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Lattice QCD and flavour physics (II): Impact of lattice on the

Lattice QCD and flavour physics (II): Impact of lattice on the Unitarity Triangle Analysis. Vittorio Lubicz. OUTLINE:. Role of lattice QCD in the UT Fit: the UT-lattice analysis UT-lattice vs. UT-angles : comparison and role of V ub

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Lattice QCD and flavour physics (II): Impact of lattice on the

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  1. Lattice QCD and flavour physics (II): Impact of lattice on the Unitarity Triangle Analysis Vittorio Lubicz OUTLINE: • Role of lattice QCD in the UT Fit: the UT-lattice analysis • UT-lattice vs. UT-angles: comparison and role of Vub • “Experimental” determination of lattice parameters ApeNEXT workshop, Arcetri, February 8-10, 2007

  2. VudVub + VcdVcb + VtdVtb = 0 * * * ρ η (bu)/(bc) 2+2 f+,F(1),… ρ η md (1– )2 +2 fBd BBd 2 md/ ms (1– )2 +2 ξ ρ η K [(1–)+ P] BK η ρ THE “UT-LATTICE” ANALYSIS: UTA IN THE PRE-BFACTORIES ERA: CP-conserving sizes + εK Hadronic matrix elements from LATTICE QCD 4 CONSTRAINTS 2 PARAMETERS

  3. 1) Confirmation of the CKM origin of CP in K-K mixing 2) Prediction of sin2β 3) Prediction of Δms Already before the starting of the B factories 3 IMPORTANT RESULTS FOR FLAVOUR PHYSICS A great success of (quenched) Lattice QCD calculations !!

  4. 1) INDIRECT EVIDENCE OFCP Ciuchini et al. (“pre-UTFit” paper),2000 εK UTsizes

  5. Measurements 2) PREDICTION OFSin2β Predictions exist since 1995 Ciuchini et al.,1995:Sin2βUTA= 0.65 ± 0.12 Ciuchini et al.,2000:Sin2βUTA= 0.698 ± 0.066 ICHEP 2006: Sin2βJ/ψK0= 0.675 ± 0.026

  6. 3) PREDICTION OFΔms Ciuchini et al.,2000: Δms= (16.3 ± 3.4) ps-1 UTFit Coll.,2006: Δms= (18.4 ± 2.4) ps-1 CDF, 2006: Δms= (17.77 ± 0.10 ± 0.07) ps-1

  7. fBBB 1/2 |Vub/Vcb| εK Δmd Δmd/Δms BK ξ f+,F,… THE LATTICE INPUT PARAMETERS

  8. Bd,s mixing: fBs/fB and ξ fB and therefore the ratio fBs/fB are affected by the “potentially large” effect of chiral logarithms: Recent history of ξ “Old” estimates (<2002): fBs/fB≈ 1.14-1.18 Kronfeld and Ryan (2002) fBs/fB = 1.32 ± 0.10 ETMC HPQCD (2005) fBs/fB = 1.20 ± 0.03 But the present estimate still relies on a single calculation. Further determinations at low quark masses are required.

  9. K–K mixing: εK and BK C.Dawson@Latt’05 K K Nf=0 QUENCHED ERROR BK= 0.58 ± 0.03 ± 0.06 ^ BK= 0.79 ± 0.04 ± 0.09 BK = 0.50 ± 0.02 ± ?? Nf=2, RBC BK = 0.62 ± 0.14Nf=2+1 HPQCD & UKQCD (Gavela et al.) 1987 BK = 0.90 ± 0.20 ^ C.Dawson@Latt’05 Stat. ETMC, Nf=2: work in progress

  10. εK Δmd Δmd/Δms |Vub/Vcb| UT-LATTICE sin2β angle α angle γ UT-ANGLES cos2β sin(2β+γ) Direct determinations of the UT angles are now available from non-leptonic B decays UTA IN THE BFACTORIES ERA:

  11. UT-lattice UT-angles  = 0.188 ± 0.036  = 0.134 ± 0.039  = 0.371 ± 0.027  = 0.335 ± 0.020 The errors have comparable sizes The UT-angles fit does not depend on theoretical calculations (the treatment of theoretical errorsis not an issue)

  12. b->u decays and the Vub puzzle ~2σ There is some tension in the fit, particularly between sin2β and Vub Sin2β = 0.675 ± 0.026 from the direct measurement Sin2β = 0.755 ± 0.040 from the rest of the fit

  13. EXCLUSIVE Vub = (35.0 ± 4.0) 10-4 Form factors from LQCD and QCDSR excl. INCLUSIVE Vub = (44.9 ± 3.3) 10-4 Model dependent (BLNP, DGE,..) Non perturbative parameters most not from LQCD (fitted from experiments) incl. The tension is between the inclusive Vuband the rest of the fit ~3σ AVERAGE Vub = (40.9 ± 2.5) 10-4

  14. S.Hashimoto@ICHEP’04 The discrepancy for Vub inclusive is almost at the 3σ level A New Physics effect is unlikely in this tree-level process i) Statistical fluctuation ii) Problem with the theoretical calculations and/or the estimate of the uncertainties LATTICE QCD: improve Vub exclusive to solve the tension

  15. “EXPERIMENTAL” DETERMINATION OF THE LATTICE PARAMETERS

  16. “EXPERIMENTAL” DETERMINATION OF LATTICE PARAMETERS UT-angles UT-lattice The new measurements ofΔmsandBR(B→τντ) allows a simultaneous fit of the hadronic parameters: Take the angles from experiments and extract fBs√BBs, fB√BBd orξand fB

  17. ^ BK = 0.75± 0.09 ^ BK = 0.79 ± 0.04 ± 0.08 UTA Lattice [Dawson]

  18. ^ BK = 0.75± 0.09 ^ BK = 0.79 ± 0.04 ± 0.08 UTA Lattice [Dawson] 2% ! fBs√BBs = 261 ± 6 MeV UTA Lattice [Hashimoto] fBs√BBs = 262 ± 35 MeV

  19. ^ BK = 0.75± 0.09 ^ BK = 0.79 ± 0.04 ± 0.08 UTA Lattice [Dawson] 2% ! fBs√BBs = 261 ± 6 MeV UTA Lattice [Hashimoto] fBs√BBs = 262 ± 35 MeV UTA ξ = 1.24 ± 0.08 Lattice [Hashimoto] ξ = 1.23 ± 0.06 The agreement is spectacular!

  20. Note: the scale is 6 times larger!! BEFOREΔms

  21. You may have got the impression that Lattice QCD calculations are becoming irrelevant for the UTA. But this is not true… They are crucial to perform the UTA when looking for signature of New Physics

  22. K-K MIXING IN NP MODELS Clover APE 1999 Overlap Babich et al. 2006 Domain wall CP-PACS 2006

  23. K-K MIXING Bd-Bd MIXING CONSTRAINTS ON THE MSSM M.Ciuchini, E.Franco, D.Guadagnoli, V.L., V.Porretti, L.Silvestrini (in preparation) Super-CKM basis: all gauge interactions governed by the CKM matrix. Additional sources of flavour violation in squark masses.

  24. YEARS OF (ρ-η) DETERMINATIONS The result of a remarkable experimental and theoretical progress

  25.  = 0.163  0.028  = 0.2226 0.0028  = 0.344  0.016  = 0.3052 0.0024 UT fit at a Super B factory: 2006 vs. 2015

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