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

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.