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 <math altimg="si1.svg"><msub><mrow><mi>Z</mi></mrow><mrow><mi>V</mi></mrow></msub></math> 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 <math altimg="si1.svg"><msub><mrow><mi>Z</mi></mrow><mrow><mi>V</mi></mrow></msub></math> 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 <math altimg="si1.svg"><msub><mrow><mi>Z</mi></mrow><mrow><mi>V</mi></mrow></msub></math> with an accuracy of about 8‰ for values of the inverse bare coupling constant <math altimg="si2.svg"><mi>β</mi><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>6</mn><mo stretchy="false">/</mo><msubsup><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math> in the range <math altimg="si3.svg"><mn>5.3</mn><mo>≤</mo><mi>β</mi><mo>≤</mo><mn>11.5</mn></math>.