Numerical investigation of Schwinger–Dyson and Bhete–Salpeter equations with Gauss potential at the framework of the quarkonium model

The mathematical model of “quarkonium” is considered on the basis of Schwinger–Dyson equation for the quark mass function and Bethe–Salpeter equation for the bound states. The software for numerical investigations of the model is constructed, and the solutionsto the boundary problems for these equations with the Gauss potential for pion are obtained. The several renormalization schemes of the quark wave function “inside” emeson are considered. It is shown that in the considered renormalization scheme the model with the Gauss potential describes the quark dynamical mass, due to the spontaneous chiral symmetry breaking, as well as the mass and the leptonic decay constant of pion.