Transition GPDs and exclusive electroproduction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mo>−</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1232</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> final states
P. Kroll, K. Passek-Kumerički
Abstract
We investigate exclusive electroproduction of ${\ensuremath{\pi}}^{\ensuremath{-}}{\mathrm{\ensuremath{\Delta}}}^{++}$ within the handbag approach in which the helicity amplitudes factorize into generalized parton distributions (GPDs) and hard partonic subprocesses. We define the $p\ensuremath{-}\mathrm{\ensuremath{\Delta}}$ transversity GPDs while the helicity nonflip 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 $p\ensuremath{-}\mathrm{\ensuremath{\Delta}}$ 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 ${\ensuremath{\gamma}}^{*}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\mathrm{\ensuremath{\Delta}}}^{++}$ are predicted in the large-${N}_{C}$ limit.