Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation

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We use various methods of Borel integration to calculate the binding ground energies and masses of b-bbar and t-tbar quarkonia. The methods take into account the leading infrared renormalon structure of the hard+soft part of the binding energies E(s), and of the corresponding quark pole masses mq, where the contributions of these singularities in M(s) = 2 mq + E(s) cancel. Beforehand, we carry out the separation of the binding energy into its hard+soft and ultrasoft parts. The resummation formalisms are applied to expansions of mq and E(s) in terms of quantities which do not involve renormalon ambiguity, such as MSbar quark mass, and alphaₛ. The renormalization scales are different in calculations of mq, E(s) and E(us). The MSbar mass of b quark is extracted, and the binding energies of t-tbar and the peak (resonance) energies for (t+tbar) production are obtained.