Regge Trajectories in a Multichannel Quark Model

Abstract

Meson trajectories are considered in a nonrelativistic quark model. The model, in a specific example involving the $\ensuremath{\rho}$ trajectory, incorporates a $\ensuremath{\pi}\ensuremath{\pi}$ channel and two quark-antiquark $q\overline{q}$ (or nucleon-antinucleon) channels in spin triplet states. A harmonic-oscillator potential provides the attractive $q\overline{q}$ potential, and a Yukawa potential is used in the $\ensuremath{\pi}\ensuremath{\pi}$ channel. A short-range potential of exponential type couples the $\ensuremath{\pi}\ensuremath{\pi}$ and $q\overline{q}$ channels. The model gives infinitely rising trajectories with resonances of small finite width capable of decaying into pions, but not into quarks. The $\ensuremath{\rho}$ trajectory deviates considerably from a straight line in the negative-energy region. The model is capable of imposing exchange degeneracy in a natural way.