Pion-nucleon scattering and the nucleon sigma term in an extended sigma model
Abstract
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
π
N scattering amplitudes satisfy the relevant chiral low-energy theorems, such as the Weinberg-Tomozawa relation for the isovector 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 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 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
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.