A covariant constituent-quark formalism for mesons

TL;DR

This paper develops a covariant model within the Covariant Spectator Theory to study meson structures and spectra, improving numerical stability and accuracy by reformulating the equations to explicitly remove singularities.

Contribution

It introduces a reformulation of the relativistic meson equations that removes singularities, enhancing numerical stability and accuracy in the Covariant Spectator Theory framework.

Findings

Improved numerical stability in solving meson equations.

Accurate solutions for mesonic spectra using the reformulated equations.

Enhanced understanding of relativistic meson structure.

Abstract

Using the framework of the Covariant Spectator Theory (CST) [1] we are developing a covariant model formulated in Minkowski space to study mesonic structure and spectra. Treating mesons as effective $q\bar{q}$ states, we focused in [2] on the nonrelativistic bound-state problem in momentum space with a linear confining potential. Although integrable, this kernel has singularities which are difficult to handle numerically. In [2] we reformulate it into a form in which all singularities are explicitely removed. The resulting equations are then easier to solve and yield accurate and stable solutions. In the present work, the same method is applied to the relativistic case, improving upon the results of the one-channel spectator equation (1CSE) given in [3].