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 developmentsand future measurements :- in a short timescale (B-Factories/TeVatron II)- in a longer timescale (bridging today LHC)

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

Structure of the Workshop

1-2/2 A 3(i)

1-2/2 A2

A 3(1--i) -A2 1

u

c

t

d s b

bd, s b

Vtd ,Vts

B Oscillationsd, s

Vtb

c,u

B decays

b

Vub,Vcb

The CKM MatrixIn the Wolfenstein parameterization

4 parameters : ,A,

To be continued atB-Factories and TeVatron

• Theoretical assumptions• Theoretical uncertainties

Possible measurements

Theory UT parameters

Measurements

Measurements

Error Meaning (discussion)Statistical Methods to extract UT parameters

•Analysis Methods•Analysis Systematic

WORKING GROUP

I LifetimesVcb Vub

c,u

B decays

b

Vub,Vcb

Inclusive Determination of Vcb

b c

l

Vcb

Average by LEP Working Groups

BR sl + b

Vcb

Determination of Vcb limited by theoretical uncertainties …..

The expression of Vcb in the low scale running HQ masses formalism (as an example)*

Can these parameters be determined experimentally ?

Vcb = 0.0415 ( 1 - 0.012 2 0.010 mb + 0.006 s + 0.007

mb

(Fermi movement inside the hadron)

( also named )

2

Vcbmbpert* In “Upsilon expansion” formalism :

From CLEO measurements

Other experiments should perform this analysis …….

Value agreed at the end of the Workshop

Part of theoretical error on Vcb becomes experimental

from the determination of 2and mb

Vcb(inclusive)= ( 40.7 ± 0.7 ± 0.8 ) 10-3

It was ± 2.0 and of theo. origin !

Exclusive Determination of Vcb

)(|)(|||48

222

2

wGwFVG

dw

dcb

F

(*).DB vvw

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 MQ F(1) 1

Strategy : Measure d/dw and extrapolate to w=1 to extract F(1) Vcb

Syst. dominated by the

knowledge of the D**

(for LEP)

F(1

) |V

cb|2

2

F(1)

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

3 determinations

What’s next to improve Vcb

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 ,mb extraction

Unquenched F(1) calculations

Studies of eventual correlation between inclusive and excluive determinations

Form factors measurements in BD*l

Combing the inclusive and the exclusive measurements :

Vcb = (41.8 ± 1.0 ) 10-3

Challenge measurement from LEP

Inclusive determination of Vub

Using several discriminant variables to distinguish between the transitions :

b c b u

Vub

B Xu l

Results from all the LEP experiments

At the Workshop we agreed on

Vub(inclusive) = (4.09 ± 0.46 ± 0.36) 10-3

New determination

Exclusive determination of Vub

B l

Vub = (3.68 ± 0.55 +0.28 (syst.))10-3 (in ISGW2 Model)- 0.37

Vub = (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

What’s next to improve Vub

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 Vub determinations

Correspondence between Dl and B l

All lifetimes of weakly decaying B hadrons have been precisely measured

Very important test of the B decay dynamics

Lifetimes

(B0d) = 1.543 ± 0.015 ps ( 1.0%)

(B+) = 1.658 ± 0.014 ps ( 0.9%)(B0

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+)/ (B0) about 5 effect in agreement with theory

(B0s)/ (B

0) about 1 effect in agreement with theory

Is there a problem for B ?

Theory News…..

Next improvements :

(B+)/ (B0) from B factories

But more important (B0

s) and ( B ) from TeVatron …. and B Bc, c

Experiment side:

Theory side:

Improvements of the Lattice QCD calculations

md ms

WORKING

GROUP

IIRadiative and Leptonic B decays

Rare K decays

d, s b

d, sb

Vtd ,Vts

B Oscillations

Present

Future

)cos1(2

1 /

)( 000 tmeP qt

BBBq

qqq

Study of the time dependent behaviour

of the Oscillation B0 -B0

TextBook Plot

BeforeB-Factories

md

LEP/SLD/CDF precisely measured the md frequencymd = 0.498 ± 0.013 ps-1 LEP/SLD/CDF (2.6 %)

B-factories confirmed the value improving the precision by a factor 2md = 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 )

)cos1(2

1 /

)( 000 tmeP qt

BBBq

qqq

A

Combination of different limits using the amplitude methods

Combination using A and A

ms

ms excluded at 95% CL

A + 1.645A < 1

At given msA = 0 no oscillation A = 1 oscillation

Sensitivity same relation with A = 0

1.645A < 1

Measurement of A at each ms

ms > 14.9 ps-1 at 95% CL

Sensitivity at 19.3 ps-1

“Hint of signal”at ms=17.5 ps-1 but with significance at 1.

Expectation inThe Standard Model

ms [14.1-21.6] ps-1 at 95% CL

Very important achievement. The ms information has to be included in the CKM Fitsusing the Likelihood Method.( in the past this was a source of differences between the groups performing CKM fits)

WORKING

GROUP

IIICKM Fits Strategies

the angle Vud,Vus

Two subgroups :

1-2/2 A 3(i)

1-2/2 A2

A 3(1--i) -A2 1

u

c

t

d s b

bd, s b

Vtd ,Vts

B Oscillationsd, s

Vtb

c,u

B decays

b

Vub,Vcb

The CKM MatrixIn the Wolfenstein parameterization

4 parameters : ,A,

bu / bc | Vub \ Vub |2 2 +

md |Vtd|2fBd2 BBd f(mt) 2 +

md \ md |Vtd \ Vtd |2 fBd2 BBd

\ fBs2 BBs

2 +

K f(A,BK..)

Ex : BK = 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

Where the difference is coming from ?

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

K ( Vcb4 * BK)

Differences are small and physics conclusions quantitatively the same

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 Likelihoodsas obtained from linear sum of Exp.+Theo. errors

Using Likelihoodsas obtained from convolution of Exp. Theo. errors

Both methods use the same likelihood

Differences almost disappears

Another example with sin2 (without K )

[0.14-0.30]

[0.24-0.39]

at 95%CL

= 0.220 ± 0.040 = 0.315 ± 0.038

at 68%CL

Which are the predictions : sin2, , ms

sin2 [0.57-0.81] [43.6-67.3]o at 95%CL

ms [14.1-21.6] ps-1

sin2 = 0.78 ± 0.08 From B J/ K0s

First crucial test done

Winter 2002

1995

1988

Mainly thanks to m

easurements

done at LE

P after the end of data taking

What will happen next ?

Proceedings by Summer : Yellow Book + simultaneous publicationin 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