Numerical investigation of Schwinger-Dyson and Bethe-Salpeter equations with Gauss and oscillator potentials in the framework of the quarkonium model

摘要

The potential model of quarkonium is considered on the basis of the Schwinger-Dyson equation for the quark mass function and the Bethe-Salpeter equation for the bound states. The software for numerical investigation of the model is constructed. Solutions to these equations for the effective potential as the sum of the Gauss and oscillator potentials for pion are obtained. Some modifications for the Schwinger-Dyson equation are considered. As shown, the considered approximation describes the mass and the leptonic decay constant of the pion ground state. However, for the masses of the pion radial excited states this scheme gives the estimations that are smaller than the available experimental data. 10 refs., 4 tabs. (Atomindex citation 26:061057)