Hyperasymptotic approximation to the plaquette and determination of the gluon condensate

TL;DR

This paper develops a hyperasymptotic expansion for the plaquette in SU(3) gluodynamics, accurately capturing renormalon effects, and uses it to determine the gluon condensate independently of renormalization schemes.

Contribution

It introduces a hyperasymptotic approximation for the plaquette that includes leading renormalon effects and provides a scheme-independent determination of the gluon condensate.

Findings

Precise hyperasymptotic expansion of the plaquette.

Scheme-independent value of the gluon condensate: 3.15(18) r_0^{-4}.

Inclusion of subleading effects in the analysis.

Abstract

We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. Subleading effects are also considered. The perturbative series is regulated using the principal value prescription for its Borel integral. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: $\langle G^2 \rangle_{\rm PV} (n_f=0)=3.15(18)\; r_0^{-4}$.