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

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 $2\mathcal{H}\mathcal{D}\mathcal{M}+\mathcal{T}$, 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 $H_{1,2}^{\pm }$. 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 $2\mathcal{H}\mathcal{D}\mathcal{M}+\mathcal{T}$. 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 $2\mathcal{H}\mathcal{D}\mathcal{M}+\mathcal{T}$. 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.

39 pages, 9 figures and 3 tables, added subsection on Constraint from $B\to X_s\gamma$, version accepted for publication in IJMPA

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• Naturalness Implications within the Two-Real-Scalar-Singlet beyond the SM