Implications for theΔNπInteraction andσTerm from Low-EnergyπNScattering

Abstract

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