Charged pion photoproduction with the Δ(1232) baryon beyond the resonance region

We investigate the charged pion photoproduction off the proton target with the Δ(1232) baryon, i.e., γp→π-Δ++(1232) and γp→π+Δ0(1232), based on the effective Lagrangian method, beyond the resonance region, √(s) > or approx. 2 GeV. We employ the π- and ρ-meson Regge trajectories in the t channel, in addition to the proton and Δ pole, in the s and u channels, respectively, and the contact-interaction contributions. A specific scheme for the form factor which satisfies the Ward-Takahashi identity, crossing symmetry, and on-shell condition is taken into account. We also consider a smooth interpolation between the Regge and Feynman propagators for the t-channel meson exchanges as a function of the Mandelstam variable s. We present the numerical results for the energy and angular dependences of the cross sections and the double- and single-polarization observables. It turns out that the present framework reproduces the experimental data qualitatively very well. In particular, the interpolation between the two propagators plays a crucial role in reproducing the high-energy experimental data correctly. The π+ decay-angle distribution is also studied using the Δ++-decay frame, i.e., the Gottfried-Jackson frame. The present results will be a useful guide for future high-energy photon-beam experiments.