1. on behalf of the Collaboration http://www.utfit.org
Vincenzo Vagnoni
on behalf of the Collaboration
M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, F. Parodi, M. Pierini, P. Roudeau, C. Schiavi, L. Silvestrini, V. Sordini, A. Stocchi, V. V.
Bologna
CP Violation, Rare decays, CKM

2. The Unitarity Triangle
The unitarity relations of the CKM matrix in the SM can be pictured as triangles in the complex plane
Amongst several triangles, the so-called Unitarity Triangle has sides of comparable sizes O(3) and is defined by
Wolfenstein parametrization of the CKM  4 parameters: l, A, r, h
1-l2/2 l -l u c d s b
A l3(1-r-ih)
-Al2 t
A l3(r-ih)
Al2 1
Several measurements (over-)constrain in different ways the CKM parameters in the SM and need to be consistently combined in one fit
Consistency of the fit allows to test the SM description of CPV  see V. Vagnoni in the BST session for extended UT fits including New Physics quantities

3. The UTfit method and the inputs CKM param. of the measurements
Experimental Inputs
CKM param. of the measurements
Theoretical Inputs
Standard Model +
OPE, HQET,
Lattice QCD
from quarks
to hadrons
 see M. Bona in the Lattice session for the impact and importance of Lattice QCD in UT fits
...
...
...
For details see: UTfit Collaboration hep-ph/ hep-ph/ hep-ph/ hep-ph/
Mr. Bayes
Joint probability density function for , 

4. Standard constraints for the SM analysis in the r-h plane
68% (95%) CL
Pre-beauty factory era(-like) constraints
Vub/Vcb eK
Dmd
Dmd/Dms
Beauty factory era constraints  
sin(2b)
cos(2b)

5.  from , ,  All combined
SU(2) analysis (neglecting EWP) for  and 
All combined
Gronau, London Phys. Rev. Lett. 65, 3381–3384 (1990)
unknowns
observables
Dalitz analysis for 
Snyder, Quinn Phys.Rev.D48, (1993)

6. Tree level determination of  from B±D(*)0K(*)±u B- c s K-
Vcb W l
Interference if same D0 and D0 final states
Favoured
GLW (Gronau,London,Wyler)
Uses CP eigenstates of D0 decays D0
ADS (Atwood, Dunietz, Soni) b u B- K- c s W
D 0
Vub = |Vub | e-ig
Colour suppressed
Dalitz Method – GGSZ analyze D0 three-body decays on the Dalitz plane
strong amplitude (the same for
Vub and Vcb mediated transitions
Break-through of B-factories, but statistically limited and extremely challenging!
strong phase difference between
Vub and Vcb mediated transitions
rB is a crucial parameter - the sensitivity on  depends on it

7. Tree level determination of  from B±D(*)0K(*)± (II)
rDK=0.074±0.033
rD*K=0.059±0.043
rDK*=0.19±0.09
Combination of GLW+ADS+Dalitz methods
 = (78 ± 30)o U (-102±30)o
Error increased significantly with respect to previous estimates!
 rB(D*K) smaller, effect of D*K less relevant  but dominant effect comes from the Dalitz model  we now use the full covariance matrix provided by Belle to account for the error on the Dalitz model since BaBar does not provide it yet Being this measurement basically NP-free, it is crucial to improve it if one wants to disentangle tiny NP effects

8. cos2 from BJ/K*0 and BD00
an angular analysis allows to extract both sin2 and cos2
BD00
 accessible by means of a Dalitz analysis of 3-body D0 decays analogously to the GGSZ method
Statistically limited, but useful to remove the ambiguity from sin2, suppressing one of the two allowed bands
Non-SM solution excluded at 95% CL

9. This year’s main novelty: ms measurement at CDF
hep-ex/
ms = (stat.) ± 0.07 (syst.) ps-1
-0.18
16.96 ps-1 < ms < ps-1 (95% C.L.)
Prediction for ms in SM UT fits without using the measurement as input
ms = 19.0 ± 2.4 ps-1
[14.7, 24.2] ps-1 at 95%
Experimental measurement much more precise than indirect determination  extremely powerful constraint in SM analysis - improvements in Lattice QCD involved parameters would be important to fully exploit md & ms measurements nowadays known at about 1%...
Dmd/Dms
Dmd
13% error
5% error

10. NP free measurement of Vub vs NP sensitive indirect determination
Pre-ICHEP06 situation: tension in the fit due to excessive Vub inclusive
NP free measurement of Vub vs NP sensitive indirect determination
Vub= (3.80 ± 0.27 ± 0.47) 10-3
exclusive from HFAG value of experimental BR + quenched LQCD
O.K.
3
Vub= (4.38 ± 0.19 ± 0.27) 10-3
from inclusive determination (HFAG average) x
2.5
Combining
Inclusive & exclusive
Vub= (4.20 ± 0.20) 10-3
Vub= (3.48 ± 0.20) 10-3
Prediction of UTfit without using Vub as input

11. from indirect determination From direct measurement
Effect of the tension on indirect predictions: sin2
Tension made evident by comparing the measurement of sin2 with its indirect determination from the fit
sin2 =0.791±0.034
from indirect determination
sin2 compatibility plots
with Vub
without Vub
2
O.K.
OLD input
sin2=0.687±0.032
From direct measurement

12. Tension sligthly reduced with Summer 06 updates on Vub (but still there)
updated with current HFAG averages
sin2 weight in the fit is increased due to its reduced error and to the increase of the Vub error
Vub=(4.09±0.25)10-3
(incl. + excl. average)
Error increased
central value decreased
with Vub
without Vub
updated
sin2=0.675±0.026
From direct measurement
(central value and error decreased)
1.5

13. Fit results with angles vs sides+K
Precision on  comparable due to the precise sin2 measurement, while ms induces a smaller error on 
Crucial to improve measurements of the angles, in particular  (tree level NP-free determination)
 = ± 0.052
[0.103, 95%
 = ± 0.037
[0.103, 95%
Still imperfect agreement in  due to sin2 and Vub discrepancy
 = ± 0.023
[0.271, 95%
 = ± 0.027
[0.323, 95%

14. Fit results with all contraints in Standard Model analysis
 = ± 0.029
[0.107, 95% Prob.
 = ± 0.017
[0.307, 95% Prob.

15. Conclusions
No clean evidence of deviations from the Standard Model description is emerging so far
Slight discrepancies due to an excess in Vub inclusive, but insufficient to claim for significant hints that something is wrong in the SM
However, if SM picture is correct, Vub should go down to ~3.5·10-3 sooner or later... sin2 docet!
Two of the existing sectors (at least) must be improved in order to test in deep the SM CKM picture
In order to fully exploit the great experimental precision of the md and ms measurements, improvements in the Lattice QCD computation of and the SU(3) breaking parameter  are needed
see M. Bona at the Lattice session
NP-free quantities must improve in particular, in order to disentangle NP effects:
Vub/Vcb
 from tree level decays
See V. Vagnoni in the BST session
We are most probably beyond the era of alternatives to the SM description of CP violation, and should instead look for corrections
Need very precise measurements in the Bd and Bs sectors to spot out tiny effects (LHCb, SuperB?)
The bottle of champagne can still wait in the fridge another little bit...