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 $\pi N$ 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 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 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 $s\bar{s}$ content of the nucleon. Using chiral rotations the Lagrangian of this extended sigma model reproduces the lowest-order $\pi N$ chiral perturbation theory Lagrangian.

21 pages, 1 postscript figure, submitted to Phys. Rev

References in corpus (4)

• Octet and Decuplet Baryons in a Covariant and Confining Diquark-Quark Model
• The UA(1) problem and the role of correlated q qbar exchange in effective theories of QCD
• Partially conserved axial current constraints on pion production/absorption within nonrelativistic dynamics
• On the chiral low-density theorem

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