The lattice scale at large beta in quenched QCD

TL;DR

This paper refines the estimate of lattice spacing in quenched QCD at large beta values using renormalized coupling data, showing asymptotic freedom behavior and minimal systematic errors.

Contribution

It extends lattice spacing estimates at higher beta values by employing Schroedinger functional formalism and asymptotic freedom, achieving precise error bounds.

Findings

Asymptotic freedom describes data well for beta ≥ 7

Effective four-loop term fits the data with current parameters

Systematic error on lattice spacing is between 1% and 3%

Abstract

In this paper we extend the estimate of the value of the lattice spacing a in units of the r0 scale at values of the bare coupling larger than those available. By using results from the computation of the renormalised coupling in the Schroedinger functional formalism we find that from beta \simeq 7 onward the behaviour predicted by asymptotic freedom at tree loop describes very well the data if a value of (r0 Lambda) slightly lower then the latest available is used. We also show that, by sticking to the current value, an effective four loop term can describe as well the data. The systematic relative error on the lattice spacing induced by the choice of the procedure is between 1% and 3% for 6.92 < beta < 8.5.