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

TL;DR

This paper non-perturbatively determines the scale dependence of the static axial current in quenched QCD using a recursive finite-size scaling approach, connecting bare and renormalization group invariant currents.

Contribution

It introduces a non-perturbative method to calculate the scale dependence of the static axial current in quenched QCD within the Schrödinger functional scheme, including continuum extrapolation.

Findings

Connected bare current to renormalization group invariant current.

Renormalized existing data on F_B^{bare} and performed continuum extrapolation.

Studied the function h(d/L,u) related to static quark-antiquark propagation.

Abstract

We non-perturbatively calculate the scale dependence of the static axial current in the Schroedinger 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 F_B^{bare} and extrapolate to the continuum limit. We also study an interesting function h(d/L,u) derived from the Schroedinger functional amplitude describing the propagation of a static quark-antiquark pair.