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

TL;DR

The paper investigates radiatively induced $H_{1,2}^+ W^- Z$ interactions in flavour-conserving three-Higgs-doublet models (3HDMs) by computing the one-loop form factors under exact alignment. It organizes the loop amplitudes into UV-finite, gauge-invariant subsets and analyzes three representative 3HDM Yukawa textures (Type-II, Lepton-specific, Democratic), applying theoretical and experimental constraints including $h\to\gamma\gamma$, EWPO, and $B\to X_s\gamma$. The results show that the form factors $F_{1Z}$ and $F_{2Z}$ can be enhanced relative to the two-Higgs doublet model, with $|F_{1Z}|$ reaching up to $\mathcal{O}(4\!\times\!10^{-2})$ and $|F_{2Z}|$ up to $\mathcal{O}(3\!\times\!10^{-2})$ in favorable scenarios, and that the mass splittings between charged and neutral scalars drive the size of custodial-symmetry-violating contributions. The study also examines LHC prospects via vector-boson-fusion production of $H_{1,2}^+$ at $\sqrt{s}=14$ TeV, predicting $\sigma\times\text{BR}$ around $\mathcal{O}(0.1\rm\ fb)$ for certain mass configurations and highlighting cascade decays such as $H_1^+\to H_2^+ H_2$ as smoking-gun signals of a 3HDM. Overall, the work provides quantitative predictions for a loop-induced $H^+ W^- Z$ vertex in 3HDMs and outlines concrete collider strategies to test two charged scalars as a hallmark of the 3HDM framework.

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 $H_1^+$ 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.

Figures (18)

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• Figure 4: Allowed parameter points for the Type-II 3HDM. The color-coding is explained in the legends.
• Figure 5: Allowed parameter points for the lepton-specific 3HDM. The color-coding is explained in the legends.