On the reliable measurement of the gluon condensate in lattice QCD

TL;DR

This paper introduces an indirect lattice QCD method to measure the gluon condensate by analyzing heavy quark correlators, accounting for continuum contributions and finite size effects.

Contribution

It presents a novel approach to determine the gluon condensate using heavy quark correlators and provides a practical nonperturbative heavy quark mass definition.

Findings

Continuum spectrum contributions are significant and align with expectations.

Finite size effects are negligible for heavy quarks on moderate lattices.

The method enables a more reliable extraction of the gluon condensate.

Abstract

We propose to calculate the gluon condensate in lattice QCD in an indirect way by extracting it from the correlator of hadronic currents of heavy quarks. Moments (derivatives with respect to momentum at vanishing momentum) of the vector and pseudoscalar correlators are evaluated. The contribution of the continuum spectrum in addition to the low-lying resonance is observed in accordance with qualitative expectations. Finite size effects are observed and shown to be insignificant for heavy quarks and moderate lattices. A practical definition of the nonperturbatively renormalized heavy quark mass is given.