Transition GPDs and exclusive electroproduction of $\pi -\Delta (1232)$ final states

Abstract

We investigate exclusive electroproduction of ${\pi }^{-}{\Delta }^{++}$ within the handbag approach in which the helicity amplitudes factorize into generalized parton distributions (GPDs) and hard partonic subprocesses. We define the $p-\Delta$ transversity GPDs while the helicity non-flip GPDs are taken from the literature. For the numerical estimates of observables we utilize large-$N_C$ results in order to relate a few of the $p-\Delta$ GPDs to the proton-proton ones and neglect all other GPDs. In the calculation of the twist-2 and twist-3 subprocess amplitudes we take into account quark transverse momenta in combination with Sudakov suppressions. The partial cross sections for ${\gamma }^{\ast }p\to {\pi }^{-}{\Delta }^{++}$ are predicted in the large-$N_C$ limit.

Comments: 31 pages, 6 figures