Proton Compton scattering in a unified proton-Delta Model

Abstract

We develop a field-theoretic model for the description of proton Compton scattering in which the proton and its excited state, the \Delta+ resonance, are described as part of one multiplet with a single Rarita-Schwinger wavefunction. In order to describe the phenomena observed, it is necessary to incorporate both minimal and non-minimal couplings. The minimal coupling reflects the fact that the \Delta+ is a charged particle, and in this model the minimal coupling contributes also to the M1 magnetic transition via the \gamma N\Delta vertex. The non-minimal couplings consist of five electromagnetic form-factors, which are accessed at fixed and vanishing momentum-transfer squared with real photons in Compton scattering experiments, therefore it is possible to extract a rather well-determined set of optimal parameters which reasonably well fit the data in the resonance region 140-450 MeV. The crucial parameter which determines the \gamma N\Delta transition amplitude and therefore the height of the resonance peak is equal to 3.66 +- 0.03, in units of \mu_N. We find that this parameter also primarily determines the contributions to magnetic polarizability in this model. In the low-energy region up to 140 MeV, we separately fit the electric and magnetic polarizabilities, while keeping the other parameters fixed and obtain values in line with previous approaches. The basic model is then extended by incorporating the sigma-meson channel with the currently favored parameters, and the pion vertex corrections.