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CKM Fits: What the Data Say

This presentation discusses the latest results from the CKMfitter group regarding the Cabibbo-Kobayashi-Maskawa (CKM) matrix and its parameters. Key focus areas include precision measurements of |Vud|, |Vus|, |Vcb|, and the CKM angles. The implications of these measurements on potential new physics, particularly in the context of CP violation and isospin analysis, are also explored. The ongoing challenges and theoretical uncertainties in the CKM framework highlight its significance in our understanding of flavor physics.

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CKM Fits: What the Data Say

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  1. CKM Fits: What the Data Say Stéphane T’Jampens LAPP (CNRS/IN2P3 & Université de Savoie) On behalf of the CKMfitter group http://ckmfitter.in2p3.fr

  2. Q q W– Q VqQ 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% ( ) The CKM Matrix: Four Unknowns Measurement of Wolfenstein parameters:

  3. +0.33 -0.18 Dms : 17.31 (stat.) ± 0.07 (syst.) ps-1 Inputs: Dms hep-ex/0603029 17 < Dms < 21 ps-1 @90 C.L. hep-ex/0606027

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

  5. Inputs (major changes): sin2 • “The” raison d’être of the B factories: 0.710 ± 0.034 ± 0.019 [BABAR(348m)] 0.642 ± 0.031 ± 0.017 [Belle (532m)] sin2b= 0.674 ± 0.026 (0.023 stat-only) 0.070 ± 0.028 ± 0.018 [BABAR] -0.018 ± 0.021 ± 0.014 [Belle] ICHEP ‘06 C(J/yK0) = 0.012 ± 0.022 (0.017 stat-only) • Conflict with sin2efffrom s-penguin • modes ? (New Physics (NP)?) 0.55 ± 0.11 ± 0.02 [BABAR(347m)] 0.64 ± 0.10 ± 0.02 [Belle (532m)] sin2b (h’K0)= 0.60 ± 0.08 0.12 ± 0.34 [BABAR(347m)] 0.44 ± 0.27 ± 0.05 [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. Penguin : competitive ? Tree : dominant Inputs (major changes): angle a • Time-dependent CP observable : realistic scenario Time-dependent CP analysis of B0  +–alonedetermineseff : but, we need  ! Isospin analysis ( can be resolved up to an 8-fold ambiguity within [0,])

  7. Isospin Analysis: B→ pp “agreement”: 2.6σ BABAR & Belle

  8. BABAR (347m) +0.11 -0.13 fL00 0.86 ± 0.06 BR00 (1.2±0.4±0.3)x10-6 a = [ 94 ± 21 ] º Isospin Analysis: B→ rr +0.05 -0.07 BABAR & Belle • Isospin analysis :

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

  10. +11 -9 aB-Factories = [ 93 ] º +5 -19 aGlobal Fit = [ 98 ] º Isospin Analysis: angle a [B→pp /rp /rr] (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. Inputs: Putting it all together t h e g l o b a l C K M f i t

  12. 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. BABAR (347m) Belle (386m) r0g 0.77 ± 0.07 1.25 +0.21 -0.19 +0.37 +0.07 -0.33 -0.06 r+g 1.06 ± 0.09 0.55 +0.35 -0.31 +0.42 +0.09 -0.36 -0.08 Radiative Penguin Decays: BR(B→rg)/BR(B→K*g)

  15. NP Parameterization in Bs system Grossman, PL B380, 99 (1996) Dunietz, Fleischer, Nierste, PRD 63, 114015 (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=1.05+0.06 (deg) Bs mixing: very sensitive probe to NP

  16. 0.2 fb-1 NP in Bs System s(Dms)= 0.035, s(sin(2c)=0.1 Dms, DGs and AsSL 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. s(Dms)=0.01 s(sin2b)=0.02 s(g) = 5º s(a) = 10º Prospective: LHCb 2fb-1 (2010 ?)? note: “expected” improvement from Lattice QCD is taken into account. 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. Do Not Miss: hep-ph/0607246 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

  21. G. Isidori – Beauty ‘03

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

  23. 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! • 3P() d >> 0.95 0 Everything you wanted to know about limits

  24. 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. Everything you wanted to know about limits

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