New methods for B meson decay constants and form factors from lattice NRQCD

TL;DR

This paper introduces new lattice QCD methods to accurately determine B meson decay constants and form factors by normalizing scalar and pseudoscalar currents, providing systematic error tests and updated precise values.

Contribution

It presents a novel normalization approach for scalar and pseudoscalar currents in lattice QCD, improving the precision of B meson decay constant calculations and systematic error assessment.

Findings

New lattice QCD values for $f_B$, $f_{B_s}$, and their ratio.

Validation of methods against previous axial current results.

Updated decay constants with reduced uncertainties.

Abstract

We determine the normalisation of scalar and pseudoscalar current operators made from non-relativistic $b$ quarks and Highly Improved Staggered light quarks in lattice Quantum Chromodynamics (QCD) through $\mathcal{O}(\alpha_s)$ and $\Lambda_{\text{QCD}}/m_b$. We use matrix elements of these operators to extract $B$ meson decay constants and form factors, then compare to those obtained using the standard vector and axial-vector operators. This provides a test of systematic errors in the lattice QCD determination of the $B$ meson decay constants and form factors. We provide a new value for the $B$ and $B_s$ meson decay constants from lattice QCD calculations on ensembles that include $u$, $d$, $s$ and $c$ quarks in the sea and those which have the $u/d$ quark mass going down to its physical value. Our results are $f_B=0.196(6)$ GeV, $f_{B_s}=0.236(7)$ GeV and $f_{B_s}/f_B =1.207(7)$, agreeing well with earlier results using the temporal axial current. By combining with these previous results, we provide updated values of $f_B=0.190(4)$ GeV, $f_{B_s}=0.229(5)$ GeV and $f_{B_s}/f_B = 1.206(5)$.