Some Aspects ofπNScattering in theP11State

Abstract

A study of $\pi N$ scattering in the $P_{11}$ state is presented within the framework of the unitary $f$ matrix, or boundary-condition model. Inelastic channels treated are $\sigma N$ and $\pi N^{*}$, where $\sigma$ is a $I=0\mathrm{}$, $J=0^{+}$ $\pi \pi$ pair. The mass spread of the inelastic channel is taken into account in a unitary manner. It is apparent from an examination of the fits to the data that the $\sigma N$ channel is vastly preferred as an inelastic mode; the reasons are fully discussed in the text. The crossover of the phase shift at 175 MeV is seen to be impossible with a conventional force input. From a study of eigenphases we conclude that there is no Breit-Wigner resonance in any eigenchannel. Also, by means of the eigenphase representation, we demonstrate a source of possible discrepancies in recent phase-shift analyses. The value of $m_{\sigma }$ obtained for a best fit, 550 MeV, is compared with other values obtained by various authors. Finally, we examine the effects of the $P_{11}$ "object" on the Gell-Mann-Okubo mass formula.