Low energy analysis of pi N -> pi N

We derive a representation for the pion nucleon scattering amplitude that i s valid to the fourth order of the chiral expansion. To obtain the correct analytic structure of the singularities in the low energy region, we have p erformed the calculation in a relativistic framework (infrared regularizati on). The result can be written in terms of functions of a single variable. We study the corresponding dispersion relations and discuss the problems en countered in the straightforward nonrelativistic expansion of the infrared singularities. As an application, we evaluate the corrections to the Goldbe rger-Treiman relation and to the low energy theorem that relates the value of the amplitude at the Cheng-Dashen point to the sigma -term. While chiral symmetry does govern the behaviour of the amplitude in the vicinity of thi s point, the representation for the scattering amplitude is not accurate en ough to use it for an extrapolation of the experimental data to the subthre shold region. We propose to perform this extrapolation on the basis of a se t of integral equations that interrelate the lowest partial waves and are a nalogous to the Roy equations for pi pi scattering.