Non-perturbative renormalization of the static axial current in quenched QCD Original Research Article

We non-perturbatively calculate the scale dependence of the static axial current in the Schrödinger functional scheme by means of a recursive finite-size scaling technique, taking the continuum limit in each step. The bare current in the O(a) improved theory as well as in the original Wilson regularization is thus connected to the renormalization group invariant one. The latter may then be related to the current at the B-scale defined such that its matrix elements differ from the physical (QCD) ones by O(1/M). At present, a (probably small) perturbative uncertainty enters in this step. As an application, we renormalize existing unimproved data on FBbare and extrapolate to the continuum limit. We also study an interesting function h(d/L,u) derived from the Schrödinger functional amplitude describing the propagation of a static quark–antiquark pair.