The role of finite-size effects on the spectrum of equivalent photons in proton-proton collisions at the LHC

Photon-photon interactions represent an important class of physics processes at the LHC, where quasi-real photons are emitted by both colliding protons. These reactions can result in the exclusive production of a final state $X$, $p+p \rightarrow p+p+X$. When computing such cross sections, it has already been shown that finite size effects of colliding protons are important to consider for a realistic estimate of the cross sections. These first results have been essential in understanding the physics case of heavy-ion collisions in the low invariant mass range, where heavy ions collide to form an exclusive final state like a $J/\Psi$ vector meson. In this paper, our purpose is to present some calculations that are valid also for the exclusive production of high masses final states in proton-proton collisions, like the production of a pair of $W$ bosons or the Higgs boson. Therefore, we propose a complete treatment of the finite size effects of incident protons irrespective of the mass range explored in the collision. Our expectations are shown to be in very good agreement with existing experimental data obtained at the LHC.