Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation

Abstract

It had been known that the Borel transforms of the twice quark pole mass 2mq and of the QCD static potential V(r) have leading infrared renormalons at b = 1/2 such that they cancel in the sum. The renormalon residue of 2mq had been determined with reasonably high precision from the known perturbative coefficients of the ratio , where is the renormalon-free mass of the quark q. These values of the residues are used here to estimate the hitherto unknown part of the three-loop coefficient of the static potential V(r). Further, the method takes into account the fact that the ultrasoft energy regime contributions must be excluded from the analysis. In the quarkonium, the aforementioned estimated part of the three-loop term turns out to give a contribution to the binding energy comparable to the nonpertubative contribution.