Solution of two-body relativistic bound-state equations with confining plus Coulomb interactions

Abstract

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus linear confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound-state problem. Such a treatment is most easily carried out in momentum space. However, the position-space linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schr\"odinger equation in momentum space for all partial waves. Furthermore, we generalize the linear and Coulomb potentials to relativistic kernels in four-dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three-dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus confining interactions for all partial waves.