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 ZV 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 ZV 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 ZV with an accuracy of about 8‰ for values of the inverse bare coupling constant β=6/g02 in the range 5.3≤β≤11.5.