Some Aspects ofπNScattering in theP11State

Abstract

A study of $\ensuremath{\pi}N$ scattering in the ${P}_{11}$ state is presented within the framework of the unitary $f$ matrix, or boundary-condition model. Inelastic channels treated are $\ensuremath{\sigma}N$ and $\ensuremath{\pi}{N}^{*}$, where $\ensuremath{\sigma}$ is a $I=0$, $J={0}^{+}$ $\ensuremath{\pi}\ensuremath{\pi}$ 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 $\ensuremath{\sigma}N$ 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 ${m}_{\ensuremath{\sigma}}$ 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.