Future prospects of mass-degenerate Higgs bosons in the $CP$-conserving two-Higgs-doublet model

The scenario of two mass-degenerate Higgs bosons within the general two-Higgs-doublet model (2HDM) is revisited. We focus on the global picture when two $CP$-even Higgs bosons of $h$ and $H$ are nearly mass-degenerate. A global fit to the signal strength of the 125 GeV Higgs measured at the LHC is performed. Based on the best-fit result of the 2HDM mixing angles $(\alpha ,\beta )$, theoretical constraints, charged and $CP$-odd Higgs boson direct search constraints and the electroweak precision constraints are imposed to the 2HDM parameter space. We present the signal predictions of the $(4b,2b2\gamma )$ channels for the benchmark models at the LHC 14 TeV runs. We also study the direct Higgs boson pair productions at the LHC, and the Z-associated Higgs boson pair production search at the ILC 500 GeV runs, as well as the indirect probes at the CEPC 250 GeV run. We find that the mass-degenerate Higgs boson scenario in the Type-II 2HDM can be fully probed by these future experimental searches.

Figure 1

The global fit of two mass-degenerate Higgs bosons in the Type-I (left panel) and Type-II (right panel) 2HDM on the $(\alpha ,\beta )$ plane. The yellow and green regions are the $(1,2)\sigma$ allowed regions of the LHC $7\oplus 8\oplus 13\mathrm{TeV}$ Higgs data fitting, and the benchmark points are marked by red stars.

Figure 2

The unitarity (yellow) and stability (gray) excluded regions for Type-I (left) and Type-II (right) 2HDM, with the $M_h\approx M_H=125\mathrm{GeV}$ scenario. The best-fit points of $(\alpha ,\beta )=(0.04,1.40)$ for Type-I case and $(\alpha ,\beta )=(-0.25,1.31)$ for Type-II case are taken as in Table 3. On the right panel, we fix $M_{\pm }=600\mathrm{GeV}$ to evade the B-physics constraints in the Type-II case.

Figure 3

The dependences of the relevant Higgs cubic self couplings ${\lambda }_{hhh}$ (orange), ${\lambda }_{hhH}$ (blue), ${\lambda }_{hHH}$ (green), and ${\lambda }_{HHH}$ (red) on the soft mass term $m_{12}$ in the Type-I (left) and Type-II (right) 2HDM. The best-fit points of $(\alpha ,\beta )=(0.04,1.40)$ for Type-I case and $(\alpha ,\beta )=(-0.25,1.31)$ for Type-II case are taken as in Table 3. The ranges of $m_{12}$ are taken as in Eq. (14) for Type-I and Type-II cases.

Figure 4

The current LHC exclusion limits [72] to the $h/H$ degenerate case through the $A\to hZ\to b\overline{b}+{\ell }^{+}{\ell }^{-}$ final states, with an integrated luminosity of $36.1{\mathrm{fb}}^{-1}$ (blue dashed line). The best-fit points of $(\alpha ,\beta )=(0.04,1.40)$ for Type-I case and $(\alpha ,\beta )=(-0.25,1.31)$ for Type-II case are taken as in Table 3.

Figure 5

The LO cross sections of $\sigma [gg\to hh]$ (green), $\sigma [gg\to hH]$ (red), and $\sigma [gg\to HH]$ (blue) versus the soft mass $m_{12}$ in both Type-I (solid) and Type-II (dashed) 2HDM at the LHC $\sqrt{s}=14\mathrm{TeV}$ run. The best-fit points of $(\alpha ,\beta )=(0.04,1.40)$ for Type-I case and $(\alpha ,\beta )=(-0.25,1.31)$ for Type-II case are taken as in Table 3. In comparison, the LO cross section of $\sigma [gg\to h_{\mathrm{SM}}{h}_{\mathrm{SM}}]=20.5\mathrm{fb}$ (black dotted) is listed as well. Note that the allowed regions obtained from theoretical constraints in $m_{12}$ are also indicated by the gray and pink arrows for Type-I and Type-II respectively.

Figure 6

The LHC 14 TeV LO cross sections of $\sigma [gg\to (hh,hH,HH)]$ to final states of $4b$ (left panel) and $2b2\gamma$ (right panel) versus the soft mass $m_{12}$ in the Type-I (solid lines) and Type-II (dashed lines) 2HDM. The best-fit points of $(\alpha ,\beta )=(0.04,1.40)$ for Type-I case and $(\alpha ,\beta )=(-0.25,1.31)$ for Type-II case are taken as in Table 3. In comparison, the LO cross sections of $\sigma [gg\to h_{\mathrm{SM}}{h}_{\mathrm{SM}}]$ to the corresponding final states (dotted lines) are displayed as well. Note that the allowed regions obtained from theoretical constraints in $m_{12}$ are also indicated by the gray and pink arrows for Type-I and Type-II respectively.

Figure 7

The Feynman diagrams for the Higgs boson pair productions associated with a $Z$-boson at the ILC.

Figure 8

95% and 68% contours of the measurement of ${\sigma }_{ZHH,LR}$ and ${\sigma }_{ZHH,RL}$ from (1) $hh\to b\overline{b}b\overline{b}$ with $P(e^{-},e^{+})=(\pm 0.8,\mp 0.3)$ [100] and (2) $hh\to b\overline{b}{W}^{+}{W}^{-}$ with $P(e^{-},e^{+})=(-0.8,0.3)$ [101] for 500 GeV ILC with $2{\mathrm{ab}}^{-1}$ luminosity for each beam polarization configuration. The best-fit points of $(\alpha ,\beta )=(0.04,1.40)$ for Type-I case and $(\alpha ,\beta )=(-0.25,1.31)$ for Type-II case are taken as in Table 3. The tiny black line represents the prediction of the cross section (normalized according to the branching fraction) of Type-I with variation of $m_{12}$, the red line is for Type-II. The label beside each point indicates the value of corresponding $m_{12}$.

Figure 9

Left: the exclusion level of the hypothesis test of the 2HDM model against SM using $hh\to bbbb$ and $hh\to bbWW$ channels with $(P_{e^{+}},P_{e^{-}})=(\pm 0.3,\mp 0.8)$ and $2{\mathrm{ab}}^{-1}$ luminosity for each polarization states. The black (red) line represents the exclusion level for the $h/H$ degenerate in the Type-I (Type-II) 2HDM with dependence on $m_{12}$. The gray and red vertical dashed lines with arrow directions in the left panel indicate the allowed upper bounds from the 2HDM potential stability constraints for Type-I and Type-II, respectively. Right: the exclusion level the same as in the left panel, but with dependence on the luminosity cumulated for each beam polarization configuration, $m_{12}=50(0)\mathrm{GeV}$ is used for Type-I (Type-II) for presentation.