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 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.