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

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~$a{m}_b\approx 1$. We also calculate QED and isospin corrections to the (fictitious) $\hat{I}{\cdot }_s$-meson mass, which is used to tune $s$-quark masses in lattice simulations.

Results differ slightly from the first version because of two minor coding errors that were identified and fixed after posting the original draft. The analysis is otherwise unchanged. 21 pages, 12 figures