Pion-nucleon scattering and the nucleon Σ term in an extended linear Σ model -: art. no. 025205

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