The renormalised $\mathrm{O}(a)$ improved vector current in three-flavour lattice QCD with Wilson quarks

TL;DR

This paper non-perturbatively determines the improvement coefficient and renormalisation factor for the vector current in three-flavour lattice QCD with Wilson quarks, ensuring accurate continuum limit extrapolations.

Contribution

It provides the first non-perturbative results for $c_V$ and $Z_V$ in three-flavour $ m O(a)$ improved lattice QCD with Wilson quarks, using Schrödinger functional techniques.

Findings

Non-perturbative $c_V$ differs significantly from one-loop estimates.

Results cover lattice spacings from 0.04 to 0.1 fm.

Method ensures controlled quark mass effects and smooth coupling dependence.

Abstract

We present the results of a non-perturbative determination of the improvement coefficient $c_\mathrm{V}$ and the renormalisation factor $Z_\mathrm{V}$, which define the renormalised vector current in three-flavour $\mathrm{O}(a)$ improved lattice QCD with Wilson quarks and tree-level Symanzik-improved gauge action. In case of the improvement coefficient, we consider both lattice descriptions of the vector current, the local as well as the conserved (i.e., point-split) one. Our improvement and normalisation conditions are based on massive chiral Ward identities and numerically evaluated in the Schr\"odinger functional setup, which allows to eliminate finite quark mass effects in a controlled way. In order to ensure a smooth dependence of the renormalisation constant and improvement coefficients on the bare gauge coupling, our computation proceeds along a line of constant physics, covering the typical range of lattice spacings $0.04\,\mathrm{fm}\lesssim a\lesssim 0.1\,\mathrm{fm}$ that is useful for phenomenological applications. Especially for the improvement coefficient of the local vector current, we report significant differences between the one-loop perturbative estimates and our non-perturbative results.