Towards the determination of the charm quark mass on $N_\mathrm{f}=2+1$ CLS ensembles

TL;DR

This paper reports on a lattice QCD study to precisely determine the charm quark mass using multiple ensembles and improved computational techniques, aiming for accurate physical extrapolation.

Contribution

It introduces a novel combination of lattice ensembles, distance preconditioning, and multiple renormalization schemes to improve charm quark mass determination.

Findings

Successful implementation of distance preconditioning for correlation functions.

Use of multiple lattice spacings for reliable continuum extrapolation.

Enhanced stability of the charm quark mass extrapolation.

Abstract

We present the current status of our lattice QCD determination of the charm quark mass using $N_\mathrm{f}=2+1$ dynamical, non-perturbatively $\mathrm{O}(a)$ improved Wilson fermions. A subset of CLS ensembles with five different lattice spacings along the $\mathrm{Tr}[M_\mathrm{q}]=\text{const.}$ trajectory is used. For the computation of the correlation functions involving valence charm quark propagators, we employ distance preconditioning to gain the necessary precision. To stabilize the extrapolations to the physical point, we consider different definitions of the bare charm quark mass and corresponding renormalization procedures.