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

We extend an earlier lattice QCD analysis of heavy-quark current-current correlators to obtain new values for the $\overline{\mathrm{M}\mathrm{S}}$ 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 ${\bar{m}}_b({\bar{m}}_b,n_f=5)=4.1923(63)$~GeV, ${\bar{m}}_c(3\mathrm{G}\mathrm{e}\mathrm{V},n_f=4)=0.9813(34)$~GeV, and ${\bar{m}}_s(3\mathrm{G}\mathrm{e}\mathrm{V},n_f=4)=83.39(26)$~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) ${\eta }_s$-meson mass, which is used to tune $s$-quark masses in lattice simulations.