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

TL;DR

This paper calculates the one-loop radiative $H^+ W^- Z$ vertices in three Higgs doublet models, compares form factors across different types, and explores their potential detection at the 14 TeV LHC via vector boson fusion.

Contribution

It provides a detailed, gauge-invariant calculation of the $H^+ W^- Z$ vertices in 3HDMs and assesses their experimental signatures at the LHC.

Findings

Form factors are about 100% larger than in 2HDMs.

VBF production cross-section times branching ratio is around 0.1 fb.

Cascade decays can reveal the presence of two charged scalars.

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 $h \to \gamma \gamma$ signal strength and the $B \to X_s \gamma$ 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 $H_1^+$ via VBF and the subsequent $H_1^+ \to H_2^+ H_2/A_2$ decays can have $\sigma \times \text{BR}$ 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.