High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD

We use lattice QCD simulations, with MILC gluon configurations and HISQ $c$-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the $\overline{\mathrm{MS}}$ mass of the charm quark and of the $\overline{\mathrm{MS}}$ coupling. We find $m_c(3\mathrm{GeV})=0.986(10)\mathrm{GeV}$, or, equivalently, $m_c(m_c)=1.268(9)\mathrm{GeV}$, both for $n_f=4$ flavors; and ${\alpha }_{\overline{\mathrm{MS}}}(3\mathrm{GeV},n_f=4)=0.251(6)$, or, equivalently, ${\alpha }_{\overline{\mathrm{MS}}}(M_Z,n_f=5)=0.1174(12)$. The new mass agrees well with results from continuum analyses of the vector correlator using experimental data for $e^{+}{e}^{-}$ annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. Ours is also one of the most accurate determinations of the QCD coupling by any method.