Radiative $H^+_{1,2}W^- Z$ vertices in flavour conserving three Higgs-doublet scenarios

Abstract: A detailed calculation of the radiatively induced $H_{1,2}⁺ W^- Z$ vertices is carried out in the context of flavour conserving three Higgs doublet models (3HDMs). The Type-II, lepton specific and democratic versions of the 3HDM are chosen as representative cases and the \emph{alignment limit} is adopted. We arrange the amplitudes in UV-finite and gauge-invariant subsets for a sharper understanding of the underlying one-loop structure. Factoring-in various theoretical constraints and the ones from the $h \to γγ$ signal strength and the $B \to X_s γ$ branching ratio, we compute the relevant form factors and compare them among the various 3HDM types taken. The results also indicate a sizeable increment ($\sim 100\%$) over the corresponding form factors in 2HDMs. In addition, we probe the $H_{1,2}⁺ W^- Z$ vertices at the 14 TeV LHC using vector boson fusion (VBF). It is seen that production of $H_1<sup>+$ via VBF and the subsequent $H_1⁺ \to H_2⁺ H_2/A_2$ decays can have $σ\times \text{BR}$ in the $\mathcal{O}$(0.1 fb) ball park. Therefore, such a cascade can shed light on the strength of the $H_1⁺ W^- Z$ interaction and confirm the presence of two charged scalars thereby acting as a smoking gun signal of a 3HDM.