Non-perturbative renormalization of the static axial current in two-flavour QCD

TL;DR

This paper non-perturbatively determines the scale dependence of the static-light axial current in two-flavour lattice QCD, revealing significant deviations from perturbative predictions and improving precision with modified static quark discretizations.

Contribution

It provides the first non-perturbative renormalization of the static axial current in two-flavour QCD using the Schrödinger functional scheme and improved static quark actions.

Findings

Non-perturbative running differs significantly from perturbative predictions.

The renormalization factor is computed in the Schrödinger functional scheme.

Application to B_s-meson decay constant at a ~ 0.08 fm.

Abstract

We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static effective theory to the renormalization group invariant one is evaluated in the Schroedinger functional scheme, where in this case we find a significant deviation of the non-perturbative running from the perturbative prediction. An important technical ingredient to improve the precision of the results consists in the use of modified discretizations of the static quark action introduced earlier by our collaboration. As an illustration how to apply the renormalization of the static axial current presented here, we connect the bare matrix element of the current to the B_s-meson decay constant in the static approximation for one value of the lattice spacing, a ~ 0.08 fm, employing large-volume N_f=2 data at beta=5.3.