1. A big success with more than 200 participants

2. AIM OF THE WORKSHOP Make an overall status of our knowledge of the CKM parameters at the end of the era of CLEO, LEP, SLD, TeVatron I (reach consensus to start from common base) Try to define priorities for theoretical developments and future measurements : - in a short timescale (B-Factories/TeVatron II) - in a longer timescale (bridging today LHC)

3. Working Group I : V ub, V cb and Lifetimes Working Group II : V td, V ts Working Group III : CKM Fits Lattice Data Group (LDG) Forum on Averaging (for PDG + users) Talks on : Charm and Kaon Physics Structure of the Workshop

4. 1- 2 /2 A 3 (  i  )  1- 2 /2A 2 A 3 (1-  -i  ) - A 2 1 u c t dsb b d, s b V td,V ts B Oscillations d, s V tb c,u B decays b V ub,V cb The CKM Matrix In the Wolfenstein parameterization 4 parameters :, A, 

6. To be continued at B-Factories and TeVatron Theoretical assumptions Theoretical uncertainties Possible measurements Theory UT parameters Measurements Error Meaning (discussion) Statistical Methods to extract UT parameters Analysis Methods Analysis Systematic

7. WORKING GROUP I Lifetimes V cb V ub c,u B decays b V ub,V cb

8. Inclusive Determination of V cb b c l V cb Average by LEP Working Groups BR sl +  b V cb

9. Determination of V cb limited by theoretical uncertainties ….. The expression of V cb in the low scale running HQ masses formalism (as an example)* Can these parameters be determined experimentally ? V cb = 0.0415  ( 1 - 0.012  2   0.010 m b + 0.006  s + 0.007  mbmb (  Fermi movement inside the hadron) ( also named  ) 22 V cb    m b  pert  * In “Upsilon expansion” formalism :

10. From CLEO measurements

12. Other experiments should perform this analysis …….

13. Value agreed at the end of the Workshop Part of theoretical error on V cb becomes experimental from the determination of  2   and m b V cb (inclusive)= ( 40.7 ± 0.7 ± 0.8 ) 10 -3 It was ± 2.0 and of theo. origin !

14. Exclusive Determination of V cb G(w) contains kinematics factors and is known (also  1 and   ) F(w) is the form factor describing the B  D * transition At zero recoil (w=1), as M Q  F(1)  1 Strategy : Measure d  /dw and extrapolate to w=1 to extract F(1) V cb

15. Syst. dominated by the knowledge of the D** (for LEP) F(1) |V cb | 2 22

16. F(1) At the Workshop agreement on F(1) = 0.91±0.04 (Gauss.) 3 determinations

17. What’s next to improve V cb Experimental side: More and new moment analyses B-factories can perform both exclusive and inclusive analyses Theory side : More work on the theory for the  2 ,m b extraction Unquenched F(1) calculations Studies of eventual correlation between inclusive and excluive determinations Form factors measurements in B  D*l

18. Combing the inclusive and the exclusive measurements : V cb = (41.8 ± 1.0 ) 10 -3

19. Challenge measurement from LEP Inclusive determination of Vub Using several discriminant variables to distinguish between the transitions : b  c b  u V ub B  X u l

20. Results from all the LEP experiments

22. At the Workshop we agreed on V ub (inclusive) = (4.09 ± 0.46 ± 0.36) 10 -3 New determination

23. Exclusive determination of Vub B   l V ub = (3.68 ± 0.55 +0.28 (syst.))10 -3 (in ISGW2 Model) - 0.37 V ub = (3.68 ± 0.14 +0.21 (syst.)± 0.55(theo.))10 -3 - 0.29 Babar CLEO Important theoretical uncertainties from different models NOW, Lattice QCD calculations start to be precise

24. What’s next to improve V ub Experimental side: B-factories can perform inclusive/end-point/exclusive analyses Theory side : More work on the theory for the extraction of inclusive/end-point analyses Lattice QCD calculations for exclusive form factors Correlations between the different V ub determinations Correspondence between D   l and B   l

25. All lifetimes of weakly decaying B hadrons have been precisely measured Very important test of the B decay dynamics Lifetimes

26.  (B 0 d ) = 1.543 ± 0.015 ps ( 1.0%)  (B + ) = 1.658 ± 0.014 ps ( 0.9%)  (B 0 s ) = 1.464 ± 0.057 ps ( 3.9%)  (  B ) = 1.208 ± 0.051 ps ( 4.2%) Averages from LEP/SLD/Tevatron (+ B-Factories) The hierarchy was correctly predicted !  (B + )/  (B 0 ) about 5  effect in agreement with theory  (B 0 s )/  (B 0 ) about 1  effect in agreement with theory Is there a problem for  B ?

27. Theory News…..

28. Next improvements :  (B + )/  (B 0 ) from B factories But more important  (B 0 s ) and  (  B ) from TeVatron …. and  B B c,  c Experiment side: Theory side: Improvements of the Lattice QCD calculations

29. mdmd msms WORKING GROUP II Radiative and Leptonic B decays Rare K decays d, s b b V td,V ts B Oscillations

30. Present Future

31. Study of the time dependent behaviour of the Oscillation B 0 - B 0 TextBook Plot

32. Before B-Factories mdmd LEP/SLD/CDF precisely measured the  m d frequency  m d = 0.498 ± 0.013 ps -1 LEP/SLD/CDF (2.6 %) B-factories confirmed the value improving the precision by a factor 2  m d = 0.496 ± 0.007 ps -1 LEP/SLD/CDF/B-factories (1.4%) The final B-factories precision will be about 1% ( 0.004 ps -1 )

33. Combination of different limits using the amplitude methods Combination using A and  A msms  m s excluded at 95% CL A + 1.645  A < 1 At given  m s A = 0 no oscillation A = 1 oscillation Sensitivity same relation with A = 0 1.645  A < 1 Measurement of A at each  m s

34.  m s > 14.9 ps -1 at 95% CL Sensitivity at 19.3 ps -1 “Hint of signal” at  m s =17.5 ps -1 but with significance at 1.  Expectation in The Standard Model  m s [14.1-21.6] ps -1 at 95% CL

39. Very important achievement. The  m s information has to be included in the CKM Fits using the Likelihood Method. ( in the past this was a source of differences between the groups performing CKM fits)

40. WORKING GROUP III CKM Fits Strategies the angle  V ud,V us Two subgroups :

41. 1- 2 /2 A 3 (  i  )  1- 2 /2A 2 A 3 (1-  -i  ) - A 2 1 u c t dsb b d, s b V td,V ts B Oscillations d, s V tb c,u B decays b V ub,V cb The CKM Matrix In the Wolfenstein parameterization 4 parameters :, A, 

42. b  u / b  c | V ub \ V ub | 2  2 +    m d |V td | 2 f B d 2 B B d f(m t )  2 +    m d \  m d |V td \ V td | 2 f Bd 2 B B d \ f B s 2 B B s  2 +    K f(A,  B K..) 

44. Ex : B K = 0.87 ± 0.06 (gaus) ± 0.13 (theo.) Treatment of the inputs Rfit Bayesian p.d.f. from convolution (sum in quadrature) Likelihood Delta Likelihood Likelihood obtained summing linearly the two errors Delta Likelihood [0.68-1.06] [0.76-0.98]At 68% CL

47. Where the difference is coming from ? Difference comes from how the inputs are treated : At present mainly from: F(1), inclusive V cb, B K Breakdown of the error is important The splitting between Gaussian and theoretical error is crucial and somehow arbitrary Results of the Workshop : theoretical error reduced and origin of the error better defined  K ( V cb 4 * B K )

48. Differences are small and physics conclusions quantitatively the same

49. The difference ( which is by the way small ) on the CKM quantities coming from the different methods, is essentially due to the different treatment of the theoretical errors Using Likelihoods as obtained from linear sum of Exp.+Theo. errors Using Likelihoods as obtained from convolution of Exp. Theo. errors Both methods use the same likelihood Differences almost disappears

50. Another example with sin2  (without  K )

51.  [0.14-0.30]  [0.24-0.39] at 95%CL  = 0.220 ± 0.040  = 0.315 ± 0.038 at 68%CL

52. Which are the predictions : sin2 , ,  m s sin2  [0.57-0.81]  [43.6-67.3] o at 95%CL  m s [14.1-21.6] ps -1 sin2  = 0.78 ± 0.08From B  J/  K 0 s First crucial test done

53. Winter 2002 1995 1988 Mainly thanks to measurements done at LEP after the end of data taking

54. What will happen next ? Proceedings by Summer : Yellow Book + simultaneous publication in other laboratories (Slac/Tevatron/Cornell..) We hope with significant improvement from B-factories Next Workshop, late Spring 2003 in UK ( Lake District ) Aim is to have a LHC preparation workshop in year B LHC -2 But may well be need for a further a Workshop before…. B Physics has been intensively studied during last 10 years at LEP/SLD/TeVatron and CLEO and spectacular improvements have been obtained in the last years