Geometrical scaling description for the exclusive production of vector mesons and deeply virtual Compton scattering

In this work, we investigate the exclusive production of particles in scattering processes in the so-called saturation region. Within this scheme the phenomenon of geometric scaling takes place: cross sections are functions only of a dimensionless combination of the relevant kinematic variables, which happens both in inclusive and diffractive cases, as in the production of vector mesons. In particular, the scaling variable is given in general by $\tau = Q^2/Q_s^2$, where $Q^2$ is the photon virtuality and $Q_s$ represents the saturation scale, which drives the energy dependence and the corresponding nuclear effects. Based on the scaling property, we are able to derive a universal expression for the cross sections for the exclusive vector meson production and deeply virtual Compton scattering (DVCS) in both photon-proton and photon-nucleus interactions. This phenomenological result describes all available data from DESY-HERA for $\rho$, $\phi$ and $J/\psi$ production and DVCS measurements. A discussion is also carried out on the size of nuclear shadowing corrections on photon-nucleus interaction.