Ward identity determination of ZS/ZP for Nf=3 lattice QCD in a Schrodinger functional setup

We derive chiral Ward identities for lattice QCD with Wilson quarks and N-f >= 3 flavours, on small lattices with Schrodinger functional boundary conditions and vanishingly small quark masses. These identities relate the axial variation of the non-singlet pseudoscalar density to the scalar one, thus enabling the non-perturbative determination of the scale-independent ratio Z(S)/Z(P) of the renormalisation parameters of these operators. We obtain results for N-f = 3 QCD with tree-level Symanzik-improved gluons and Wilson-Clover quarks, for bare gauge couplings which cover the typical range of large-volume N-f = 2+1 simulations with Wilson fermions at lattice spacings below 0.1 fm. The precision of our results varies from 0.3 to 1%, except for the coarsest lattice, where it is 2%. We discuss how the Z(S)/Z(P) ratio can be used in the non-perturbative calculations of O(a) improved renormalised quark masses.