Dynamical Model for Negative-Parity Regge Trajectories in the Pion-Nucleon System

Abstract

The Cook-Lee model for the "second" pion-nucleon resonance (1512, ${\frac{3}{2}}^{-}$) has been generalized to arbitrary initial and final baryons. It is shown that the virtual production of $S$-wave $\rho$ mesons included in $\pi +S^{+}\to \rho +S^{+}$, where $S^{+}$ is the set of all positive-parity resonances originating in the nucleon and the 3-3 resonance, generates the pair of trajectories $S^{-}$ comprised of a series with $(T, J^P)=(\frac{1}{2}, {\frac{3}{2}}^{-}), (\frac{1}{2}, {\frac{7}{2}}^{-}), \cdots \mathrm{and} (\frac{1}{2}, {\frac{5}{2}}^{-}), (\frac{1}{2}, {\frac{9}{2}}^{-}), \cdots$. In addition, subsidiary trajectories $(\frac{1}{2}, {\frac{1}{2}}^{-}), (\frac{1}{2}, {\frac{5}{2}}^{-}), \cdots$ and $(\frac{3}{2}, {\frac{1}{2}}^{-}), (\frac{3}{2}, {\frac{5}{2}}^{-}), \cdots$ are obtained.