Partial-wave analysis of the reactionπN→ππNin the c.m energy range 1300-2000 MeV

A partial-wave analysis of the reaction $\pi N\to \pi \pi N$ has been carried out in the energy region 1300-2000 MeV. Two continuous solutions have been found; they are very similar in regions where data exist, but differ in the continuation of amplitudes through a gap between our low- and high-energy data. The second solution ("B") gives a much better fit to the data. These new partial-wave amplitudes provide important information on the inelastic couplings of the nucleon resonances to the $N\rho$, $N\epsilon$, and $\Delta \pi$ channels. A new resonance, $D_{13}\mathrm{}\left(1700\right)\mathrm{}$, long predicted by the quark model, has been observed coupling to two inelastic channels—$\epsilon N$ and $\Delta \pi$, and the existence of a $P_{13}\mathrm{}\left(1700\right)\mathrm{}$ state is corroborated. Our preferred solution indicates a second new resonance, $P_{33}\mathrm{}\left(1700\right)\mathrm{}$, coupled strongly to the $\Delta \pi$ channel.