Pion–nucleon scattering in an effective chiral field theory with explicit spin- [formula omitted] fields

Abstract

We analyze elastic–pion nucleon scattering to third order in the so-called small scale expansion. It is based on an effective Lagrangian including pions, nucleons and deltas as active degrees of freedom and counting external momenta, the pion mass and the nucleon–delta mass splitting as small parameters. The fermion fields are considered as very heavy. We present results for phase shifts, threshold parameters and the sigma term. We discuss the convergence of the approach. A detailed comparison with results obtained in heavy-baryon chiral perturbation theory to third and fourth order is also given.