Determination of $m_c$ from $N_f = 2+1$ QCD with Wilson fermions

TL;DR

This paper reports preliminary results for the charm quark mass in $N_f=4$ QCD using $N_f=2+1$ Wilson fermion ensembles, emphasizing the control of lattice spacing and quark mass dependence, with dominant errors from renormalization and scale setting.

Contribution

First determination of the charm quark mass in $N_f=4$ QCD using non-perturbatively improved Wilson fermions on $N_f=2+1$ ensembles with multiple lattice spacings.

Findings

Charm quark mass determined with controlled lattice spacing dependence.

Multiple lattice spacings and quark mass trajectories used for thorough analysis.

Main uncertainties stem from renormalization and scale setting procedures.

Abstract

We present preliminary results for the charm quark mass in the $N_f=4$ RGI scheme. These were obtained using $N_f=2+1$ CLS ensembles with $\mathcal{O}(a)$ non-perturbatively improved Wilson fermions. We employed five different lattice spacings, ranging down to $a\lesssim 0.04$ fm and realized approximately physical pion and kaon masses, with ensembles spread out along three different trajectories in the quark mass plane, enabling a thorough study of the dependence on the lattice spacing and the light and strange sea quark masses. We sketch our analysis strategy and find that the dominant errors at present are due to the renormalization and scale setting uncertainties.