Absorbing discretisation effects with a massive renormalization scheme: the charm-quark mass

TL;DR

This paper introduces a numerical implementation of the massive SMOM renormalization scheme to accurately determine the charm quark mass, reducing discretization effects compared to previous schemes.

Contribution

The first numerical implementation of the massive SMOM scheme is used to calculate the charm quark mass with improved discretization control.

Findings

Charm quark mass in the MSbar scheme: 1.008(13) GeV at 3 GeV

Charm quark mass at the charm scale: 1.292(12) GeV

Reduced discretization effects compared to SMOM scheme

Abstract

We present the first numerical implementation of the massive SMOM (mSMOM) renormalization scheme and use it to calculate the charm quark mass. Based on ensembles with three flavours 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 discretisation 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 $\overline{m}_c(\overline{m}_c) = 1.292(12)\,\mathrm{GeV}$.