Exclusive doubly charged Higgs boson pair production in $pp$ collisions at the LHC

The type II seesaw model predicts the existence of a doubly charged Higgs boson ($H ^{\pm\pm}$), which can be produced through the Drell - Yan process and photon -- induced interactions at hadronic colliders. In recent years, such reactions have been largely investigated in inclusive processes, where both incident protons breakup and a large number of particles is produced in addition to the doubly charged Higgs pair. In this paper, we investigate, for the first time, the possibility of searching for $H ^{\pm\pm}$ in exclusive processes, which are characterized by two rapidity gaps and two intact very forward protons in final state. We estimate the associated cross section making use of the exclusive nature of the final state, together with the use of timing information provided by forward proton detectors. Moreover, the background is estimated considering distinct amounts of pile-up. Our results indicate that the exclusive doubly charged Higgs pair production is a promising way to search for signatures of the type II seesaw and to obtain lower mass bounds on $H ^{\pm\pm}$.