Non-perturbative renormalization of the axial current in $N_f = 3$ lattice QCD with Wilson fermions and tree-level improved gauge action

TL;DR

This paper non-perturbatively calculates the renormalization factor of the axial current in 3-flavor lattice QCD with Wilson fermions, using Schrödinger functional states to minimize cutoff effects, and provides an interpolation formula connecting to perturbative results.

Contribution

It presents a new non-perturbative determination of the axial current renormalization factor in 3-flavor lattice QCD with Wilson fermions, including an interpolation formula to connect with perturbative theory.

Findings

Non-perturbative $Z_A$ values for various couplings.

Interpolation formula linking non-perturbative and perturbative $Z_A$.

Results applicable at lattice spacings around 0.09 fm and below.

Abstract

We non-perturbatively determine the renormalization factor of the axial vector current in lattice QCD with $N_f=3$ flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity and it is imposed among Schr\"{o}dinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of $\approx 0.09$ fm and below. An interpolation formula for $Z_A(g_0^2)$, smoothly connecting the non-perturbative values to the 1-loop expression, is provided together with our final results.