Pion-nucleon scattering in a new approach to chiral perturbation theory

We study pion-nucleon scattering with a chiral Lagrangian of pions, nucleons, and $\Delta$ isobars. The scattering amplitude is evaluated to one-loop $Q^3$ order, where $Q$ is a generic small momentum, using an approach which is equivalent to heavy baryon chiral perturbation theory. We obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to 100 MeV. A $\sigma$ term greater than 45 MeV is favored, but the value is not well determined.