Dynamics of theN*(52−)

A dynamical model of the $D_{15}$ pion-nucleon resonance is considered. Since the branching ratio for decay into the $\pi N$ channel is less than ½, we first treat the case in which the resonance is produced in $\pi N^{*}$ scattering. The coupling to the $\rho N^{*}$ inelastic channel is assumed to dominate the forces, and the $\frac{N}{D}$ equations, solved in a pole approximation, are employed. We next consider the generalization of this model to $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry and obtain a resonant octet. Finally we treat the three-channel problem with the $\pi N$ channel included. The calculated mass and branching ratio of the resonance are in good agreement with experiment but the total width is too small.