Abstract

We use various methods of Borel integration to calculate the binding ground energies and masses of bb? and tt? 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 m q, where the contributions of these singularities in M(s) = 2m q + 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?q and ?s(?). The renormalization scales ? are different in calculations of mq, E(s) and E(us). The mass m?b is extracted, and the binding energies Ett? and the peak (resonance) energies Eres for tt? production are obtained.