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

A modified linear Sigma model that allows for g(A) = 1.26 by addition of ve ctor and pseudovector pi N coupling terms was discussed by Bjorken and Naue nberg and by Lee. In this extended linear Sigma model the elastic pi N scat tering 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 isospi n symmetric pi N scattering length with experiment is substantially improve d 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 mat rix 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 perturba tion theory Lagrangian.