The scalar gluonium correlator: large-beta_0 and beyond

TL;DR

This paper analyzes the scalar gluonium correlator in QCD, exploring perturbative corrections, large-order behavior, and renormalon structures, linking them to fundamental QCD parameters and the vacuum state.

Contribution

It extends the understanding of the scalar gluonium correlator by studying its all-order behavior using the large-beta_0 approximation and discussing renormalon effects and low-energy theorems.

Findings

Large-order behavior governed by ultraviolet renormalon

Infrared renormalon poles related to operator product expansion

Low-energy theorem links correlator to gluon condensate

Abstract

The investigation of the scalar gluonium correlator is interesting because it carries the quantum numbers of the vacuum and the relevant hadronic current is related to the anomalous trace of the QCD energy-momentum tensor in the chiral limit. After reviewing the purely perturbative corrections known up to next-next-to-leading order, the behaviour of the correlator is studied to all orders by means of the large-beta_0 approximation. Similar to the QCD Adler function, the large-order behaviour is governed by the leading ultraviolet renormalon pole. The structure of infrared renormalon poles, being related to the operator product expansion are also discussed, as well as a low-energy theorem for the correlator that provides a relation to the renormalisation group invariant gluon condensate, and the vacuum matrix element of the trace of the QCD energy-momentum tensor.