Propagator of the Δ resonance and determination of the magnetic moment of the Δ+ from the γp→γπ°p reaction -: art. no. 024002

The photon-proton scattering reactions gamma p ->pi(o)p,gamma p ->gamma p, and gamma p ->gamma pi(o)p are investigated in the framework of the three-dimensional time-ordered approach using different models of the on-shell Delta propagators. These Delta propagators are taken from the unitary separable models of the pi N elastic-scattering amplitude and from the relativistic Breit-Wigner shape representation of the nonunitary pi N amplitude in the tree approach. The numerical calculations are performed with the complete set of the one-particle (pi-,omega-, and rho-meson, nucleon, and Delta) exchange diagrams. It is found that the numerical calculations of the above reactions in the Delta-resonance region are very sensitive to the model of the Delta propagator. This sensitivity is explained by the difference between the input pi N elastic-scattering observables used for the construction of the Delta propagator. It is shown, that after additional approximation our calculations reproduce the tree-level model calculations with the Breit-Wigner shape Delta propagator. This model is in good agreement with the gamma p ->pi(o')p(') reaction and with the preliminary data for the gamma p ->gamma(')pi(o')p(') reaction. Conversely, it is demonstrated, that the relativistic Breit-Wigner shape Delta propagators, obtained from the nonunitary pi N amplitudes in the tree approximation, is inconsistent to apply for reproduction of the gamma p scattering observables because they do not describe the pi N scattering data in the Delta resonance region. It is emphasized, that to extract the magnitude of the Delta(+) magnetic moment from the cross sections of the gamma p ->gamma(')pi(')N(') reaction it is necessary to fix the form of the Delta propagator based on the unified description of the two body pi p ->pi N,gamma p ->pi N basic channels together with the essential gamma p ->pi pi N and gamma p ->gamma p reactions.