High-Precision $f_{B_s}$ and HQET from Relativistic Lattice QCD

TL;DR

This paper presents a highly precise lattice QCD calculation of the $B_s$ decay constant, providing empirical evidence for HQET predictions and demonstrating the potential for 2% accuracy in $B_s$ and $B$ physics calculations.

Contribution

The study introduces a new, highly accurate lattice QCD determination of $f_{B_s}$ and confirms the HQET $1/ ext{sqrt}(m_h)$ dependence with empirical data.

Findings

$f_{B_s} = 0.225(4)$ GeV, nearly three times more precise than previous results.

First empirical evidence supporting HQET's leading $1/ ext{sqrt}(m_h)$$ dependence.

Calculated $m_{B_s}-m_{ ext{eta}_b}/2$ mass difference agrees with experiment within 11 MeV.

Abstract

We present a new determination of the $B_s$ leptonic decay constant from lattice QCD simulations that use gluon configurations from MILC and a highly improved discretization of the relativistic quark action for both valence quarks. Our result, $f_{B_s} = 0.225(4)$\,GeV, is almost three times more accurate than previous determinations. We analyze the dependence of the decay constant on the heavy quark's mass and obtain the first empirical evidence for the leading $1/\sqrt{m_h}$ dependence predicted by Heavy Quark Effective Theory (HQET). As a check, we use our analysis technique to calculate the $m_{B_s}-m_{\eta_b}/2$ mass difference. Our result agrees with experiment to within errors of $11\,\mathrm{MeV}$ (better than 2%). We discuss how to extend our analysis to other quantities in $B_s$ and $B$ physics, making 2%-precision possible for the first time.