Further study of the global minimum constraint on the two-Higgs-doublet models: LHC searches for heavy Higgs bosons

The usually considered vacuum of the two-Higgs-doublet model (2HDM) could be unstable if it locates at a local but not global minimum (GM) of the scalar potential. By requiring the vacuum to be a GM, we obtain an additional constraint, namely the GM constraint, on the scalar potential. In this work, we explore the GM constraint on the $CP$-conserving general 2HDM. This constraint is found to put limits on the soft ${\mathbb{Z}}_2$ breaking mass parameter $m_{12}^2$ and also squeeze the heavy $CP$-even Higgs boson mass into larger values for the $m_{12}^2<0$ case. Combined with the current global signal fits from the LHC measurements of the 125 GeV Higgs boson, we discuss the phenomenological implications for the heavy Higgs boson searches at the LHC.

Figure 1

The combined LHC run-I and run-II constraints on the 125 GeV Higgs boson signal strengths in terms of 2HDM parameters $\cos (\beta -\alpha )$ and $\tan \beta$. Both Type I (left) and Type II (right) cases are displayed.

Figure 2

The GM constraints in the $(M_{\mathrm{\Phi }},\sqrt{|m_{12}^2|})$ plane, where $m_{\mathrm{\Phi }}$ is defined as the degenerate heavy Higgs boson mass $M_H=M_A=M_{\pm }\equiv M_{\mathrm{\Phi }}$. The gray regions have already been excluded by the simplistic unitarity and BFB bounds, and the tree-level GM constraints further exclude the yellow regions, leaving only the blue regions allowed by all these constraints. When the loop corrections and the $s$ dependence are included, the unitarity and BFB bounds shift to the red curves, and the GM boundaries shift to the black curves. The left and the right panels assume Type I 2HDM with $\cos (\beta -\alpha )=0.1$ and Type II 2HDM with $\cos (\beta -\alpha )=0.01$, respectively.

Figure 3

The GM constraints (excluding yellow) combined with the unitarity and BFB constraints (excluding gray) on some benchmarks tabulated in Table 2, with $\cos (\beta -\alpha )=0$ and $\tan \beta =1.0$. The loop corrections and the $s$ dependence have been included. The blue regions are the largest allowed regions by all the constraints in the grid scan—see the text for more details.

Figure 4

The decay branching fractions of $\mathrm{Br}[H\to hh]$, for the Type I model (left panel) and Type II model (right panel). The solid or dashed curves represent the parameter regions that are allowed or excluded by the GM conditions, respectively. The loop corrections and the $s$ dependence have been included.

Figure 5

The current LHC 13 TeV search limits on the resonance productions of SM-like Higgs boson pairs, for the Type I model (left panel) and Type II model (right panel). The red and blue hatched regions have been excluded by the $hh\to b\overline{b}\gamma \gamma$ and $hh\to b\overline{b}b\overline{b}$, respectively. The black contours represent the theoretically (including the GM and unitarity and BFB constraints) allowed regions.

Figure 6

The current LHC 13 TeV search limits on the $A\to ZH$ in the BP-1 case with $\cos (\beta -\alpha )=0$ and $\tan \beta =1.0$ input. The red hatched regions have been excluded by the LHC 13 TeV searches for $A\to ZH$. The black contours represent the theoretically (including the GM and unitarity and BFB constraints) allowed regions.

Figure 7

Similar to Fig. 6, but for the LHC 13 TeV search limits on $H\to ZA$ in the BP-2 case.

Figure 8

Similar to Fig. 6, but for the LHC 13 TeV search limits on $H\to ZA$ in the BP-3 case.

Figure 9

Similar to Fig. 6, but for the LHC 13 TeV search limits on $A\to ZH$ in the BP-4 case.