The forgotten channels: charged Higgs boson decays to a $W^\pm$ and a non-SM-like Higgs boson

The presence of charged Higgs bosons is a generic prediction of multiplet extensions of the Standard Model (SM) Higgs sector. Focusing on the Two-Higgs-Doublet-Model (2HDM), we discuss the charged Higgs boson collider phenomenology in the theoretically and experimentally viable parameter space. While almost all existing experimental searches at the LHC target the fermionic decays of charged Higgs bosons, we point out that the bosonic decay channels -- especially the decay into a non-SM-like Higgs boson and a $W$ boson -- often dominate over the fermionic channels. Moreover, we revisit two genuine BSM effects on the properties of the discovered Higgs boson -- the charged Higgs contribution to the diphoton rate and the Higgs decay to two light Higgs bosons -- and their implication for the charged Higgs boson phenomenology. As main result of the present paper, we propose five two-dimensional benchmark scenarios with distinct phenomenological features in order to facilitate the design of dedicated LHC searches for charged Higgs bosons decaying into a $W$ boson and a light, non-SM-like Higgs boson.