On the retardation effect in the bound q q-bar system in the framework of Bethe-Salpeter equation

Logunov-Tavkhelidze quasipotential approach is used to evaluate the dynamical retardation effect in the bound q q-bar system masses. The confining q q-bar kernel of Bethe-Salpeter equation is taken to be a 4-dimensional oscillator in the momentum space. The ambiguities arising during the straightforward covariantization of the static q q-bar potential are discussed. The first-order perturbative corrections to the meson masses due to the dynamical retardation effect are calculated. The solvability of the first-order quasipotential equation is considered. The numerical solution of this equation with the positive binding energy is obtained. 22 refs., 2 figs