Singularity-Free Two-Body Equation with Confining Interactions in Momentum Space

Abstract

We are developing a covariant model for all mesons that can be described as quark-antiquark bound states in the framework of the Covariant Spectator Theory (CST) in Minkowski space. The kernel of the bound-state equation contains a relativistic generalization of a linear confining potential which is singular in momentum space and makes its numerical solution more difficult. The same type of singularity is present in the momentum-space Schrödinger equation, which is obtained in the nonrelativistic limit. We present an alternative, singularity-free form of the momentum-space Schrödinger equation which is much easier to solve numerically and which yields accurate and stable results. The same method will be applied to the numerical solution of the CST bound-state equations.