Renormalon free part of an ultrasoft correction to the static QCD potential

TL;DR

This paper investigates the ultrasoft correction to the static QCD potential, focusing on renormalon cancellations and nonperturbative effects at very short distances using perturbative methods and the large-beta_0 approximation.

Contribution

It introduces a formulation to separate renormalon uncertainties from the ultrasoft correction and proposes a method to analyze the local gluon condensate without renormalon contamination.

Findings

Renormalon uncertainties are canceled at LO in the multipole expansion.

The ultrasoft correction can be separated into renormalon-free and uncertain parts.

A new approach to examine the local gluon condensate without $u=2$ renormalon issues.

Abstract

Perturbative calculations of the static QCD potential have the $u=3/2$ renormalon uncertainty. In the multipole expansion performed within pNRQCD, this uncertainty at LO is known to get canceled against the ultrasoft correction at NLO. To investigate the net contribution remaining after this renormalon cancellation, we propose a formulation to separate the ultrasoft correction into renormalon uncertainties and a renormalon independent part. We focus on very short distances $\Lambda_{\rm QCD} r \lesssim 0.1$ and investigate the ultrasoft correction based on its perturbative evaluation in the large-$\beta_0$ approximation. We also propose a method to examine the local gluon condensate, which appears as the first nonperturbative effect to the static QCD potential, without suffering from the $u=2$ renormalon.