Phenomenology of renormalons and the OPE from lattice regularization: the gluon condensate and the heavy quark pole mass

TL;DR

This paper investigates the perturbative and non-perturbative aspects of the gluon condensate and heavy quark pole mass using lattice regularization, confirming renormalon predictions and extracting key non-perturbative parameters.

Contribution

It provides high-order perturbative calculations and confirms the renormalon structure of the operator product expansion for the gluon condensate and heavy quark self-energy.

Findings

Perturbative series reach asymptotic regime with renormalon behavior.

Non-perturbative corrections extracted match theoretical expectations.

Results are consistent with operator product expansion and renormalon models.

Abstract

We study the operator product expansion of the plaquette (gluon condensate) and the self-energy of an infinitely heavy quark. We first compute their perturbative expansions to order $\alpha^{35}$ and $\alpha^{20}$, respectively, in the lattice scheme. In both cases we reach the asymptotic regime where the renormalon behavior sets in. Subtracting the perturbative series, we obtain the leading non-perturbative corrections of their respective operator product expansions. In the first case we obtain the gluon condensate and in the second the binding energy of the heavy quark in the infinite mass limit. The results are fully consistent with the expectations from renormalons and the operator product expansion.