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 2*mq and of the QCD q-barq static potential V(r) have leading infrared renormalons at b=1/2 such that they cancel in the sum. The renormalon residue of 2*mq had been determined with reasonably high precision from the known perturbative coefficients of the ratio mq/(bar mq), where (bar mq) is the barMS 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 b-barb quarkonium, aforementioned estimated part of the three-loop term turns out to give a contribution to the binding energy comparable to the nonpertubative contribution.
Cite
@article{arxiv.hep-ph/0309262,
title = {Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation},
author = {Gorazd Cvetic},
journal= {arXiv preprint arXiv:hep-ph/0309262},
year = {2008}
}
Comments
8 pages, 4 eps-figures, revtex4; the version as it will appear in J.Phys.G.; the first paragraph, the paragraph containing Eqs.(31)-(32), and the last paragraph are new; some new references were added; numerical results are unchanged