Dynamical model for Pion - Nucleon Bremsstrahlung

A dynamical model based on effective Lagrangians is proposed to describe the bremsstrahlung reaction $\pi N\to \pi N\gamma$ at low energies. The $\mathrm{\Delta }(1232)$ degrees of freedom are incorporated in a way consistent with both, electromagnetic gauge invariance and invariance under contact transformations. The model also includes the initial and final state rescattering of hadrons via a T-matrix with off-shell effects. The $\pi N \gamma$ differential cross sections are calculated using three different T-matrix models and the results are compared with the soft photon approximation, and with experimental data. The aim of this analysis is to test the off-shell behavior of the different T-matrices under consideration.