By means of the inverse amplitude method we unitarize the elastic pion-nucleon scattering amplitudes obtained from heavy baryon chiral perturbation theory to $\mathcal{O}{(q}^3).\mathrm{}$ Within this approach we can enlarge their applicability range and generate the $\Delta \mathrm{}\left(1232\right)\mathrm{}$ resonance. We can find a reasonable description of the pion nucleon phase shifts with $\mathcal{O}{(q}^2)$ parameters in agreement with the resonance saturation hypothesis. However, the uncertainties in the analysis of the low energy data as well as the large number of chiral parameters, which can have strong correlations, allow us to obtain very good fits with rather different sets of chiral constants.

• Received 27 December 1999

DOI:https://doi.org/10.1103/PhysRevD.62.017502