Heavy charged scalars from $c\bar{s}$ fusion: A generic search strategy applied to a 3HDM with $\mathrm{U}(1) \times \mathrm{U}(1)$ family symmetry

We describe a class of three Higgs doublet models (3HDMs) with a softly broken $\mathrm{U}(1) \times \mathrm{U}(1)$ family symmetry that enforces a Cabibbo-like quark mixing while forbidding tree-level flavour changing neutral currents. The hierarchy in the observed quark masses is partly explained by a softer hierarchy in the vacuum expectation values of the three Higgs doublets. As a consequence, the physical scalar spectrum contains a Standard Model (SM) like Higgs boson $h_{125}$ while exotic scalars couple the strongest to the second quark family, leading to rather unconventional discovery channels that could be probed at the Large Hadron Collider. In particular, we describe a search strategy for the lightest charged Higgs boson $H^{\pm}$, through the process $c\bar s\to H^{+}\to W^+\,h_{125}$, using a multivariate analysis that leads to an excellent discriminatory power against the SM background. Although the analysis is applied to the proposed class of 3HDMs, we employ a model-independent formulation such that it can be applied to any other model with the same discovery channel.