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

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