Pion - nucleon scattering and the nucleon sigma term in an extended linear sigma model

A modified linear sigma model that allows for g A = 1.26 by addition of vector and pseudovector πN coupling terms was discussed by Bjorken and Nauenberg and by Lee. In this extended linear sigma model the elastic πN scattering amplitudes satisfy the relevant chiral low-energy theorems, such as the Weinberg-Tomozawa relation for the isovector πN scattering length and in some cases Adler's " consistency condition ". The agreement of the isospin symmetric πN scattering length with experiment is substantially improved in this extended sigma model as compared with the original linear one. We show that the nucleon sigma term (Σ N) in the linear-and the extended sigma models with three different kinds of chiral symmetry breaking terms are identical. Within the tree approximations the formal operator expression for the Σ N term and the value extracted from the πN scattering matrix coincide. Large values of Σ N are easily obtained without any s¯ s content of the nucleon. Using chiral rotations the Lagrangian of this extended sigma model reproduces the lowest-order πN chiral perturbation theory Lagrangian.