Ward identity determination of ZS/ZP for Nf=3 lattice QCD in a Schr\"odinger functional setup
Abstract
We derive chiral Ward identities for lattice QCD with Wilson quarks and Nf ≥ 3 flavours, on small lattices with Schr\"odinger 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 ZS/ZP of the renormalisation parameters of these operators. We obtain results for Nf=3 QCD with tree-level Symanzik-improved gluons and Wilson-Clover quarks, for bare gauge couplings which cover the typical range of large-volume Nf = 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 ZS/ZP ratio can be used in the non-perturbative calculations of O(a) improved renormalised quark masses.