Non-perturbative renormalization of the QCD flavour-singlet local vector current

TL;DR

This paper non-perturbatively computes the renormalization constant of the flavor-singlet local vector current in lattice QCD with three massless flavors, using finite temperature simulations and shifted boundary conditions.

Contribution

It introduces a method to determine the renormalization constant $Z_V$ non-perturbatively with about 0.8% accuracy in lattice QCD with Wilson fermions.

Findings

$Z_V$ determined with 0.8% accuracy across a range of couplings

Method applicable to flavor-singlet vector currents in lattice QCD

Provides data for $Z_V$ at various lattice spacings

Abstract

We compute non-perturbatively the renormalization constant of the flavour-singlet local vector current $Z_V$ in lattice QCD with 3 massless flavours. Gluons are discretized by the Wilson plaquette action while quarks by the O($a$)-improved Wilson--Dirac operator. The constant $Z_V$ is fixed by comparing the expectation values (1-point functions) of the conserved and local vector currents at finite temperature in the presence of shifted boundary conditions and at non-zero imaginary chemical potential. Monte Carlo simulations with a moderate computational cost allow us to obtain $Z_V$ with an accuracy of about 8\textperthousand\, for values of the inverse bare coupling constant $\beta=6/g_0^2$ in the range $5.3 \leq \beta \leq 11.5$.