m_b and f_Bs from a combination of HQET and QCD

TL;DR

This paper combines HQET and QCD in lattice simulations to accurately compute the b-quark mass and B_s meson decay constant, achieving continuum extrapolation and interpolation for precise results.

Contribution

It introduces a novel method combining HQET and relativistic QCD in lattice QCD to determine b-quark properties with improved accuracy.

Findings

f_Bs = 191(6) MeV

M_b = 6.89(11) GeV

m_b(m_b) = 4.42(7) GeV

Abstract

We compute the mass of the b-quark and the B_s meson decay constant in quenched lattice QCD using a combination of HQET and the standard relativistic QCD Lagrangian. We start from a small volume, where one can directly deal with the b-quark, and compute the evolution to a big volume, where the finite size effects are negligible through step scaling functions which give the change of the observables when L is changed to 2L. In all steps we extrapolate to the continuum limit, separately in HQET and in QCD for masses below m_b. The point m_b is then reached by an interpolation of the continuum results. With r_0=0.5 fm and the experimental B_s and K masses we find f_Bs=191(6) MeV and the renormalization group invariant mass M_b=6.89(11) GeV, translating into m_b(m_b)=4.42(7) GeV in the MS-bar scheme.