# 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

## TL;DR

This paper non-perturbatively determines key improvement coefficients and normalization factors for O(a) improved quark mass renormalisation in N_f=3 Wilson fermions, aiding precise lattice QCD calculations.

## Contribution

It provides the first non-perturbative calculation of Z_m*Z_P/Z_A, b_m, and b_A-b_P for N_f=3 Wilson fermions in the Schroedinger functional scheme, relevant for lattice QCD.

## Key findings

- Results cover typical gauge couplings for large-volume N_f=2+1 QCD.
- Coefficients are determined for lattice spacings below 0.1 fm.
- Results facilitate non-perturbative O(a) improved quark mass calculations.

## Abstract

We determine non-perturbatively the normalisation constant Z_m*Z_P/Z_A as well as the Symanzik coefficients b_m and b_A-b_P, required in O(a) improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in N_f=3 QCD with O(a) improved massless sea and non-degenerate valence quarks in the finite-volume Schroedinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume N_f=2+1 QCD simulations with Wilson fermions at lattice spacings below 0.1 fm, are of particular use for the non-perturbative calculation of O(a) improved renormalised quark masses.