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 ΛQCDr≲0.1 and investigate the ultrasoft correction based on its perturbative evaluation in the large-β0 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.
Highlights
The static QCD potential plays an important role to investigate the QCD dynamics
We focused on the very short distances and used the large-β0 approximation in the perturbative evaluation of δEUS
This is compatible with the fact that the first nonperturbative effect is given by the local gluon condensate
Summary
The static QCD potential plays an important role to investigate the QCD dynamics. It has been investigated extensively by using perturbation theory, effective field theory and lattice simulations. The distances considered here are ΛQCDr 0.1, where δEUS as well as VS can be evaluated perturbatively since the ultrasoft scale satisfies αs(r−1)/r ≫ ΛQCD In this range, the leading nonperturbative correction is given through the local gluon condensate.. We circumvent this problem by including the u = 2 renormalon uncertainty of δEUS in the local gluon condensate, which results in the cancellation of the u = 2 renormalon in the local gluon condensate This renormalon cancellation is explicitly confirmed in this Letter using the large-β0 approximation. Each term does not have the u = 3/2 and u = 2 renormalons Such a result can be used to extract the local gluon condensate numerically, for instance, by comparing lattice simulations with the calculation presented here. We will see how a renormalon free part is identified in connection with the cutoff scales
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