New high-precision $b$, $c$, and $s$ masses from pseudoscalar-pseudoscalar correlators in $n_f=4$ lattice QCD

TL;DR

This paper presents highly precise lattice QCD calculations of the $b$, $c$, and $s$ quark masses using pseudoscalar correlators, including QED corrections, and analyzes discretization errors.

Contribution

It provides the most accurate $b$, $c$, and $s$ quark mass values to date, with detailed analysis of lattice discretization effects and QED corrections.

Findings

$\overline{m}_b(\overline{m}_b)=4.1923(63)$ GeV

$\overline{m}_c(3\text{ GeV})=0.9813(34)$ GeV

$\overline{m}_s(3\text{ GeV})=83.39(26)$ MeV

Abstract

We extend an earlier lattice QCD analysis of heavy-quark current-current correlators to obtain new values for the $\overline{\mathrm{MS}}$ masses of the $b$, $c$, and $s$~quarks. The analysis uses gluon configurations from the MILC collaboration with vacuum polarization contributions from $u$, $d$, $s$, and~$c$ quarks ($n_f=4$), and lattice spacings down to~0.032~fm. We find that $\overline{m}_b(\overline{m}_b, n_f=5)=4.1923(63)$~GeV, $\overline{m}_c(3~\mathrm{GeV}, n_f=4)=0.9813(34)$~GeV, and $\overline{m}_s(3~\mathrm{GeV}, n_f=4)=83.39(26)$~MeV. These results are corrected for QED by including (quenched) QED in the simulations. They are among the most accurate values by any method to date. We give a detailed analysis of finite lattice-spacing errors that shows why the HISQ discretization of the quark action is particularly useful for $b$-quark simulations even for lattices where~$am_b\approx1$. We also calculate QED and isospin corrections to the (fictitious) $\eta_s$-meson mass, which is used to tune $s$-quark masses in lattice simulations.