Strongly first-order electroweak phase transition by relatively heavy additional Higgs bosons

We discuss first-order electroweak phase transition in models with extended Higgs sectors for the case with relatively heavy additional scalar bosons. We first show that, by the combination of the sphaleron decoupling condition, perturbative unitarity, and vacuum stability, mass upper bounds on additional scalar bosons can be obtained at the TeV scale even at the alignment limit where the lightest Higgs boson behaves exactly like the SM Higgs boson at tree level. We then discuss phenomenological impacts of the case with the additional scalar bosons with the mass near 1 TeV. Even when they are too heavy to be directly detected at current and future experiments at hadron colliders, the large deviation in the triple Higgs boson coupling can be a signature for first-order phase transition due to quantum effects of such heavy additional Higgs bosons. On the other hand, gravitational waves from the first-order phase transition are found to be weaker in this case as compared to that with lower masses of additional scalar bosons.

Figure 1

The allowed parameter regions for $m_{H^{\pm }}=m_A=m_H$, $\sin (\beta -\alpha )=1$ and $\tan \beta =1$, 1.5 and 2. The red region is excluded by the sphaleron decoupling condition. The blue region represents that the electroweak phase transition has not been completed. The gray region is excluded by the unitarity bound. The green region indicates that the phase transition is two step where the first phase transition is a second-order phase transition, or the single step second-order phase transition. The strongly first-order electroweak phase transition cannot be realized in Scenario 1 with $\tan \beta >2$.

Figure 2

The allowed regions in the THDM with $m_{H^{\pm }}=m_A=m_H+m_Z$, $\sin (\beta -\alpha )=1$ and $\tan \beta =1$, 2, 2.5. The definition of the regions for each color is the same in Fig. 1.

Figure 3

The allowed parameter regions in THDM with $m_{H^{\pm }}=m_A=m_H+1.5m_Z$, $\sin (\beta -\alpha )=1$ and $\tan \beta =1.5$. In addition to the theoretical constraints described in Fig. 1, the constraint from the vacuum stability is shown. Upper bounds on the additional Higgs boson masses are given by perturbative unitarity and vacuum stability in Scenario 3.

Figure 4

The allowed parameter regions in the THDM for $\sin (\beta -\alpha )=1$ and $\sin (\beta -\alpha )=0.999$. For comparison, we show the left figure in Fig. 1 again as the left panel. The upper bounds on the masses of the additional Higgs bosons are around 1.2 TeV for $\sin (\beta -\alpha )=0.999$. The definition of the regions for each color is the same in Fig. 1.

Figure 5

The GW spectra in each benchmark scenario. The solid (dashed) lines are the cases that the wall velocity is 95% (40%) of the light speed.