Absorbing discretization effects with a massive renormalization scheme: The charm-quark mass

We present the first numerical implementation of the massive symmetric-momentum-subtraction (mSMOM) renormalization scheme and use it to calculate the charm-quark mass. Based on ensembles with three flavors of dynamical domain-wall fermions with lattice spacings in the range 0.11–0.08 fm, we demonstrate that the mass scale which defines the mSMOM scheme can be chosen such that the extrapolation has significantly smaller discretization effects than the SMOM scheme. Converting our results to the $\overline{\mathrm{MS}}$ scheme we obtain ${\overline{m}}_c(3\mathrm{GeV})=1.008(13)\mathrm{GeV}$ and ${\overline{m}}_c({\overline{m}}_c)=1.292(12)\mathrm{GeV}$.