Removal of singularities from the covariant spectator theory

TL;DR

This paper introduces a modified kernel for the covariant spectator theory that effectively removes singularities in two-particle scattering calculations while preserving convergence, improving the theoretical framework for scalar particle interactions.

Contribution

The paper presents a new modification of the OBE kernel that eliminates singularities in the CST without ad-hoc fixes, ensuring better mathematical consistency.

Findings

Successfully removes spurious singularities from the kernel.

Maintains convergence of the two-body CST equation.

Applicable to scattering of identical scalar particles.

Abstract

A modification of the one boson exchange (OBE) kernel for the covariant spectator theory (CST) is presented and discussed. When applied to the scattering of two identical particles, the previously used kernels either introduced spurious singularities, or removed them in an ad-hoc way. The new modification not only removes these singularities, but also maintains the convergence of the two-body CST equation (sometimes called the Gross equation) when used to describe the scattering of two identical scalar particles.