Ward identity determination of Z_S/Z_P for N_f=3 lattice QCD in a Schrödinger functional setup

Heitger J., Joswig F., Vladikas A.

Research article (journal) | Peer reviewed

Abstract

We derive chiral Ward identities for lattice QCD with Wilson quarks and Nf≥3 flavours, on small lattices with Schrödinger 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 0.1fm. 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.