Bethe-Salpeter study of radially excited vector quarkonia

We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a Poincare invariant generalization of screened linear confining potential. In order to get a reliable description the Lorentz scalar confining interaction is complemented by the effective one gluon exchange. Within the presented model we reasonably reproduce all known radial excitations of the vector charmonia. We have found that J/psi is the only charmonium left below naive quark-antiquark threshold 2m(c), while the all excited states are situated above this threshold. We develop a method which is able to provide a solution of full four dimensional Bethe-Salpeter equation for the all excited states. We discuss the consequences of the use of the free propagators for calculation of excited states above the threshold. The Bethe-Salpeter string breaking scale mu similar or equal to 350 MeV appears to be relatively larger then the one defined in various potential models mu similar or equal to 150 MeV.