Self-Consistency and the Roper Resonance

Abstract

It is suggested that the Roper resonance $R$ is primarily an $N$ + ($S$-wave $\pi \pi$ pair) self-consistent bound state Calculations are done with a simple model, coupled $S_0+N$, $\pi +N$ channels in the $J^p={\frac{1}{2}}^{+}$, $T=\frac{1}{2}$ state, where $S_0$ is a $\pi \pi$ $S$-wave state with mass 700 MeV. When the $\pi +N$ channel is neglected, the $R$ is self-consistently generated by the $R$ exchange force in the $S_0+N$ channel. When the $\pi +N$ channel is included, the $R$ bootstrap survives, and is stable against large variations in the cutoff associated with $N^{*}$ exchange.