Off-shell suppression of renormalons in non-relativistic QCD boundstates

We study an effect of the off-shellness of the quark and antiquark inside a heavy quarkonium system on IR renormalons contained in the perturbative computations of the quarkonium energy levels. We demonstrate that, when the off-shellness pQ2−mQ2∼αS2mQ2 is larger than mQΛQCD, renormalons in the energy levels as calculated in perturbative QCD are suppressed by a factor ΛQCD/(αS2mQ) as compared to those in 2mpole+VQCD(r). In this case the residual O(ΛQCD4) renormalon has the same dimension as that of the leading gluon-condensate contribution.