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

The Cook-Lee model for the "second" pion-nucleon resonance (1512, 3/2^-) has been generalized to arbitrary initial and final baryons. It is shown that the virtual production of S-wave ρ mesons included in π+S⁺→ρ+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 $(T, {J}P)=(1/2, {3/2}^{{-}}), (1/2, {7/2}^{{-}}), {⋯} and (1/2, {5/2}^{{-}}), (1/2, {9/2}^{{-}}), {⋯}$. In addition, subsidiary trajectories $(1/2, {1/2}^{{-}}), (1/2, {5/2}^{{-}}), {⋯}$ and $(3/2, {1/2}^{{-}}), (3/2, {5/2}^{{-}}), {⋯}$ are obtained.