1. CKM Fits: What the Data Say
Stéphane T’Jampens
LAPP (CNRS/IN2P3 & Université de Savoie)
On behalf of the CKMfitter group

2. The CKM Matrix: Four UnknownsQ q
VqQ
Q  q
from |Vud| (nuclear transitions) and |Vus| (semileptonic K decays)  combined precision: 0.5%
from |Vcb| (inclusive and exclusive semileptonic B decays)  combined precision: 2%
from (mainly) CKM angle measurements:  combined precision: 20% ( ), 7% ( )
Measurement of Wolfenstein parameters:

3. Dms : 17.31 (stat.) ± 0.07 (syst.) ps-1
Inputs: Dms
hep-ex/
17 < Dms < 21 C.L.
hep-ex/
Dms : (stat.) ± 0.07 (syst.) ps-1
+0.33
-0.18

4. |Vub| (incl.) [10-3] = 4.48 ± 0.24 ± 0.39 (our average)
Inputs (major changes): |Vub| (incl.)
|Vub| (incl.) [10-3] = 4.48 ± 0.24 ± 0.39 (our average)

5. Inputs (major changes): sin 2
“The” raison d’être of the B factories:
0.710 ± ± [BABAR(348m)]
0.642 ± ± [Belle (532m)]
sin2b =
0.674 ± (0.023 stat-only)
0.070 ± ± [BABAR]
± ± [Belle]
ICHEP ‘06
C(J/yK0) =
0.012 ± (0.017 stat-only)
Conflict with sin2eff from s-penguin
modes ? (New Physics (NP)?)
0.55 ± 0.11 ± [BABAR(347m)]
0.64 ± 0.10 ± [Belle (532m)]
sin2b (h’K0)=
0.60 ± 0.08
0.12 ± [BABAR(347m)]
0.44 ± 0.27 ± [Belle (386m)]
NB: a disagreement would falsify the SM. The interference NP/SM amplitudes introduces hadronic uncertainties
 Cannot determine the NP parameters cleanly
sin2b (fK0)=
0.31 ± 0.21
NP can contribute differently among the various s-penguin modes
Meaning of the average?

6. Inputs (major changes): angle a
Tree : dominant
Penguin : competitive ?
Time-dependent CP observable :
realistic scenario
Time-dependent CP analysis of B0  +– alone determines eff : but, we need  !
Isospin analysis
( can be resolved up to an 8-fold ambiguity within [0,])

7. Isospin Analysis: B→ pp
BABAR (347m)
Belle (532m)
Average
S
–0.53 ± 0.14 ± 0.02
–0.61 ± 0.10 ± 0.04
–0.58 ± 0.09
C
–0.16 ± 0.11 ± 0.03
–0.55 ± 0.08 ± 0.05
–0.39 ± 0.07
“agreement”: 2.6σ
BABAR & Belle

8. Isospin Analysis: B→ rr
BABAR (347m)
Belle (275m)
Average
Srr
–0.19 ± 0.21
0.08 ± 0.41 ± 0.09
–0.13 ± 0.19
Crr
–0.07 ± 0.15 ± 0.06
0.0 ± 0.3 ± 0.09
–0.06 ± 0.14
+0.05
-0.07
BABAR & Belle
± 0.06
fL00
BABAR (347m)
(1.2±0.4±0.3)x10-6
BR00
+0.11
-0.13
Isospin analysis :
a = [ 94 ± 21 ] º

9. Isospin analysis B→pp:
Isospin Analysis: angle aeff [B→ pp/rr]
Isospin analysis B→pp:
Isospin analysis B→rr:
|a-aeff| < 32.1º (95% CL)
|a-aeff| < 22.4º (95% CL)

10. (include new rp Dalitz BABAR)
Isospin Analysis: angle a [B→pp /rp /rr]
aB-Factories = [ ] º
+11 -9
aGlobal Fit = [ ] º +5
-19
(include new rp Dalitz BABAR)
B→rr: at very large statistics, systematics and model-dependence will become an issue
B→ρ Dalitz analysis: model-dependence is an issue !

11. Putting it all together
t h e g l o b a l C K M f i t
Inputs:

12. CP-insensitive observables imply CP violation !
The global CKM fit: Testing the CKM Paradigm
CP Conserving
CP Violating
CP-insensitive observables imply CP violation !
Angles (no theory)
No angles (with theory)

13. The global CKM fit: Testing the CKM Paradigm (cont.)
ICHEP 2006
Tree (NP-Free)
Loop
[No NP in DI=3/2 b→d EW penguin amplitude
Use a with b (charmonium) to cancel NP amplitude]
CKM mechanism: dominant source of CP violation
The global fit is not the whole story: several DF=1 rare decays are not yet measured
 Sensitive to NP

14. Radiative Penguin Decays: BR(B→rg)/BR(B→K*g)
0.55
1.25
Belle (386m)
BABAR (347m)
± 0.09
± 0.07
r+g
r0g
+0.21
-0.19
+0.35
-0.31

15. NP Parameterization in Bs system
Grossman, PL B380, 99 (1996)
Dunietz, Fleischer, Nierste, PRD 63, (2001)
Hypothesis: NP in loop processes only (negligible for tree processes)
Mass difference: Dms = (Dms)SM rs2
Width difference: DGsCP = (DGs)SMcos2(2c-2qs)
Semileptonic asymmetry:
AsSL=-Re(G12/M12)SM sin(2qs)/rs2
Syf = sin(2c-2qs)
NP wrt to SM:
reduces DGs
enhances Dms
UT of Bd system: non-degenerated
 (hd,sd) strongly correlated to the determination of (r,h)
UT of Bs system: highly degenerated
 (hs,ss) almost independent of (r,h)
Bs mixing phase very small in SM: c= (deg)
Bs mixing: very sensitive probe to NP

16. NP in Bs System Dms, DGs and AsSL s(Dms)= 0.035, s(sin(2c)=0.1
0.2 fb-1
First constraint for NP in the Bs sector
Still plenty of room for NP
Large theoretical uncertainties: LQCD
hs ~<= 3 (hd ~<=0.3, hK ~<= 0.6)

17. Prospective: LHCb 2fb-1 (2010 ?)?
note: “expected” improvement from Lattice QCD is taken into account.
s(Dms)=0.01
s(sin2b)=0.02
s(a) = 10º
s(g) = 5º
assumptions:

18. Conclusion
CKM mechanism: success in describing flavor dynamics of many constraints from vastly different scales.
With the increase of statistics, lots of assumptions will be needed to be reconsidered [e.g., extraction of a from B→3p,4p, etc., PEW, …]
Bs: an independent chapter in Nature’s book on fundamental dynamics
there is no reason why NP should have the same flavor structure as in the SM
Bs transitions can be harnessed as powerful probes for NP (c: “NP model killer”)
Before claiming NP discovery, be sure that everything is “under control”
(assumptions, theoretical uncertainties, etc.)
There are still plenty of measurements yet to be done

19. hep-ph/0607246 Bayesian Statistics at Work: the Troublesome
Do Not Miss:
hep-ph/
Bayesian Statistics at Work:
the Troublesome
Extraction of the CKM Angle a
(J. Charles, A. Höcker, H. Lacker
F.R. Le Diberder and S. T’Jampens)

20. BACKUP SLIDES

22. G. Isidori – Beauty ‘03

23. Everything you wanted to know about limits
Bayes at work
Zero events seen
P(n; )=e-n/n! x =   
Posterior P()
P(0 events|)
(Likelihood)
Prior: uniform
3 P() d= 0.95
Same as Frequentist limit - Happy coincidence
Roger Barlow: YETI06
Everything you wanted to know about limits

24. Bayes at work again Is that uniform prior really credible? x =   
Prior: uniform in ln l
P(0 events|)
Posterior P()
Upper limit totally different!
3 P() d >> 0.95
Roger Barlow: YETI06
Everything you wanted to know about limits

25. Everything you wanted to know about limits
Bayes: the bad news
The prior affects the posterior. It is your choice. That makes the measurement subjective. This is BAD. (We’re physicists, dammit!)
A Uniform Prior does not get you out of this.
Roger Barlow: YETI06
Everything you wanted to know about limits