Pion-nucleon phase shifts in heavy baryon chiral perturbation theory

Abstract

We calculate the phase shifts in pion-nucleon scattering using the heavy baryon formalism. We consider phase shifts for the pion energy range of $140$ to $200$ MeV. We employ two different methods for calculating the phase shifts—the first using the full third order calculation of the pion-nucleon scattering amplitude and the second by including the resonances $\Delta$ and $N^{*}$ as explicit degrees of freedom in the Lagrangian. We compare the results of the two methods with phase shifts extracted from fits to the pion-nucleon scattering data. We find good to fair agreement between the calculations and the phase shifts from scattering data.