Non-perturbative determination of improvement coefficients $$b_\mathrm{m}$$ and $$b_\mathrm{A}-b_\mathrm{P}$$bA-bP and normalisation factor $$Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$$ZmZP/ZA with $$N_\mathrm{f}= 3$$Nf=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 Schrodinger 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.