A covariant constituent-quark formalism for mesons

Abstract

Using the framework of the Covariant Spectator Theory (CST), we are developing a covariant model formulated in Minkowski space to study mesonic structure and spectra. Treating mesons as effective qq ̄ states, we focused on the nonrelativistic bound-state problem in momentum space with a linear confining potential. Although integrable, this kernel has sin- gularities which are difficult to handle numerically. 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) presented in some previous works.