f_B and two scales problems in lattice QCD

TL;DR

This paper introduces a new lattice QCD method to calculate f_B and f_{B_s} that minimizes systematic errors and allows for continuum extrapolation, providing estimates close to experimental values.

Contribution

A novel non-perturbative recursive finite size technique for calculating decay constants in lattice QCD, reducing systematic errors and applicable to two-scale problems.

Findings

Estimated f_B = 170(11)(5)(22) MeV

Estimated f_{B_s} = 192(9)(5)(24) MeV

Method can be generalized to other two-scale lattice QCD problems

Abstract

A novel method to calculate f_B on the lattice is introduced, based on the study of the dependence of finite size effects upon the heavy quark mass of flavoured mesons and on a non-perturbative recursive finite size technique. We avoid the systematic errors related to extrapolations from the static limit or to the tuning of the coefficients of effective Lagrangian and the results admit an extrapolation to the continuum limit. We perform a first estimate at finite lattice spacing, but close to the continuum limit, giving f_B = 170(11)(5)(22) MeV. We also obtain f_{B_s} = 192(9)(5)(24) MeV. The first error is statistical, the second is our estimate of the systematic error from the method and the third the systematic error from the specific approximations adopted in this first exploratory calculation. The method can be generalized to two--scale problems in lattice QCD.