Hunting a charged Higgs boson pair in proton-proton collisions

We explore the production and possible detection of a charged scalar Higgs pair $H^-H^+$ decaying into the final state $\mu\nu_{\mu}cb$ in proton-proton collisions at the LHC and its next step, the High Luminosity LHC (HL-LHC). The charged scalars are predicted within the theoretical framework of the Two-Higgs Doublet Model of type III (2HDM-III). As a test and validation of the model, we identify regions of the 2HDM-III parameter space that accommodate the current excess of events at $3\sigma$ in the process $\mathcal{BR}(t\to H^{\pm}b)\times \mathcal{BR}(H^{\pm}\to cb)$ for $M_{H^{\pm}}=130$ GeV, as reported by the ATLAS collaboration. Theoretical and additional experimental constraints are also included. Based on this, we propose realistic scenarios that could be brought under experimental scrutiny at the HL-LHC. Assuming the most favorable scenario, we predict a signal significance at the level of $5\sigma$ for a charged scalar boson mass $M_{H^{\pm}}$ in the $100-350$ GeV range.