On lattice actions for static quarks

TL;DR

This paper introduces new discretizations for static quark actions that significantly improve the signal-to-noise ratio in static-light correlation functions, with thorough testing and non-perturbative renormalization results.

Contribution

It presents novel discretizations of static quark actions that enhance signal quality and provides detailed scaling tests and renormalization constants in lattice QCD.

Findings

Exponential improvement in signal-to-noise ratio over Eichten-Hill regularization.

Small scaling violations in O(a) improved theory.

Non-perturbative determination of renormalization constants.

Abstract

We introduce new discretizations of the action for static quarks. They achieve an exponential improvement (compared to the Eichten-Hill regularization) on the signal to noise ratio in static-light correlation functions. This is explicitly checked in a quenched simulation and it is understood quantitatively in terms of the self energy of a static quark and the lattice heavy quark potential at zero distance. We perform a set of scaling tests in the Schroedinger functional and find scaling violations in the O(a) improved theory to be rather small -- for one observable significantly smaller than with the Eichten-Hill regularization. In addition we compute the improvement coefficients of the static light axial current up to O(g_0^4) corrections and the corresponding renormalization constants non-perturbatively. The regularization dependent part of the renormalization of the b-quark mass in static approximation is also determined.