Implications for theΔNπInteraction andσTerm from Low-EnergyπNScattering

Abstract

A model for low-energy $\ensuremath{\pi}N$ scattering consisting of $N$, $\ensuremath{\rho}$, $\ensuremath{\Delta}$, and $\ensuremath{\sigma}$ exchanges together with current-algebra constraints is presented. We derive the $\ensuremath{\Delta}$ contributions to the scattering amplitude using a general $\ensuremath{\Delta}$ propagator and $\ensuremath{\pi}N\ensuremath{\Delta}$ interaction. We show that the data are consistent with the simplest structure for both the $\ensuremath{\Delta}$ propagator and the interaction, A $\ensuremath{\sigma}$ term of 42 \ifmmode\pm\else\textpm\fi{} 10 MeV at the Cheng-Dashen point is found, and predictions of the $\ensuremath{\sigma}$ term at $t=0$, the $\ensuremath{\pi}\mathrm{NN}$ coupling constant, and the isospin-even $s$-wave scattering length are made.