Non-perturbative determination of improvement coefficients b_m and b_A-b_P and normalisation factor Z_m*Z_P/Z_A with N_f=3 Wilson fermions

We determine non-perturbatively the normalisation parameter $Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$ as well as the Symanzik coefficients $b_\mathrm{m}$ and $b_\mathrm{A}-b_\mathrm{P}$ , required in $\mathrm{O}(a)$ improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in $N_\mathrm{f}=3$ QCD with $\mathrm{O}(a)$ improved massless sea and non-degenerate valence quarks in the finite-volume Schrödinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume $N_\mathrm{f}=2+1$ QCD simulations with Wilson fermions at lattice spacings below $0.1\,\mathrm{fm}$ , are of particular use for the non-perturbative calculation of $\mathrm{O}(a)$ improved renormalised quark masses.