Solving momentum-space integral equations for quarkonia spectra with confining potentials

Abstract

Singular integral equations for quarkonia (qq\ifmmode\bar\else\textasciimacron\fi{}) spectra are solved in momentum space for different choices of confining potentials by introducing a regularization procedure. The method is sufficiently general to treat nonlocal potentials and combinations of singular potentials. Through nonrelativistic model applications we demonstrate the stability and accuracy of the method. The method works in all partial waves. A first-order correction to the eigenenergies brings calculated results for soluble model problems into remarkable agreement with exact results. Extensions of the method to solve the nonrelativistic spectra of three-quark systems and to solve the relativistic Bethe-Salpeter equation are discussed.