Mass-degenerate Higgs bosons at 125 GeV in the two-Higgs-doublet model

The analysis of the Higgs boson data by the ATLAS and CMS Collaborations appears to exhibit an excess of $h\to \gamma \gamma$ events above the Standard Model (SM) expectations, whereas no significant excess is observed in $h\to Z{Z}^{*}\to \mathrm{\text{four lepton}}$ events, albeit with large statistical uncertainty due to the small data sample. These results (assuming they persist with further data) could be explained by a pair of nearly mass-degenerate scalars, one of which is an SM-like Higgs boson and the other is a scalar with suppressed couplings to $W^{+}{W}^{-}$ and $ZZ$. In the two-Higgs-doublet model, the observed $\gamma \gamma$ and $Z{Z}^{*}\to \mathrm{\text{four lepton}}$ data can be reproduced by an approximately degenerate $CP$-even ($h$) and $CP$-odd ($A$) Higgs boson for values of $\sin (\beta -\alpha )$ near unity and $0.70\lesssim \tan \beta \lesssim 1$. An enhanced $\gamma \gamma$ signal can also arise in cases where $m_h\simeq m_H$, $m_H\simeq m_A$, or $m_h\simeq m_H\simeq m_A$. Since the $Z{Z}^{*}\to 4$ leptons signal derives primarily from an SM-like Higgs boson whereas the $\gamma \gamma$ signal receives contributions from two (or more) nearly mass-degenerate states, one would expect a slightly different invariant mass peak in the $Z{Z}^{*}\to \mathrm{\text{four lepton}}$ and $\gamma \gamma$ channels. The phenomenological consequences of such models can be tested with additional Higgs data that will be collected at the LHC in the near future.

Figure 1

Left panel: $R_{\gamma \gamma }$ as a function of $\tan \beta$ for $h$ (blue/black), $A$ (green/gray), and the total observable rate (cyan/light-gray), obtained by summing the rates with intermediate $h$ and $A$, for the unconstrained scenario. Right panel: Total rate for $R_{\gamma \gamma }$ as a function of $\tan \beta$ for the constrained (red/black) and unconstrained (green/gray) scenarios.

Figure 2

Allowed region in the $R_{\gamma \gamma }^{\mathrm{VBF}}\mathrm{\text{−}}{R}_{\gamma \gamma }$ plane with (red/black) and without (green/gray) the $B$-physics constraints.

Figure 3

Left panel: Total $R_{\tau \tau }$ ($h$ and $A$ summed) as a function of $R_{\gamma \gamma }$ for the constrained (red/black) and unconstrained (green/gray) scenarios. QCD corrections aside, this figure also holds approximately for $R_{bb}$. Right panel: $R_{bb}^{\mathrm{VH}}$ ($h$ and $A$ summed) as a function of $R_{\gamma \gamma }$ for the constrained (red/black) and unconstrained (green/gray) scenarios.

Figure 4

$R_{\gamma \gamma }$ as a function of $\tan \beta$ for $h$ (blue/black), $A$ (green/gray), and the total observable rate, obtained by summing the rates with intermediate $h$ and $A$ (cyan/light-gray).

Figure 5

Left panel: Allowed region in the $R_{\gamma \gamma }^{\mathrm{VBF}}\mathrm{\text{−}}{R}_{\gamma \gamma }$. Right panel: $R_{\tau \tau }$ as a function of $R_{\gamma \gamma }$ for $h$ (blue/black), $A$ (green/gray), and the total observable rate, obtained by summing the rates with intermediate $h$ and $A$ (cyan/light-gray).

Figure 6

Left panel: Allowed region in the $R_{\gamma \gamma }^{\mathrm{VBF}}\mathrm{\text{−}}{R}_{\gamma \gamma }$ plane for the constrained (red/black) and unconstrained (green/gray) scenarios. Right panel: Allowed region in the $R_{\gamma \gamma }\mathrm{\text{−}}{R}_{\tau \tau }$ plane for the constrained (red/black) and unconstrained (green/gray) scenarios.

Figure 7

Left panel: Values obtained in the $\tan \beta \mathrm{\text{−}}\sin (\beta -\alpha )$ plane for the points generated, which satisfy $0.8<R_{\gamma \gamma }<1.5$. Right panel: Values for $R_{\gamma \gamma }$ as a function of $\tan \beta$ for the constrained (red/black) and unconstrained (green/gray) scenarios.

Figure 8

Left panel: Allowed region in the $R_{\gamma \gamma }^{\mathrm{VBF}}\mathrm{\text{−}}{R}_{\gamma \gamma }$ plane for the constrained (red/black) and unconstrained (green/gray) scenarios. Right panel: Allowed region in the $R_{\gamma \gamma }\mathrm{\text{−}}{R}_{\tau \tau }$ plane for the constrained (red/black) and unconstrained (green/gray) scenarios.

Figure 9

Values obtained in the $\tan \beta \mathrm{\text{−}}\sin (\beta -\alpha )$ plane for the points generated for the constrained (red/black) and unconstrained (green/gray) scenarios.

Figure 10

Left panel: Allowed region in the $R_{\gamma \gamma }^{\mathrm{VBF}}\mathrm{\text{−}}{R}_{\gamma \gamma }$ plane for the constrained (red/black) and unconstrained (green/gray) scenarios. Right panel: Allowed region in the $R_{\gamma \gamma }\mathrm{\text{−}}{R}_{\tau \tau }$ plane for the constrained (red/black) and unconstrained (green/gray) scenarios.

Figure 11

Left panel: Total $R_{\gamma \gamma }$ ($h$, $H$, and $A$ summed) as a function of $\tan \beta$ for the constrained (red/black) and unconstrained (green/gray) scenarios. Right panel: Allowed region in the $R_{\gamma \gamma }^{\mathrm{VBF}}\mathrm{\text{−}}{R}_{\gamma \gamma }$ plane for the constrained (red/black) and unconstrained (green/gray) scenarios.