Chiral symmetry patterns of excited mesons with the Coulomb-like linear confinement

Abstract

The spectrum of $\bar{q}q$ mesons in a model where the only interaction is a linear Coulomb-like instantaneous confining potential is studied. The single-quark Green function as well as the dynamical chiral symmetry breaking are obtained from the Schwinger-Dyson (gap) equation. Given the dressed quark propagator, a complete spectrum of "usual" mesons is obtained from the Bethe-Salpeter equation. The spectrum exhibits restoration of chiral and $U(1{)}_A$ symmetries at large spins and/or radial excitations. This property is demonstrated both analytically and numerically. At large spins and/or radial excitations higher degree of degeneracy is observed, namely all states with the given spin fall into reducible representations $[(0,1/2)\oplus (1/2,0)]\times [(0,1/2)\oplus (1/2,0)]$ that combine all possible chiral multiplets with the given $J$ and $n$. The structure of the meson wave functions as well as the form of the angular and radial Regge trajectories are investigated.

Comments: 1. Order of references has been changed and one reference has been added; 2. A short discussion of nonrelativistic and semirelativistic quark models has been added in the conclusion part on referee's request. To appear in Phys. Rev. D