A big success with more than 200 participants

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)

Structure of the Workshop Working Group I : Vub, Vcb and Lifetimes Working Group II : Vtd, Vts Working Group III : CKM Fits Lattice Data Group (LDG) Forum on Averaging (for PDG + users) Talks on : Charm and Kaon Physics

The CKM Matrix d s b u c t -Al2 4 parameters : l ,A, r, h 1-l2/2 l In the Wolfenstein parameterization 4 parameters : l ,A, r, h The CKM Matrix d s b u 1-l2/2 l A l3(r-ih) b c,u Vub,Vcb c -l 1-l2/2 Al2 B decays t A l3(1-r-ih) -Al2 1 Vtb b d, s Vtd ,Vts B Oscillations

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

WORKING GROUP I b c,u Vub,Vcb B decays Lifetimes Vcb Vub

Inclusive Determination of Vcb BR sl + t b Average by LEP Working Groups

mb m2p Vcb = 0.0415  ( 1 - 0.012 m2p - 0.010 mb + 0.006 as + 0.007 r Determination of Vcb limited by theoretical uncertainties ….. The expression of Vcb in the low scale running HQ masses formalism (as an example)* Vcb = 0.0415  ( 1 - 0.012 m2p - 0.010 mb + 0.006 as + 0.007 r mb (l1 Fermi movement inside the hadron) ( also named L) m2p Can these parameters be determined experimentally ? * In “Upsilon expansion” formalism : Vcb = 0.0419  ( 1 + 0.017 l1 - 0.012 mb  0.019 pert)

From CLEO measurements

Other experiments should perform this analysis …….

Vcb(inclusive)= ( 40.7 ± 0.7 ± 0.8 ) 10-3 Part of theoretical error on Vcb becomes experimental from the determination of m2p and mb Value agreed at the end of the Workshop Vcb(inclusive)= ( 40.7 ± 0.7 ± 0.8 ) 10-3 It was ± 2.0 and of theo. origin !

Exclusive Determination of Vcb G(w) contains kinematics factors and is known (also r1 and r2) F(w) is the form factor describing the B D* transition At zero recoil (w=1), as MQ  F(1)  1 Strategy : Measure dG/dw and extrapolate to w=1 to extract F(1) Vcb

F(1) |Vcb|2 Syst. dominated by the knowledge of the D** (for LEP) r2

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

What’s next to improve Vcb Experimental side: More and new moment analyses B-factories can perform both exclusive and inclusive analyses Form factors measurements in BD*ln Theory side : More work on the theory for the m2p ,mb extraction Unquenched F(1) calculations Studies of eventual correlation between inclusive and excluive determinations

Vcb = (41.8 ± 1.0 ) 10-3 Combing the inclusive and the exclusive measurements : Vcb = (41.8 ± 1.0 ) 10-3

Vub Inclusive determination of Vub from LEP b  c b  u Challenge measurement from LEP Using several discriminant variables to distinguish between the transitions : b  c b  u B  Xu l n

Results from all the LEP experiments

At the Workshop we agreed on New determination At the Workshop we agreed on Vub(inclusive) = (4.09 ± 0.46 ± 0.36) 10-3

B ® p(r) l n Exclusive determination of Vub Vub = (3.68 ± 0.55 +0.28 (syst.))10-3 (in ISGW2 Model) - 0.37 Babar Vub = (3.68 ± 0.14 +0.21 (syst.)± 0.55(theo.))10-3 CLEO - 0.29 Important theoretical uncertainties from different models NOW, Lattice QCD calculations start to be precise

What’s next to improve Vub Experimental side: B-factories can perform inclusive/end-point/exclusive analyses Correspondence between Dpln and B  pln 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 Vub determinations

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

Averages from LEP/SLD/Tevatron (+ B-Factories) t(B0d) = 1.543 ± 0.015 ps ( 1.0%) t(B+) = 1.658 ± 0.014 ps ( 0.9%) t(B0s) = 1.464 ± 0.057 ps ( 3.9%) t(LB) = 1.208 ± 0.051 ps ( 4.2%) The hierarchy was correctly predicted ! t(B+)/ t(B0) about 5s effect in agreement with theory t(B0s)/ t(B0) about 1s effect in agreement with theory Is there a problem for LB ?

Theory News…..

t(B0s) and t( LB ) from TeVatron …. and B Bc, c Next improvements : Experiment side: t(B+)/ t(B0) from B factories But more important t(B0s) and t( LB ) from TeVatron …. and B Bc, c Theory side: Improvements of the Lattice QCD calculations

II WORKING GROUP Dmd Dms B Oscillations d, s b Vtd ,Vts Radiative and Leptonic B decays Rare K decays

Present Future

Study of the time dependent behaviour of the Oscillation B0 -B0 TextBook Plot

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

Dms Dms excluded at 95% CL Measurement of A at each Dms At given Dms Combination of different limits using the amplitude methods Measurement of A at each Dms Combination using A and sA Dms excluded at 95% CL A + 1.645sA < 1 At given Dms A = 0 no oscillation A = 1 oscillation Sensitivity same relation with A = 0 1.645sA < 1

“Hint of signal” at Dms=17.5 ps-1 but with significance at 1.7s Expectation in The Standard Model Dms > 14.9 ps-1 at 95% CL Dms [14.1-21.6] ps-1 at 95% CL Sensitivity at 19.3 ps-1

Very important achievement. The Dms 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)

WORKING GROUP III CKM Fits Strategies the angle g Vud,Vus Two subgroups :

The CKM Matrix d s b u c t -Al2 4 parameters : l ,A, r, h 1-l2/2 l In the Wolfenstein parameterization 4 parameters : l ,A, r, h The CKM Matrix d s b u 1-l2/2 l A l3(r-ih) b c,u Vub,Vcb c -l 1-l2/2 Al2 B decays t A l3(1-r-ih) -Al2 1 Vtb b d, s Vtd ,Vts B Oscillations

bu / bc | Vub \ Vub |2 r2 + h2 Dmd |Vtd|2fBd2 BBd f(mt) (1-r)2 + h2 Dmd \ Dmd |Vtd \ Vtd |2 fBd2 BBd \ fBs2 BBs eK f(A,h,r,BK..) h(1-r)

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

Where the difference is coming from ? eK ( Vcb4 * BK) Difference comes from how the inputs are treated : At present mainly from: F(1), inclusive Vcb, BK 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

Differences are small and physics conclusions quantitatively the same

Both methods use the same likelihood 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 Both methods use the same likelihood Using Likelihoods as obtained from convolution of Exp. Theo. errors Differences almost disappears

Another example with sin2b (without eK )

r = 0.220 ± 0.040 h = 0.315 ± 0.038 at 68%CL r [0.14-0.30] at 95%CL

Which are the predictions : sin2b, g, Dms g [43.6-67.3]o at 95%CL Dms [14.1-21.6] ps-1 sin2b = 0.78 ± 0.08 From B  J/y K0s First crucial test done

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

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 What will happen next ? Proceedings by Summer : Yellow Book + simultaneous publication in other laboratories (Slac/Tevatron/Cornell..) Next Workshop, late Spring 2003 in UK ( Lake District ) We hope with significant improvement from B-factories Aim is to have a LHC preparation workshop in year B LHC -2 But may well be need for a further a Workshop before….