The continuum limit of $f_B$ from the lattice in the static approximation

TL;DR

This paper analyzes the continuum extrapolation of the static approximation of the B meson decay constant from lattice data, identifying systematic effects and providing a refined estimate of its value.

Contribution

It introduces a novel method to analyze systematic effects in the continuum extrapolation of lattice QCD data for $f_B^{stat}$, improving accuracy of the estimate.

Findings

Statistical evidence for scaling at inverse lattice spacings > 2 GeV

Lack of asymptotic scaling across all energy scales considered

Estimated $f_B^{stat}$ in the continuum: 230(35) MeV

Abstract

We present an analysis of the continuum extrapolation of $f_B$ in the static approximation from lattice data. The method described here aims to uncover the systematic effects which enter in this extrapolation and has not been described before. Our conclusions are that we see statistical evidence for scaling of $f_B^{stat}$ for inverse lattice spacings $\gtap 2$ GeV but not for $\ltap 2$ GeV. We observe a lack of {\em asymptotic} scaling for a variety of quantities, including $f_B^{stat}$, at all energy scales considered. This can be associated with finite lattice spacing systematics. Once these effects are taken into account, we obtain a value of 230(35) MeV for $f_B^{stat}$ in the continuum where the error represents uncertainties due to both the statistics and the continuum extrapolation. In this method there is no error due to uncertainties in the renormalization constant connecting the lattice and continuum effective theories.