Low energy analysis of πN→πN

We derive a representation for the pion nucleon scattering amplitude that isvalid to the fourth order of the chiral expansion. To obtain the correctanalytic structure of the singularities in the low energy region, we haveperformed the calculation in a relativistic framework (infraredregularization). The result can be written in terms of functions of a singlevariable. We study the corresponding dispersion relations and discuss theproblems encountered in the straightforward nonrelativistic expansion of theinfrared singularities. As an application, we evaluate the corrections to theGoldberger-Treiman relation and to the low energy theorem that relates thevalue of the amplitude at the Cheng-Dashen point to the \sigma-term. Whilechiral symmetry does govern the behaviour of the amplitude in the vicinity ofthis point, the representation for the scattering amplitude is not accurateenough to use it for an extrapolation of the experimental data to thesubthreshold region. We propose to perform this extrapolation on the basis of aset of integral equations that interrelate the lowest partial waves and areanalogous to the Roy equations for \pi\pi scattering.Comment: 97 pages (LaTeX), 16 figures. Two references added, correction in table one. Published versio