Unified Formulation of Effective Nonlinear Pion-Nucleon Lagrangians

Abstract

It is shown that a nonlinear Lagrangian model with chiral $\mathrm{SU}\left(2\right)\mathrm{}\otimes \mathrm{SU}\left(2\right)\mathrm{}$ symmetry for the $\pi -N$ system proposed earlier, when complemented with an exact partially conserved axial-vector current term, provides a systematic and unified treatment of various phenomenological Lagrangians that are found in the recent literature. A detailed comparison is made for three special cases, showing agreement with current algebra and experimental data for $\pi -N$ and $\pi -\pi$ scattering lengths.