Non-diagonal DVCS and studies of hadronic structure with $N \to N^*$ transition GPDs

Transition generalized parton distributions (GPDs) describe matrix elements of nonlocal partonic QCD operators between the ground and excited baryon states and provide new tools for quantifying and interpreting the structure of baryon resonances in QCD. We discuss a description of non-diagonal Deeply Virtual Compton Scattering process involving a transition between a nucleon and a nucleon resonance in the $\pi N$ system within the framework of transition GPDs. We address the physical content of $N \to N^*$ and $N \to \Delta$ transition GPDs, review the existing theoretical models and present theoretical estimates of related observables for the kinematic conditions corresponding to the experimental studies with JLab@12GeV. We also discuss the perspective of exploring resonance production with help of transition GPDs and consider the application of the Froissart-Gribov projections to study excitation of nucleon resonances by means of QCD probes with spin-$J$.