Enlighting the transverse structure of the proton via double parton scattering in photon-induced interactions

In the present paper we address double parton scattering (DPS) in quasi-real photon-proton interactions. By using electromagnetic and hadronic models of the photon light cone wave functions, we compute the so-called effective cross-section, $\sigma_{eff}^{\gamma p}$ which allows us to calculate the DPS contribution to these processes under dedicated assumptions. In particular, for the four-jet photoproduction in HERA kinematics we found a sizeable DPS contribution. We show that if the photon virtuality $Q^2$ could be measured and thus the dependence of $\sigma_{eff}^{\gamma p}$ on such a parameter exposed, information on the transverse distance between partons active in proton could be extracted. To this aim, we set lower limits on the integrated luminosity needed to observe such an effect which would allow the extraction of novel information on the proton structure.