Proton Compton scattering in a unified proton-Δ+model

Abstract

We develop a field-theoretic model for the description of the proton Compton scattering in which the proton and its excited state, the ${\ensuremath{\Delta}}^{+}$ resonance, are described as parts of one multiplet with a single Rarita-Schwinger wave function. To describe the observed phenomena, it is necessary to incorporate both minimal and nonminimal couplings. The minimal coupling reflects the fact that the ${\ensuremath{\Delta}}^{+}$ is a charged particle, and in this model the minimal coupling contributes also to the $\ensuremath{\gamma}N\ensuremath{\Delta}$ magnetic transition. The nonminimal couplings consist of five electromagnetic form factors, which are accessed at fixed and vanishing momentum transfer squared with real photons in the Compton scattering experiments, therefore it is possible to extract a somewhat well-determined set of optimal parameters which fit the data in the resonance region 140--450 MeV reasonably well. The crucial parameter which determines the $\ensuremath{\gamma}N\ensuremath{\Delta}$ transition amplitude and therefore the height of the resonance peak is equal to $1.83\ifmmode\pm\else\textpm\fi{}0.03$, in units of ${\ensuremath{\mu}}_{N}$. We find that this parameter is also the primary determinant of the contributions to the 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. In addition to proton Compton scattering, the model is applicable to a broad range of processes in the few hundred MeV energy range, whenever the proton appears in some intermediate off-shell state.