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

A modified linear Σ 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 Σ 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 Σ model as compared with the original linear one. We show that the nucleon sigma term (Σ_N) in the linear and the extended Σ models with three different kinds of chiral symmetry breaking terms are identical. Within the tree approximation 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 ss̅ content of the nucleon. Using chiral rotations the Lagrangian of this extended Σ model reproduces the lowest-order πN chiral perturbation theory Lagrangian.