B-meson decay constants with domain-wall light quarks and nonperturbatively tuned relativistic b-quarks

Transcription

1 B-meson decay constants with domain-wall light quarks and nonperturbatively tuned relativistic b-quarks RBC and UKQCD collaborations Oliver Witzel Center for Computational Science Lattice 2013, Mainz, Germany

2 Motivation: CKM unitarity triangle fit η 1 winter13 SM fit β γ m d m s m d ε K V ub V cb -0.5 BR(B τν) α sin(2β+γ) [ ρ

3 Motivation: B 0 B 0 Mixing Allows us to determine the CKM matrix elements Dominant contribution in SM: box diagram with top quarks } VtdV tb forb d mixing VtsV M q = G F 2m2 W tb forb s mixing 6π 2 η B S 0 M Bq fb 2 q B Bq VtqV tb 2 t Nonperturbative contribution: f 2 q B Bq Define the SU(3) breaking ratio ξ 2 = f 2 B s B Bs /f 2 B d B Bd B 0 W W B 0 CKM matrix elements are extracted by b q W M s = M B s ξ 2 V ts 2 B 0 t t B 0 M d M Bd V td 2 W q b b q t q b Experimental error of M q is better than a percent; lattice uncertainty for ξ is about 3%

4 Motivation: Rare B-decays B τν [UTfit Phys.Lett. B687 (2010) 61] f B is needed for the Standard-Model prediction of BR(B τν) Strong sensitivity to NP because FCNC processes are suppressed by the Glashow-Iliopoulos-Maiani (GIM)-mechanism in the SM Helicity suppressed charged current decays: potential sensitivity to tree-level effects of new scalar particles (charged Higgs bosons in multi-higgs extensions of the SM, e.g. type-ii Two Higgs Doublet Model or MSSM) B s µ + µ [Buras et al. Eur.Phys.J. C72 (2012) 2172, Buras et al. arxiv: [hep-ph]] f Bs is needed for Standard-Model prediction of BR(B s µ + µ ) Measured by LHCb with 3.5σ significance [LHCb Phys.Rev.Lett. 110 (2013) 02180], at EPS2013: combination of LHCb and CMS results gives > 5σ significance in agreement with SM Both are sensitive to new physics!

5 Our Project Use domain-wall light quarks and nonperturbatively tuned relativistic b-quarks to compute at few-percent precision B 0 B 0 mixing Decay constants f B and f Bs B πlν form factor [T. Kawanai, Tue 14:20 Room C] g B Bπ coupling constant [B. Samways, Tue 16:40 Room C] Tuned RHQ parameters using bottom-strange states and high statistics Validated tuning procedure by computing b b masses and splittings Use mostly-nonperturbative renormalization scheme for f B, f Bs and B πlν Use one-loop mean-field improved lattice perturbation theory for small correction, and to renormalize B-mixing matrix elements [ [C. Lehner, Tue 14:40 Room C]

6 2+1 Flavor Domain-Wall Gauge Field Configurations Domain-wall fermions for the light quarks (u, d, s) [Kaplan Phys.Lett. B288 (1992) 342] [Shamir Nucl.Phys. B406 (1993) 90] Iwasaki gauge action [Iwasaki UTHEP-118(1983)] Configurations generated by RBC and UKQCD collaborations [C. Allton et al. Phys.Rev. D78 (2008) , Y. Aoki et al. Phys.Rev. D83 (2011) ] s = 0 s = L s 1 approx. # time L a(fm) m l m s m π (MeV) # configs. sources

7 Relativistic Heavy Quark Action for the b-quarks Relativistic Heavy Quark action developed by Christ, Li, and Lin [Christ et al. Phys.Rev. D76 (2007) ; Lin and Christ Phys.Rev. D76 (2007) ] Builds upon Fermilab approach [El-Khadra et al. Phys.Rev. D55 (1997) 3933] by tuning all parameters of the clover action non-perturbatively; close relation to the Tsukuba formulation [S. Aoki et al. Prog.Theor.Phys. 109 (2003) 383] Heavy quark mass is treated to all orders in (m b a) n Expand in powers of the spatial momentum through O( pa) Resulting errors will be of O( p 2 a 2 ) Allows computation of heavy-light quantities with discretization errors of the same size as in light-light quantities Applies for all values of the quark mass Has a smooth continuum limit

8 Nonperturbative Tuning of the RHQ Action Parameters [Phys.Rev. D86 (2012) ] Start from an educated guess for our three parameters m 0 a, c P, and ζ Probe parameter space at seven points by measuring spin-averaged mass: M = (M Bs + 3M B s )/4 hyperfine-splitting: M = M B s M Bs ratio: M 1 /M 2 = M rest /M kinetic Assume linearity to relate parameters and observables Obtain tuned parameters corresponding to physical b-quarks by requiring that M and M agree with experiment and that M 1 = M 2 ζ 3.5 σ ζ m a σ cp σ m0a c P

9 Predictions for the Heavy-Heavy States [Phys.Rev. D86 (2012) ] RHQ action describes heavy-light as well as heavy-heavy mesons Tuning the parameters in the B s -system we can predict bottomonium states and mass splittings and thereby test the method We find good agreement with experiment within errors M [GeV] χ b1 χ b0 ϒ η b experiment continuum a fm a 0.11 fm 1S 1P 1P 1S 1P h b M ϒ M ηb M M χb1 χb [MeV] Υ = 9410(30)(38) MeV η b = 9350(33)(37) MeV χ b1 = 9851(35)(39) MeV χ b0 = 9808(35)(39) MeV h b = 9862(36)(39) MeV M Υ M ηb = 49(02)(17) MeV M χb1 M χb0 = 38(01)(16)

10 B-meson Decay Constant Calculation Use point-source light quark and generate Gaussian smeared-source heavy quark Computation performed with seven parameter box and interpolated to the tuned RHQ parameters Axial current is 1-loop O(a) improved Use mostly nonperturbative renormalization Combined chiral and continuum extrapolation using heavy meson χpt b t 0 t Aµ q

11 Mostly Nonperturbative Renormalization For f B, f Bs and B π we compute mostly non-perturbative renormalization factors á la [El-Khadra et al. Phys.Rev. D64 (2001) ] ZV bl = ϱ bl ZV bbz V ll Compute Z ll V and Z bb V non-perturbatively and only ϱbl perturbatively Enhanced convergence of perturbative series of ϱ bl w.r.t. Z bl V because tadpole diagrams cancel in the ratio Bulk of the renormalization is due to flavor conserving factor ZV ll Z V bb 3 ϱ bl is expected to be of O(1); receiving only small corrections For domain-wall fermions Z A = Z V + O(m res ) i.e. we know Z ll [Y. Aoki et al. Phys.Rev. D83 (2011) ] and compute Z bb v V ourselves

12 Determination of Z bb v t Vµ t 0 b b t sink Z bb V B V bb,0 B = 2m B C B 2 (T ) C3 B B (T,t) lim T,t ZV bb Z bb v (t) s Z bb V = 5.237(12) χ 2 /dof = 0.34, p = 95% m l sea = m l sea = PRELIMINARY time slice a 24m l sea PRELIMINARY Z bb v a 32m l sea Z bb v (34) (13) (37) (12) (15) Avg. (24) (25) Avg. (32) (76) PT (24) 1-loop 10.72(16)(0) PT (32) 1-loop 5.725(74)(1) PT values:

13 Preliminary Results for f B and f Bs On the lattice we PRELIMINARY compute Φ Bq f B = Φ ren B q a 3/2 32 / M Bq Partially quenched data are highly correlated Variance-covariance matrix is statistically well resolved Linearly interpolate to get f Bs and fit to extrapolate to f B

14 Preliminary Results Φ Bs a 3/2 ren Φ Bs m l sea = m l sea = m l sea = a 3/2 Φ Bs = 0.158(4) f Bs = 235(6) MeV 46)0-1-2%6= m l sea = m l sea = a 2 [fm 2 ] Data for Φ Bs show no sea-quark mass dependence Average data at same lattice spacing and assume a 2 scaling to remove light-quark and gluon discretization errors Remaining heavy-quark discretization errors will be estimated with heavyquark power counting and included in the systematic error budget

15 Preliminary Results Φ Bd Fit only chiral data i.e. a 24 m q < 0.01 (m π < 420 MeV) using an analytic function in the quark masses and lattice spacing [ Φ B = Φ csea msea2b/(4πf l ) 2 + c val m val 2B/(4πf ) 2 + c a a 2 /(a32 2 4πf )2] PRELIMINARY

16 Preliminary Results Φ Bs /Φ Bd Fit only chiral data i.e. a 24 m q < 0.01 (m π < 420 MeV) using an analytic function in the quark masses and lattice spacing [ Φ Bs /Φ B = R Φ 1 + csea msea2b/(4πf l ) 2 + c val m val 2B/(4πf ) 2 + c a a 2 /(a32 2 4πf )2] PRELIMINARY

17 Comparison f Bs HPQCD 2013 (HISQ+NRQCD) 2+1 this work (stat. error only) HPQCD 2012 (Asqtad+NRQCD) f Bs /f B HPQCD 2013 (HISQ+NRQCD) 2+1 this work (stat. error only) HPQCD 2012 (Asqtad+NRQCD) FNAL/MILC 2011 (Asqtad+Fermilab) RBC/UKQCD 2010 (DWF+HQET) HPQCD 2011 (Asqtad+HISQ) FNAL/MILC 2011 (Asqtad+Fermilab) 2 ALPHA 2012 (Wilson+HQET) ETM 2012 (TM+HQET) MeV 2 ALPHA 2012 (Wilson+HQET) f B HPQCD 2013 (HISQ+NRQCD) ETM 2012 (TM+HQET) 2+1 this work (stat. error only) HPQCD 2012 (Asqtad+NRQCD) HPQCD 2012 (Asqtad+HISQ/ratio) FNAL/MILC 2011 (Asqtad+Fermilab) 2 ALPHA 2012 (Wilson+HQET) ETM 2012 (TM+HQET) MeV

18 Observations SU(2) HMχPT is valid for m u,d m s. Are our data chiral enough? Our data do not show visible signs of SU(2) chiral logarithms. Strong correlations among partially quenched data are troublesome. Are light valence-quark masses too close to each other? Preliminary Results f Bs = 235(6) MeV f B = 198(6) MeV f Bs /f B = 1.19(5) f Bs /f B = 1.173(7) f B = 200(5) MeV Overall consistent results Outlook We are finalizing the analysis of f B, f Bs and f Bs /f B Next we start the computation of B 0 B 0 mixing Statistical errors only! Derived (gray) results neglect correlations! Future data will be obtained at physical pions on the and Möbius domain-wall ensembles