transitions: |V ud | = 0.97418 ± 0.00027 –Latest neutron lifetime measurement is off by 6.5  w.r.t. average |V us | –Average of different semi-leptonic kaon decays: |V us | = 0.2255 ± 0.0019 –Precision is limited by the accuracy on f + (0) (theory), calculations differ up to 2% (but lattice agrees with historical determination from Roos- Leutwyler) |V cd | –Best precision still obtained from the ratio of double-muon to single-muon production in  / interactions |V cd | = 0.230 ± 0.011 |V cs | –Unquenched QCD calculations of the D s meson decay constant and D form factor allow one to extract V cs from semi-leptonic and leptonic decays. The average gives: |V cs |=1.04 ± 0.06 Highlight

4. CERN, October 2008PDG Collaboration Meeting4 Magnitude of the CKM elements (II) |V cb | –From the average of inclusive and exclusive determination the V cb V ub mini review determines (with inflated errors): |V cb | = (41.2 ± 1.1 )  10 -3 |V ub | –Determination is quite involved. Average from V cb V ub mini rev: |V ub | = (3.93 ± 0.36 )  10 -3 –To watch: determinations from inclusive and exclusive decays tend to move apart |V tb | – From single top production (w/o unitarity assumption): |V tb |> 0.74 (95% CL) |V td | and |V ts | –|V ts | now measured from B s -mixing –precise |V td /V ts | = 0.209 ± 0.001 ± 0.006 –Error already dominated by theory: Highlight

5. CERN, October 2008PDG Collaboration Meeting5 CKM Angles Chamonium modes: Sin 2  = 0.681 ± 0.025 From B  decays:  =(88 +6 -5 )˚ From tree decays (GLW, ADS, Dalitz):  = (77 +30 -32 )˚ V ud V ub * + V cd V cb *+V tb V tb *=0

6. CERN, October 2008PDG Collaboration Meeting6 Unitarity and Global Fit in SM Unitarity Checks: |V ud | 2 +|V us | 2 +|V ub | 2 = 0.9999 ± 0.0011 (1 st row) |V cd | 2 +|V cs | 2 +|V cb | 2 = 1.136 ± 0.125 (2 nd row) |V ud | 2 +|V cd | 2 +|V td | 2 = 1.002 ± 0.005 (1 st column) |V us | 2 +|V cs | 2 +|V ts | 2 = 1.134 ± 0.125 (2 nd column) Global Fit:  0.2257 +0.0009 -0.0010 A= 0.814 +0.021 -0.022  =0.135 +0.031 -0.016  =0.349 +0.015 -0.017 J=(3.05 +0.19 -0.20 )  10 -5

7. CERN, October 2008PDG Collaboration Meeting7 Constraints on the   plane Highlight

8. CERN, October 2008PDG Collaboration Meeting8 Puzzles Hints of large B s mixing phase  A= A (K +/-   )   A (K +/-  -/+ ) =0.148 ± 0.028 Sin (2  eff  (from penguin dominated modes) is moving closer to Sin (2  measured from the  Charmonium modes V ub exclusive vs. inclusive determinations Frequentistic vs. Bayesian Statistics Treatment of theoretical “systematics” Use of input hadronic parameters (e.g. pre-dictions vs. post- dictions) Consensus on lattice results ( e.g. f Ds from HPQCD and tension in D + s  l   decays) Issues (some)

9. CERN, October 2008PDG Collaboration Meeting9 Outlook Present / Near Future –B factories –Tevatron –LHC Future –Rare K Decays ( K  ? –Super Flavour Factories?