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. 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

4. 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

6. 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

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

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

9. 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 =  ( m2p mb as r mb
(l1 Fermi movement inside the hadron)
( also named L)
m2p
Can these parameters be determined experimentally ?
* In “Upsilon expansion” formalism :
Vcb =  ( l mb  pert)

10. From CLEO measurements

12. Other experiments should perform this analysis …….

13. 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)= ( ± 0.7 ± 0.8 ) 10-3
It was ± 2.0 and of theo. origin !

14. 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

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

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

17. 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

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

19. 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

20. Results from
all the LEP
experiments

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

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

24. 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

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

26. Averages from LEP/SLD/Tevatron (+ B-Factories)
t(B0d) = ± ps ( 1.0%)
t(B+) = ± ps ( 0.9%)
t(B0s) = ± ps ( 3.9%)
t(LB) = ± 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 ?

27. Theory
News…..

28. 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

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

30. Present
Future

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

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

33. 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 sA < 1
At given Dms
A = 0 no oscillation
A = 1 oscillation
Sensitivity same relation with A = 0
1.645sA < 1

34. “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 [ ] ps-1
at 95% CL
Sensitivity at 19.3 ps-1

39. 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)

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

41. 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

42. 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)

44. 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
[ ]
[ ]
At 68% CL

47. 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

48. Differences are small and physics conclusions
quantitatively the same

49. 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

50. Another example with sin2b
(without eK )

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

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

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

54. 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….