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

R. F. Wagenbrunn·L. Ya. Glozman
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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.

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R. F. Wagenbrunn, L. Ya. Glozman. 2007-01-24. Chiral symmetry patterns of excited mesons with the Coulomb-like linear confinement. https://doi.org/10.1103/physrevd.75.036007

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