Solutions to a gauge-invariant, equal-time two-body wave equation. Light-mass quark-antiquark system

We study systematically the equal-time relativistic equation with a confinement potential, its boundary conditions, and the resulting bag-type solutions and eigenvalues. We show that the flux is continuous across the bag boundary. The chiral symmetry of the equation for vanishing quark masses is spontaneously broken for $J=0\mathrm{}$ states because of the boundary condition. We take a model potential consisting of a linear potential and a modified Coulomb potential that vanishes at the origin and show that the Nambu-Goldstone condition on the $\pi$ meson can be implemented, and that the known $I=1\mathrm{}$ meson spectrum can be accounted for with remarkable success, provided the Coulomb coupling constant $g^2$ is chosen above the critical value 2. DOI: http://dx.doi.org/10.1103/PhysRevD.16.3305 © 1977 The American Physical Society