NeutralB-meson mixing from unquenched lattice QCD with domain-wall light quarks and staticbquarks

Abstract

We demonstrate a method for calculating the neutral B-meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static b-quarks. Our computation is performed on the ''2 þ 1'' flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of a % 0:11 fm (a À1 ¼ 1:729 GeV) and a lattice spatial volume of approximately ð1:8 fmÞ 3 . We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologicallymotivated fit function based on next-to-leading order heavy-light meson SU(2) chiral perturbation theory. For the b-quarks, we use an improved formulation of the Eichten-Hill action with static link-smearing to increase the signal-to-noise ratio. We also improve the heavy-light axial current used to compute the B-meson decay constant to Oð s paÞ using one-loop lattice perturbation theory. We present initial results for the SU(3)-breaking ratios f B s =f B d and, thereby demonstrating the viability of the method. For the ratio of decay constants, we find f B s =f B d ¼ 1:15ð12Þ and for the ratio of mixing matrix elements, we find ¼ 1:13ð12Þ, where in both cases the errors reflect the combined statistical and systematic uncertainties, including an estimate of the size of neglected Oð1=m b Þ effects.

Lattice QCD determination of m b , f B and f Bs with twisted mass Wilson fermions

“…A comparison of our N f = 2 result for the B and B s decay constants, to existing results from N f = 2 + 1 quark flavor simulations [39,40] suggests that the error due to the partial quenching of the strange quark is smaller at present than other systematic uncertainties. In this respect we mention that simulations with N f = 2 + 1 + 1 dynamical flavors are already being performed by ETMC and preliminary results for several flavor physics observables have been recently presented [41,42].…”

NeutralBmeson mixings andBmeson decay constants with static heavy and domain-wall light quarks

“…This fact requires special treatment of correlators, because even in the large separation of source and sink positions in time t, unique ground state cannot be obtained [39,40]. Especially, the Gaussian source and sink smearing used in this work requires taking into account this feature.…”

“…In this subsection, we follow discussions in Refs. [39,40] and explicitly show an extension to any form of source and sink smearing function. We start with defining our state convention.…”

“…We use partially quenched SU(3)HMχPT [47,48], whose explicit formula are also presented in Ref. [40]. The ambiguity from off-physical s quark mass effect is investigated by taking the difference between correct treatment of our simulation setup and fake treatment where the s quark mass is assumed to be on physical point.…”

“…In this work, we use next-to-leading order SU(2) heavy-light meson chiral perturbation theory (NLO SU(2)HMχPT) depicted in Ref. [40]. (See also Ref.…”