Dark matter, electroweak phase transition, and gravitational waves in the type II two-Higgs-doublet model with a singlet scalar field

In the framework of the type II two-Higgs-doublet model with a singlet scalar dark matter $S$, we study the dark matter observables, the electroweak phase transition, and the gravitational wave signals by such strongly first order phase transition after imposing the constraints of the LHC Higgs data. We take the heavy $CP$-even Higgs boson $H$ as the only portal between the dark matter and standard model (SM) sectors, and find that the LHC Higgs data and dark matter observables require $m_S$ and $m_H$ to be larger than 130 GeV and 360 GeV for $m_A=600\mathrm{GeV}$ in the case of the 125 GeV Higgs boson with the SM-like coupling. Next, we carve out some parameter space where a strongly first order electroweak phase transition can be achieved, and find benchmark points for which the amplitudes of gravitational wave spectra reach the sensitivities of the future gravitational wave detectors.

Figure 1

Scatter plots of $\sin (\beta -\alpha )$ and $\tan \beta$ satisfying the constraints of the 125 GeV Higgs boson signal data.

Figure 2

The surviving samples with the SM-like coupling projected on the planes of $m_H$ versus $\tan \beta$ and $m_H$ versus $|\sin (\beta -\alpha )|$. All of the samples are allowed by the constraints of pre-LHC and the 125 GeV Higgs boson signal data. The triangles (sky blue), circles (royal blue), squares (black), inverted triangles (purple), and pluses (red) are respectively excluded by the $H/A\to {\tau }^{+}{\tau }^{-}$, $H\to WW,ZZ,\gamma \gamma$, $H\to hh$, $A\to HZ$, and $A\to hZ$ channels at the LHC. The bullets (green) are allowed by various LHC direct searches.

Figure 3

The surviving samples projected on the planes of $m_S$ versus ${\lambda }_H$, $m_S$ versus $m_H$, and $m_S$ versus ${\sigma }_p$. All of the samples are allowed by the constraints of “pre-LHC”, the LHC Higgs data, and the relic density. The circles (royal blue) and pluses (red) are, respectively, excluded by the experimental data of the XENON1T and Fermi-LAT Collaborations, while the bullets (green) are allowed.

Figure 4

The surviving samples projected on the planes of $⟨h_1⟩$ versus $⟨h_2⟩$, $T_c$ versus $m_H$, and $T_c$ versus $\tan \beta$. All of the samples achieve a SFOEWPT.

Figure 5

The surviving samples projected on the planes of $|\sin (\beta -\alpha )$, $\tan \beta$, $m_{12}^2$ versus $m_H$, $m_{12}^2$ versus $\tan \beta$, $m_S$ versus $m_H$, and ${\lambda }_H$. All of the samples are allowed by the constraints of “pre-LHC”, the LHC Higgs data, and the DM observables. The squares achieve a SFOEWPT, and bullets fail.

Figure 6

The parameters $\alpha$ and $\beta /H_n$ characterizing the dynamics of the SFOEWPT.

Figure 7

Phase structures for BP1 (left) and BP2 (right). The lines show the field configurations at a particular minimum as a function of temperature. The arrows indicate that at that temperature ($T_C$) the two phases linked by the arrows are degenerate, and can achieve the SFOEWPT.

Figure 8

Gravitational wave spectra for BP1 and BP2.