Lattice energy sum rules and the trace anomaly

TL;DR

This paper links the additional terms in lattice energy sum rules for quark potentials and glueball masses to the trace anomaly in the energy momentum tensor, clarifying their physical origin.

Contribution

It explicitly identifies the anomalous contribution to the field energy as arising from the trace anomaly in lattice sum rules for quark potentials and glueball masses.

Findings

The additional lattice energy contributions are due to the trace anomaly.

Explicit connection between sum rules and the trace anomaly.

Clarification of the anomalous energy contribution in lattice QCD.

Abstract

We show that the additional contribution to the Michael lattice energy sum rule for the static quark-antiquark potential, pointed out recently, can be identified with the contribution to the field energy arising from the trace anomaly of the energy momentum tensor. We also exlicitely exhibit the anomalous contribution to the field energy in the sum rule for the glueball mass obtained recently by Michael.