Goldstone pion and other mesons using a scalar confining interaction

Abstract

A covariant wave equation for qq¯ interactions with an interaction kernel composed of the sum of constant vector and linear scalar confining interactions is solved for states with two quarks with identical mass. The model includes a Nambu–Jona-Lasinio–like mechanism which links the dynamical breaking of chiral symmetry to the spontaneous generation of quark mass and the appearance of a low mass Goldstone pion. A novel feature of this approach is that it automatically explains the small mass of the pion even though the linear potential is a scalar interaction in Dirac space, and hence breaks chiral symmetry. Solutions for mesons composed of light quarks (π,ρ, and low lying excited states) and heavy quarks (${\mathrm{\eta }}_{\mathit{c}}$, J/Ψ, and low lying excited states) are presented and discussed.