Diffractive rho plus lepton pair production at an electron-ion collider

In high energy electron-ion colliders, a new way to probe nucleon structure becomes available through diffractive reactions, where the incident particle produces very energetic almost forward particle. QCD describes these reactions as due exchange of Pomeron which may be perturbatively described dressed two-gluon state, provided hard scale allows factorization amplitude in terms two impact factors convoluted with propagator. We consider here process such description us access hadronic generalized parton distributions, namely electroproduction $\ensuremath{\rho}$ meson and timelike deeply virtual photon, separated by large rapidity gap. explore dependence cross section on kinematic variables study nonperturbative inputs (generalized distribution amplitude). Our leading order studies show is mainly sensitive GPD model input, but small size sections could prohibit straightforward analysis this at planned facilities.