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

Understand

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.