Constructing equivalent effective chiral Lagrangians: A systematic approach

We demonstrate a systematic method of constructing physically equivalent effective chiral Lagrangians based on the symmetry properties of low-energy hadron physics. We start by building the most general Lagrangian describing pion-nucleon systems within the chiral $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R$ context. The symmetry is then enlarged to include additional Goldstone bosons such as the axion of the Peccei-Quinn symmetry. The vector and axial-vector mesons are introduced in the context of a gauge chiral model for completeness. We work out explicitly a specific example of the equivalence of effective Lagrangian models for the nucleon-nucleon-axion bremsstrahlung process.