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A modified linear sigma model that allows for $g_A = 1.26$ by addition ofvector and pseudovector $\pi N$ coupling terms was discussed by Bjorken andNauenberg and by Lee. In this extended linear sigma model the elastic $\pi $Nscattering amplitudes satisfy the relevant chiral low-energy theorems, such asthe Weinberg-Tomozawa relation for the isovector scattering length and in somecases Adler's "consistency condition". The agreement of the isospin symmetric$\pi N$ scattering length with experiment is substantially improved in thisextended sigma model as compared with the original one. We show that thenucleon sigma term ($\Sigma_N$) in the linear- and the extended sigma modelswith 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. Largevalues of $\Sigma_N$ are easily obtained without any $s\bar s$ content of thenucleon. Using chiral rotations the Lagrangian of this extended sigma modelreproduces the lowest-order $\pi N$ chiral perturbation theory Lagrangian.Comment: 21 pages, 1 postscript figure, submitted to Phys. Re

physical review. c. nuclear physics/physical review. c, nuclear physics

Pion-nucleon scattering and the nucleon<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Σ</mml:mi></mml:math>term in an extended linear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Σ</mml:mi></mml:math>model

Pion-nucleon scattering and the nucleonΣterm in an extended linearΣmodel