Heavy Baryon Spin 3/2 Theory and Radiative Decays of the Decuplet

We study the radiative decays of the decuplet $(3/2 \to 1/2 \gamma)$ using Heavy Baryon Chiral Perturbation Theory (HBChPT). We emphasize the problems faced by the interacting spin 3/2 field theory. We argue that, to lowest order in the $1/m$ expansion, HBChPT provides a framework where R-invariance and the appropiated constraints for the interacting spin 3/2 fields are consistently incorporated. We perform a gauge invariant calculation of the decay amplitudes, to lowest order in $1/m$ and to order $w^2/\Lambda^2_\chi$ in the chiral expansion and report analytical results for the one-loop contributions to the two form factors involved in the $3/2 \to 1/2 \gamma$ transitions. Parameters independent predictions for the SU(3) forbidden decays are presented.