Neutral $B$ meson mixings and $B$ meson decay constants with static heavy and domain-wall light quarks

TL;DR

This study calculates neutral B meson mixing matrix elements and decay constants using lattice QCD with static b quarks and domain-wall light quarks, providing precise ratios and constants relevant for flavor physics.

Contribution

It presents the first lattice QCD calculation of B meson mixing parameters and decay constants employing static b quarks and domain-wall light quarks on dynamical ensembles, with continuum extrapolation.

Findings

SU(3) breaking ratio ξ=1.208(60)

f_B√B̂_B=240(22) MeV

f_Bs√B̂_Bs=290(22) MeV

Abstract

Neutral $B$ meson mixing matrix elements and $B$ meson decay constants are calculated. Static approximation is used for $b$ quark and domain-wall fermion formalism is employed for light quarks. The calculations are carried out on $2+1$ flavor dynamical ensembles generated by RBC/UKQCD Collaborations with lattice spacings $0.086$fm ($a^{-1}\sim 2.3$GeV) and $0.11$fm ($1.7$GeV), and a fixed physical spatial volume of about $(2.7{\rm fm})^3$. In the static quark action, link-smearings are used to improve the signal-to-noise ratio. We employ two kinds of link-smearings, HYP1 and HYP2, and their results are combined in taking the continuum limit. For the matching between the lattice and the continuum theory, one-loop perturbative $O(a)$ improvements are made to reduce discretization errors. As the most important quantity of this work, we obtain SU(3) breaking ratio $\xi=1.208(60)$, where the error includes statistical and systematic one. (Uncertainty from infinite $b$ quark mass is not included.) We also find other neutral $B$ meson mixing quantities $f_B\sqrt{\hat{B}_B}=240(22)$MeV, $f_{B_s}\sqrt{\hat{B}_{B_s}}=290(22)$MeV, $\hat{B}_B=1.17(22)$, $\hat{B}_{B_s}=1.22(13)$ and $B_{B_s}/B_B=1.028(74)$, $B$ meson decay constants $f_B=219(17)$MeV, $f_{B_s}=264(19)$MeV and $f_{B_s}/f_B=1.193(41)$, in the static limit of $b$ quark, which do not include infinite $b$ quark mass uncertainty.