Deeply-virtual Compton process $e^- N \to e^- \gamma \pi N$ to study nucleon to resonance transitions

We study the deeply-virtual Compton scattering (DVCS) process $e^- N \to e^- \gamma \pi N$ involving the transition between a nucleon and a nucleon resonance in the $\pi N$ system, within the framework of generalized parton distributions (GPDs). For the four lowest-lying nucleon resonances, $\Delta(1232)$, $P_{11}(1440)$, $D_{13}(1520)$, and $S_{11}(1535)$, we express the DVCS amplitude in the Bjorken limit in terms of corresponding nucleon-to-resonance GPDs. Building upon the knowledge of the well studied electromagnetic nucleon-to-resonance transition form factors, which map the quark charge densities in transverse position space, the corresponding GPDs will open the prospect to also access the longitudinal momentum distributions of quarks in the transition. We provide estimates for cross sections and beam-spin asymmetries in the first and second $\pi N$ resonance regions in the kinematics of forthcoming CLAS12 data from Jefferson Lab.