The SF running coupling with four flavours of staggered quarks

TL;DR

This paper adapts the Schr"odinger functional method to four-flavour QCD with staggered quarks, addressing lattice setup challenges and calculating boundary counterterms to improve the accuracy of the running coupling measurement.

Contribution

It introduces a modified SF setup for staggered quarks with a detailed perturbative calculation of boundary counterterms, enhancing precision in four-flavour QCD studies.

Findings

Redefinition of SF to handle even spatial and odd temporal lattice extents.

Calculation of the pure gauge ${ m O}(a)$ boundary counterterm to one-loop order.

Identification of cutoff effects due to lattice geometry constraints.

Abstract

In order to study the running coupling in four-flavour QCD, we review the set-up of the Schr\"odinger functional (SF) with staggered quarks. Staggered quarks require lattices which, in the usual counting, have even spatial lattice extent $L/a$ while the time extent $T/a$ must be odd. Setting $T=L$ is therefore only possible up to ${\rm O}(a)$, which introduces different cutoff effects already in the pure gauge theory. We re-define the SF such as to cope with this situation and determine the corresponding classical background field. A perturbative calculation yields the coefficient of the pure gauge ${\rm O}(a)$ boundary counterterm to one-loop order.