Phenomenological Analysis ofI=12Single-Pion Production Processes in the Energy Range 500 to 700 MeV

Single-pion production processes in the energy range 500 to 700 MeV are discussed. It is assumed that production occurs in the partial waves $S_1$, $P_1$, $P_3$, and $D_3$ for $I=\frac{1}{2} \mathrm{and} \frac{3}{2}$ via isobar formation in a generalized sense. Isobars treated are the $N^{*}\mathrm{}\left(1236\right)\mathrm{}$ and the low-energy tails of the $\sigma$ (assumed to be a broad resonance centered at 700 MeV) and the $\rho$. Emphasis is laid on maintaining consistency with the results of elastic phase-shift analyses. It is suggested that the major contributor to the charge channel ${\pi }^0{\pi }^{-}p$ at and above 550 MeV is $P_{11}$ decaying via $\rho N$. It is noted that a second $P_{11}$ resonance occurring in the range 600 to 800 MeV would explain several phenomena. It is indicated that $D_{13}$ very probably decays to $\sigma N$ as well as $\pi N^{*}$. A plea is entered for the presentation of future data in the form of a full production-angular-distribution analysis over the Dalitz plot.