Regge phenomenology of photoproduction of $π^-Δ^{++}$ and scaling with saturation of trajectory

Abstract

In this work we investigate the reaction $γp\toπ^-Δ^{++}$ in the Reggeized model for $π(138)+ρ(775)+a_2(1320)$ exchanges in the $t$-channel. For a convergence of the reaction cross section at high energies the minimal forms of proton and $Δ^{++}$ exchanges are introduced in the direct and crossed channels for gauge invariance of $π$ Regge-pole exchange. The role of spin-2 tensor meson $a_2$ is found to be crucial to agree with existing data at high energies. Electromagnetic multipoles of $Δ^{++}$ baryon are analyzed in the $Δ$ resonance region. Based on the constituents counting rule the scaled differential cross section at $E_γ=4$ GeV is reproduced with the Regge trajectory saturated at large momentum transfer $-t$.