Theoretical description of the plaquette with exponential accuracy

TL;DR

This paper reviews the operator product expansion of the plaquette and the determination of the gluon condensate, achieving exponential accuracy through superasymptotic and hyperasymptotic methods, confirming renormalon predictions.

Contribution

It introduces a superasymptotic and hyperasymptotic approach to accurately extract the gluon condensate from the plaquette's perturbative series, confirming theoretical expectations.

Findings

Perturbative series reaches the asymptotic regime with renormalon behavior.

Superasymptotic subtraction yields the gluon condensate with high precision.

Results confirm the predictions of renormalons and operator product expansion.

Abstract

We review recent studies of the operator product expansion of the plaquette and of the associated determination of the gluon condensate. One first needs the perturbative expansion to orders high enough to reach the asymptotic regime where the renormalon behavior sets in. The divergent perturbative series is formally regulated using the principal value prescription for its Borel integral. Subtracting the perturbative series truncated at the minimal term, we obtain the leading non-perturbative correction of the operator product expansion, i.e. the gluon condensate, with superasymptotic accuracy. It is then explored how to increase such precision within the context of the hyperasymptotic expansion. The results fully confirm expectations from renormalons and the operator product expansion.