Pion-Nucleon Scattering and theJ=2,T=0Pion-Pion Interaction

Abstract

The effect of the $J=2\mathrm{}$, $T=0\mathrm{}$ $\pi -\pi$ interaction on the $\pi -N$ invariant amplitude, $B^{\mathrm{}(+)\mathrm{}}$ is analyzed. It is found that the $\pi -N$ scattering data is inconsistent with a $J=2\mathrm{}$, $T=0\mathrm{}$ $\pi -\pi$ phase ${{\delta }_2}^0$ which rises to above 13° around 650 MeV. The data are consistent with a $\delta$-function contribution at 1200 MeV but it is impossible to say whether this corresponds to a resonant phase or only a sharp peak in the corresponding absorptive part of the amplitude.