Pion-Nucleon Scattering at Low Energies

We study pion-nucleon scattering at tree level with a chiral lagrangian of pions, nucleons, and $\Delta$-isobars using a K-matrix unitarization procedure. Evaluating the scattering amplitude to order $Q^2$, where $Q$ is a generic small momentum scale, we obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to $50$MeV. The fit can be extended to 150 MeV when we include the order-$Q^3$ contributions. Our results are independent of the off-shell $\Delta$ parameter.Comment: 13 pages, RevTex, Two tables and two figures, Minor changes, To appear in PR