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

We use various methods of Borel integration to calculate the binding ground energies and masses of bb-bar and tt-bar 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)=2mq+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 MS mass m-barq and αs(μ). The renormalization scales μ are different in calculations of mq, E(s) and E(us). The mass m-barb is extracted, and the binding energies Ett-bar and the peak (resonance) energies Eres. for tt-bar production are obtained