PION-NUCLEON SCATTERING IN CHIRAL PERTURBATION-THEORY (I) - ISOSPIN-SYMMETRICAL CASE

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 construc t all terms up to and including order 1/m(2) with fixed and free coeff icients. As an application, we discuss in detail pion-nucleon scatteri ng, In particular, we show that for this process and to third order, t he 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 empi rical phase shifts for pion laboratory momenta between 50 and 100 MeV. This leads to a satisfactory description of the phase shifts up to mo menta of about 200 MeV. We also predict the threshold parameters, whic h turn out to be in good agreement with the dispersive analysis. In pa rticular, we can sharpen the prediction for the isovector S-wave scatt ering length, 0.083 M-pi(-1) less than or equal to a(0+)(-) less than or equal to 0.093 M-pi(-1). We also consider the subthreshold paramete rs and,give a short comparison to other calculations of pi N scatterin g in chiral perturbation theory or modifications thereof. (C) 1998 Els evier Science B.V.