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

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 parts per thousand for values of the inverse bare coupling constant beta = 6/g(0)(2) in the range 5.3 <= beta <= 11.5. (C) 2022 The Author(s). Published by Elsevier B.V.