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

Abstract

Singular integral equations for quarkonia (qq\ifmmode\bar\else\textasciimacron\fi{}) spectra are solved in momentum space for nonrelativistic and relativistic Coulomb plus confinement potentials. The confinement potential in momentum space is defined using an analytical regularization scheme. Further manipulations give rise to integro-differential equations and we obtain analytical expressions for the remaining singular integrals. The procedure is tested on previously solved relativistic and nonrelativistic cases. The energies of the first few eigenstates are obtained accurately to six significant figures. The method works in all partial waves. Straightforward extensions are sufficiently general to treat nonlocal potentials and combinations of singular potentials.