Non-perturbative improvement of quark mass renormalization in the small lattice spacing region of three-flavor lattice QCD

The use of Heavy Quark Effective Theory (HQET) on the lattice as an approach to B-physics phenomenology is based on a non-perturbative matching of HQET to QCD in finite volume. As a first step to apply the underlying strategy in the three-flavor (N${}_f$ = 2+1) theory, we determine the renormalization constant and improvement coefficients relating the renormalized current and subtracted quark mass of (quenched) valence quarks in O(a) improved N${}_f$ = 3 lattice QCD. We present first results of our calculation for the relevant parameter region towards weak couplings along a line of constant physics, which corresponds to lattice resolutions a $\lesssim$ 0.02 fm and fixes the physical extent of the matching volume to L $\approx$ 0.5 fm.