We construct the complete effective chiral pion-nucleon Lagrangian to third order in small momenta based on relativistic chiral perturbation theory. We then perform the so-called heavy baryon limit and construct all terms up-to-and-including order 1/m 2 with fixed and free coefficients. As an application, we discuss in detail pionnucleon scattering. In particular, we show that for this process and to third order, the 1/m expansion of the Born graphs calculated relativistically can be recovered exactly in the heavy baryon approach without any additional momentum-dependent wave function renormalization. We fit various empirical phase shifts for pion laboratory momenta between 50 and 100 MeV. This leads to a satisfactory description of the phase shifts up to momenta of about 200 MeV. We also predict the threshold parameters, which turn out to be in good agreement with the dispersive analysis. In particular, we can sharpen the prediction for the isovector S-wave scattering length, 0.083We also consider the subthreshold parameters and give a short comparison to other calculations of πN scattering in chiral perturbation theory or modifications thereof.

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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.

We consider pion-nucleon scattering in heavy-baryon chiral perturbation theory to third order. All electromagnetic corrections appearing to this order are included. We thus have a consistent description of strong and electromagnetic effects, which allows us to isolate the strong part of the interaction in an unambiguous way. We give pion-nucleon phase shifts up to pion laboratory momenta of 100 MeV and find sizeable differences for the S-waves of the elastic channels compared to previous phase shift analyses. The precise description of the scattering process also allows us to address the question of isospin violation in the strong interaction. For the usually employed triangle relation we find an isospin breaking effect of −0.7% in the S-wave, whereas the P-waves show an effect of −1.5% and −4 to −2.5%, respectively, for pion laboratory momenta between 25 and 100 MeV.