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It had been known that the Borel transforms of the twice quark pole mass 2*mqand of the QCD q-barq static potential V(r) have leading infrared renormalonsat b=1/2 such that they cancel in the sum. The renormalon residue of 2*mq hadbeen determined with reasonably high precision from the known perturbativecoefficients of the ratio mq/(bar mq), where (bar mq) is the barMSrenormalon-free mass of the quark q. These values of the residues are used hereto estimate the hitherto unknown part of the three-loop coefficient of thestatic potential V(r). Further, the method takes into account the fact that theultrasoft energy regime contributions must be excluded from the analysis. Inthe b-barb quarkonium, aforementioned estimated part of the three-loop termturns out to give a contribution to the binding energy comparable to thenonpertubative contribution.Comment: 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 unchange

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