Covariant approach toπ+-proton bremsstrahlung

The pion-proton bremsstrahlung process is considered in a Δ-isobar model that treats the full Lorentz structure and off-shell nature of the Rarita-Schwinger spin-(3/2 propagator and vertex functions. The relativistic isobar model necessarily produces background $S_{31}$, $P_{31}$, and $D_{33}$ partial waves as well as the resonant $P_{33}$ wave, but explicit background is needed to fit the elastic data. Unitarity and gauge invariance as well as the soft photon limit are preserved in the model. The ${\pi }^{+}$-p elastic and radiative processes are treated on the same dynamical footing within a relativistic K-matrix approach. The approach is constructed in a form that formally resembles a four-dimensional scattering theory to allow a more physical or intuitive illustration of the underlying dynamics.