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

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.