$Z_S\mathrm{/}{Z}_P$ from three-flavour lattice QCD

We report on advances in the non-perturbative determination of the ratio $Z_S\mathrm{/}{Z}_P$ of the pseudoscalar to the scalar renormalization constants in three-flavour lattice QCD with Wilson-clover quarks and tree-level Symanzik improved gluons. The computations are based on the Ward identity approach, using Schr"odinger functional boundary conditions. Our results for $Z_S\mathrm{/}{Z}_P$ cover a range of couplings along a line of constant physics with lattice spacings of about 0.09 fm and below, relevant for phenomenological applications such as the calculation of renormalized quark masses.