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The CKM analysis: inputs from theory

Vittorio Lubicz. The CKM analysis: inputs from theory. This talk is dedicated to NICOLA CABIBBO. He was the "father of flavor physics“ [M .Wise] Universality of weak interactions, the Cabibbo angle, the GIM mechanism, the CKM matrix, ….

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The CKM analysis: inputs from theory

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  1. Vittorio Lubicz The CKM analysis: inputs from theory This talk is dedicated to NICOLA CABIBBO He was the "father of flavor physics“ [M .Wise]Universality of weak interactions, the Cabibbo angle, the GIM mechanism, the CKM matrix, … He has given fundamental contributions to Lattice QCD TheCabibbo-Marinari algorithm, Weak interactions on the lattice (Cabibbo-Martinelli-Petronzio), the APE project (Cabibbo, Parisi, …)

  2. OUTLINE Vud Vud Vud Vus Vus Vus Vub Vub Vub Vcd Vcd Vcd Vcs Vcs Vcs Vcb Vcb Vcb Vtd Vtd Vtd Vts Vts Vts Vtb Vtb Vtb  The 1st row unitarity test Processes: K → l , K →  l  Theory input: fK/f, f+(0) The 2nd row unitarity test Processes: D(s)→ l , D → K/ l  Theory input: fD, fDs, f+(0) The unitarity triangle analysis Processes: B→l, B→D/l, K-K, B(s)-B(s) Theory input: fB, fBs, f+(0), BK, BB(s)

  3. Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb |Vud|2 + |Vus|2 + |Vub|2 = 1 THE 1st ROW UNITARITY TEST The most stringent unitarity test Processes: K → l , K →  l  Theory input: fK/f, f+(0)

  4. Vus K [Marciano 04] Vus K π Vus/Vud from Kμ2/πμ2 decays Vus from Kl3 decays arXiv:1005.2323 [hep-ph]

  5. LQCD independent estimates of fK/f, f+(0) Vus π K Vus K 4 3 1 2 Assuming the Standard Model and combining with nuclear b decays From 20 superallowed transitions [Hardy and Towner 08] one obtains: and: The error is at the per mille level: a challenge for Lattice QCD FLAG [Flavianet Lattice Averaging Group] G.Colangelo, S.Dürr, A.Jüttner, L.Lellouch, H.Leutwyler, V.Lubicz, S.Necco, C.Sachrajda, S.Simula, T.Vladikas, U.Wenger, H.Wittig

  6. J.Flynn Latt’96 175(25) 14% ---- ---- C.Bernard Latt’00 200(30) 15% 267(46) 17% 1.16(5) 4% L.Lellouch Ichep’02 193(27)(10) 15% 276(38) 14% 1.24(4)(6) 6% UNQUENCHED Hashimoto Ichep’04 189(27) 14% 262(35) 13% 1.23(6) 5% QUENCHED N.Tantalo CKM’06 223(15)(19) 11% 246(16)(20) 10% 1.21(2)(5) 4% History of LQCD errors until 2006 For many years, uncertainties in lattice calculations have been dominated by the quenched approximation

  7. THE “PRECISION ERA” OF LATTICE QCD The Moore’s Law 1) Increasing of computational power TeraFlops machines are required to perform unquenched simulations. Available only since few years. 2) Algorithmic improvements CPU cost of a simulation (for Nf=2 Wilson fermions): - Ukawa 2001 - Del Debbio et al. 2006 M  200-300 MeV Light quark masses in the ChPT regime

  8. FLAVOUR PHYSICS ON THE LATTICE

  9. PRECISION FLAVOUR PHYSICS Experiments 2010 Lattice 2010 2006

  10. [ FLAG preliminary] Vus K = included in the FLAG average xxxxxxx Using |Vud| from nuclearb-decays: • |Vus|Kl2 = 0.2247(19) • |Vus|Unitar.= 0.2254(10) fK/f = 1.196(10) [ VL @ Lat2009 ] fK/f = { 1.193(6) [ FLAG, Nf=2+1 ] [ FLAG, Nf=2 ] 1.210(18) 0.8% preliminary Vus/Vudfrom leptonic K decays:fK/fπ

  11. Vusfrom semileptonic K decays: f+ (0) Kπ Vus Ademollo-Gatto: f+(0) = 1 - O(ms-mu)2 O(1%). But represents the largest theoret. uncertainty K π Vector Current Conservation f2 = − 0.023 Independent of Li (Ademollo-Gatto) THE LARGEST UNCERTAINTY SU(3)-ChPT Old standard estimate: Leutwyler, Roos (1984) (QUARK MODEL) f4 = −0.016 ± 0.008 f+(0) = 1 + f2 + f4 + O(p8)

  12. Vusfrom semileptonic K decays: f+ (0) Kπ Vus K π f+(0) = 0.956(8) The first lattice calculation [ FLAG prelim. ] f+(0) = 0.960(9) Nf = 0 SPQcdR 04 0.8% Nf is not the only parameter in a lattice simulation Nf = 2 ETM 09 f+(0) = 0.956(8) f+(0) = 0.959(5) Nf = 2+1 RBC/UKQCD 10 [ FLAG preliminary] Analytical model calculations tends to give larger predictions than lattice results

  13. The 1st row unitarity test [ FLAG preliminary] • |Vus|Kl3+Kl2 = 0.2255(14) • |Vus|Kl3 = 0.2263(20) • |Vus|Unitar. = 0.2254(10) • |Vus|Kl2 = 0.2247(19) ΔCKM = |Vud|2+|Vus|2+|Vub|2-1=(0±8)•10-4 Combining with |Vud| from nuclearb decays

  14. Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb THE 2nd ROW UNITARITY TEST |Vcd|2 + |Vcs|2 + |Vcb|2 = 1 ΔCKM = |Vcd|2 + |Vcs|2 + |Vcb|2 - 1 = 0.14(13) [PDG 08] Processes: D(s)→ l,D→K/ l Theory input: fD, fDs, f+(0)

  15. Leptonic D(s) mesons decays: fD, fDs 3 sigma deviation HPQCD 07 fDs = 241 ± 3 MeV PDG 08 fDs = 273 ± 10 MeV B.Dobrescu, A.Kronfeld, 0803.0512 “Evidence for nonstandard leptonic decays of Ds mesons” The 2008 summer puzzle The discrepancy led to speculations about new physics in leptonic D-decays

  16. Leptonic D(s) mesons decays: fD, fDs 3 sigma deviation HPQCD 07 fDs = 241 ± 3 MeV PDG 08 fDs = 273 ± 10 MeV The 2008 summer puzzle 2010: the puzzle solution 1 sigma agreement + 3% (2.3σ) HPQCD 10 fDs = 248.0 ± 2.5 MeV fDs = 254.6 ± 5.9 MeV HFAG 10 (CLEO-c, Belle, BaBar) - 7% (1.8σ)

  17. Vcsand Vcdfromsemileptonic D decays D→K, ETMC (Nf=2) LAT2010, prelim. D→K, HPQCD 2010 (Nf=2+1) D→, FNAL/MILC (Nf=2+1) LAT2010, prelim. New lattice calculations: HPQCD, FNAL/MILC, ETMC

  18. The 2nd row and 2nd column unitarity test Very precise experimental results from BaBar and CLEO-c CLEO-c + BaBar average The unitarity tests Using the precise lattice determination by HPQCD 2010 It will be interesting to compare with the forthcoming FNAL/MILC and ETMC results

  19. Vud Vus Vub Vcd Vcs Vcb * Vud Vub + Vcd Vcb + Vtd Vtb= 0 * * Vtd Vts Vtb THE UNITARITY TRIANGLE ANALYSIS Processes: B→l , B→D/ l , K - K, B(s) - B(s) Theory input: fB, fBs, f+(0), BK, BB, …

  20. εK Δmd Δmd/Δms |Vub/Vcb| fBBB 1/2 b→u/b→c K0–K0 Bd-Bd Bs-Bs sin(2β+γ) sin2β cos2β α γ B→J/ΨK0 B→J/ΨK*0 B→ππ,ρρ B→D(*)K B→D(*)π,Dρ THE UTA CONSTRAINTS UT-LATTICE ξ BK f+,F,… UT-ANGLES See also talks by C. Tarantino and L. Silvestrini

  21. Exclusivevs Inclusive Vub |Vub|excl.= (35.0 ± 4.0) 10-4 |Vub|incl.= (42.0 ± 1.5 ± 5.0) 10-4 IMPORTANT LONG DISTANCE CONTRIBUTIONS. THE RESULTS ARE MODEL DEPENDENT THEORETICALLY CLEAN BUT MORE LATTICE CALCULATIONS ARE WELCOME

  22. Exclusivevs Inclusive Vub * * |Vub|excl.= (35.0 ± 4.0) 10-4 |Vub|incl.= (42.0 ± 1.5 ± 5.0) 10-4 |Vub|SM-Fit = (35.5 ± 1.4) 10-4  The uncertainty of inclusive Vub estimated from the spread among different models. This is questionable  The fit in the SM favors a low value of Vub, as indicated by exclusive decays  Improve the accuracy of exclusive Vub in order to clarify the issue (see D→/K l)

  23. Exclusive Vcb Roma-TOV 2% F(1)= 0.924 ± 0.022 |Vcb|excl.= (39.0 ± 0.9) 10-3 G(1)= 1.060 ± 0.035 3% • TWO DIFFERENT APPROACHES: • “double ratios” (FNAL) • “step scaling” (TOV) • Remarkable agreement Averages from VL, C.Tarantino 0807.4605

  24. Exclusivevs Inclusive Vcb Inclusive Vcb |Vcb|excl.= (39.0 ± 0.9) 10-3 |Vcb|incl.= (41.7 ± 0.7) 10-3 |Vcb|SM-Fit = (42.7 ± 1.0) 10-3 2.5σ

  25. K0-K0 mixing: BK K K ^ BK= 0.86 ± 0.05 ± 0.14 ^ BK= 0.90 ± 0.03 ± 0.15 L.Lellouch@Latt’00 ^ S.Sharpe@Latt’96 BK= 0.731 ± 0.036 ^ BK= 0.79 ± 0.04 ± 0.08 C.Dawson@Latt’05 Pre-history * VqsVqd V.Lubicz@Latt’09 K 17% 5% 11% 17% ^ ^ ^ BK= 0.75 BK= 0.90 ± 0.20 BK= 0.33 ± 0.09 K History Quench. error QCD SR,Pich, De Rafael, 1985: 1/Nc exp.,Buras, Gerard, 1985: LQCD,Gavela et al., 1987:

  26. K0-K0 mixing: BK ^ ^ ^ BK = 0.724(12)(43)[Nf=2+1, SBW 10] BK = 0.729(25)(16)[Nf=2, ETMC 10] BK = 0.738(8)(25)[Nf=2+1, RBC/UKQCD 09] From the UT fit, assuming the Standard Model * VqsVqd ( with Kε = 0.94(2), A.Buras, D.Guadagnoli, G.Isidori ) K 5% ^ BK = 0.724(8)(28)[Nf=2+1, ALVdW 09 ] ^ ^ BK = 0.85(7) BK = 0.731(7)(35) K [ VL @ Lat2009 ]

  27. B-mesons decay constantsfB,fBs and B-B mixing,BBd/s ^ BBs= 1.33± 0.06 fBs= 238.8 ± 9.5 MeV fBs/fB = 1.231 ± 0.027 2% 4-5% 5% ^ ^ ξ= 1.243 ± 0.028 2% fBs√BBs= 275 ± 13 MeV BBd= 1.26± 0.11, fB = 192.8 ± 9.9 MeV Combining with the only modern calculation HPQCD [0902.1815]: Averages from J.Laiho, E.Lunghi, R.Van de Water, 0910.2928

  28. A look at the future

  29. 2015@SuperB 2011@LHCb The past the present and the future

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