The Higgs Potential in 2HDM extended with a Real Triplet Scalar: A roadmap

TL;DR

This paper thoroughly analyzes the Higgs potential in a 2HDM extended with a real triplet scalar, deriving theoretical constraints, performing experimental exclusion tests, and exploring the impact on scalar masses and decay channels.

Contribution

It provides the first comprehensive analysis of the 2HDM+T model, including unitarity, boundedness, Veltman conditions, and experimental constraints, revealing the parameter space and scalar mass ranges.

Findings

Scalar masses are tightly constrained by theoretical and experimental limits.

Allowed scalar mass ranges depend on the sign of the mixing angle $\alpha_1$.

Higgs decay modes $\gamma\gamma$ and $Z\gamma$ are correlated.

Abstract

We perform a comprehensive study of The Higgs potential of the two Higgs doublet model extended by a real triplet scalar field $\Delta$. This model, dubbed $2\mathcal{HDM+T}$, has a rich Higgs spectrum consisting of three CP-even Higgs $h_{1,2,3}$, one CP-odd $A_0$ and two pairs of charged Higgs $H^\pm_{1,2}$. First, we determine the perturbative unitarity constraints and a set of non trivial conditions for the boundedness from below (BFB). Then we derive the Veltman conditions by considering the quadratic divergencies of Higgs boson self energies in $2\mathcal{HDM+T}$. We find that the parameter space is severely delimited by these theoretical constraints, as well as experimental exclusion limits and Higgs signal rate measurements at LEP and LHC. Using HiggsBounds-5.3.2beta and HiggSignals-2.2.3beta public codes an exclusion test at $2\sigma$ is then performed on the physical scalars of $2\mathcal{HDM+T}$. Our analysis provides a clear insight on the nonstandard scalar masses, showing that the allowed ranges are strongly sensitive to the sign of mixing angle $\alpha_1$, essentially when naturalness is involved. For $\alpha_1 < 0$ scenario, our results place higher limits on the bounds of all scalar masses, and show that the pairs $(h_2, H_1^\pm)$ and $(h_3, H_2^\pm)$ are nearly mass degenerate varying within the intervals $[130\,,\,246]$~GeV and $[160\,,\,335]$~GeV respectively. When $\alpha_1$ turns positive, we show that consistency with theoretical constraints and current LHC data, essentially on the diphoton decay channel, favors Higgs masses varying within wide allowed ranges: $[153\,,\,973]$~GeV for $m_{A_0}$; $[151\,,\,928]$~GeV for ($m_{h_2}$, $m_{H_1^\pm}$) and $[186\,,\,979]$~GeV for ($m_{h_3}$, $m_{H_2^\pm}$). Finally, we find that the $\gamma \gamma$ and $Z\gamma$ Higgs decay modes are generally correlated.