We present the results of a non-perturbative determination of the improvement coefficient cV and the renormalisation factor ZV, which define the renormalised vector current in three-flavour 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 0.04fm≲a≲0.1fm 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.
@article{arxiv.2010.09539,
title = {The renormalised $\mathrm{O}(a)$ improved vector current in three-flavour lattice QCD with Wilson quarks},
author = {Jochen Heitger and Fabian Joswig},
journal= {arXiv preprint arXiv:2010.09539},
year = {2021}
}