Constraints on and future prospects for two-Higgs-doublet models in light of the LHC Higgs signal

We analyze the two-Higgs-doublet models (2HDMs) of Type I and Type II for consistency with the latest measurements of the $\sim 125.5\mathrm{GeV}$ Higgs-like signal at the LHC. To this end, we perform scans of the 2HDM parameter space taking into account all relevant pre-LHC constraints as well as the most recent limits coming from searches for heavy Higgs-like states at the LHC. The current status of the 2HDMs of Type I and Type II is discussed assuming that the observed 125.5 GeV state is one of the two $CP$-even Higgs bosons, either the lighter $h$ or the heavier $H$. Implications for future experiments, including expectations regarding other lighter or heavier Higgs bosons, are given. The possible importance of heavier Higgs bosons feeding the signals for the 125.5 GeV state is also evaluated.

Figure 1

Values for the quartic coupling ${\lambda }_{AAAA}$ for 2HDMs of Type I (left) and Type II (right) in the $\sin (\beta -\alpha )$ versus $\sin \alpha$ plane for $m_h\sim 125.5\mathrm{GeV}$ shown as “temperature plots.” For all points, the full set of preLHC constraints is satisfied, including all quartic couplings having absolute values below $4\pi$.

Figure 2

Constraints in the $\cos (\beta -\alpha )$ versus $\tan \beta$ plane for $m_h\sim 125.5\mathrm{GeV}$. Grey points satisfy preLHC constraints, while green points satisfy in addition the LHC limits on $H$ and $A$ production. Blue points fall moreover within the $7+8\mathrm{TeV}$ 95% C.L. ellipses in the $[{\mu }_{\mathrm{ggF}+\mathrm{ttH}}(Y),{\mu }_{\mathrm{VBF}+\mathrm{VH}}(Y)]$ plane for each of the final states considered ($Y=\gamma \gamma ,VV,b\overline{b},\tau \tau$), and the amount of FD from $H$ or $A$ production is small.

Figure 3

$C_V$ versus $C_F=C_U=C_D$ for Type I (left) and $C_V$ versus $C_D$ for Type II (right). Color scheme as in Fig. 2. We have restricted the plots to $C_V\ge 0.7$ so as to most clearly display the postLHC8-FDOK points.

Figure 4

Constraints in the $m_A$ versus $\cos (\beta -\alpha )$ plane for $m_h\sim 125.5\mathrm{GeV}$. Color scheme as in Fig. 2. The corresponding results in the $m_H$ versus $\cos (\beta -\alpha )$ and $m_{H^{\pm }}$ versus $\cos (\beta -\alpha )$ planes give essentially the same picture as for $m_A$, except that $m_H$ and $m_{H^{\pm }}$ do not go below 125 GeV and 100 GeV (300 GeV) for Type I (Type II), respectively.

Figure 5

Correlations of signal strengths for the $m_h\sim 125.5\mathrm{GeV}$ scenario following the color scheme of Fig. 2; in the upper row ${\mu }_{gg}^h(ZZ)$ versus ${\mu }_{gg}^h(\gamma \gamma )$, and in the lower row ${\mu }_{\mathrm{VBF}}^h(\gamma \gamma )$ versus ${\mu }_{gg}^h(\gamma \gamma )$.

Figure 6

Cross sections (in pb) for $gg\to H$ and $bbH$ production at $\sqrt{s}=8\mathrm{TeV}$ as a function of $\tan \beta$ for $m_H=500\mathrm{GeV}$ and 1 TeV. The results shown are for the SM limit of $\sin (\beta -\alpha )=1$.

Figure 7

The postLHC8-FDOK points in the $\cos (\beta -\alpha )$ versus $\tan \beta$ plane for the $m_h\sim 125.5\mathrm{GeV}$ scenario comparing current $h$ fits (blue) to the case that the rates for all the channels listed in Eq. (6) are within $\pm 15\%$ (cyan), $\pm 10\%$ (green) or $\pm 5\%$ (red) of the SM Higgs prediction. FDOK is also required for these latter points.

Figure 8

The postLHC8-FDOK points in the ${\mu }_{gg}^h(\gamma \gamma )$ versus $\sin \alpha$ plane for the $m_h\sim 125.5\mathrm{GeV}$ scenario, requiring that the $gg\to ZZ$ and $VV\to ZZ$ rates are both within $\pm 15\%$ (cyan), $\pm 10\%$ (green) and $\pm 5\%$ (red) of the SM predictions. The individual rates for the $\tau \tau$ and $bb$ final states are consistent with current 95% C.L. limits.

Figure 9

The postLHC8-FDOK points in the $C_{hhh}$ versus $m_A$ plane for the $m_h\sim 125.5\mathrm{GeV}$ scenario comparing current $h$ fits to the case where future measurements show that the rates for all the channels listed in Eq. (6) are within $\pm 15\%,\pm 10\%,\pm 5\%$ of the SM Higgs prediction; FDOK is required in all cases. Color scheme is as for Fig. 7.

Figure 10

We plot $[\sigma (gg\to H)+\sigma (bbH)]\mathrm{BR}(H\to ZZ)$ as functions of $m_H$, for Type I (left) and Type II (right) 2HDMs. Only FDOK points are shown. Implications of various levels of precision for future $h$ measurements are displayed. Color scheme is as for Fig. 7.

Figure 11

Scatterplots of $[\sigma (gg\to H)+\sigma (bbH)]\mathrm{BR}(H\to \tau \tau )$ and $[\sigma (gg\to A)+\sigma (bbA)]\mathrm{BR}(A\to \tau \tau )$, in pb, as functions of $m_H$ (top row) and $m_A$ (bottom row), respectively, for postLHC8-FDOK points with $m_h\sim 125.5\mathrm{GeV}$. The values of $\tan \beta$ are color coded as indicated on the plots.

Figure 12

Same information as in Fig. 11 but in the $\tan \beta$ versus $m_H$ (top row) and $\tan \beta$ versus $m_A$ (bottom row) planes with the 14 TeV cross sections color coded as indicated by the scales on the right of the plots. Only FDOK points are shown.

Figure 13

Scatterplots of $[\sigma (gg\to H)+\sigma (bbH)]\mathrm{BR}(H\to \gamma \gamma )$ as function of $m_H$ (top row) and $[\sigma (gg\to A)+\sigma (bbA)]\mathrm{BR}(A\to \gamma \gamma )$ as function of $m_A$ (bottom row), for postLHC8-FDOK points with $m_h\sim 125.5\mathrm{GeV}$. The values of $\tan \beta$ are color coded as indicated by the scales on the right of the plots.

Figure 14

Scatterplots of $[\sigma (gg\to H)+\sigma (bbH)]\mathrm{BR}(H\to t\overline{t})$ as function of $m_H$ (top row) and $[\sigma (gg\to A)+\sigma (bbA)]\mathrm{BR}(A\to t\overline{t})$ as function of $m_A$ (bottom row) at $\sqrt{s}=14\mathrm{TeV}$, for postLHC8-FDOK points with $m_h\sim 125.5\mathrm{GeV}$. The values of $\tan \beta$ are color coded as indicated by the scales on the right of the plots.

Figure 15

We plot $\sigma (gg\to H)\mathrm{BR}(H\to hh)$ and $\sigma (gg\to A)\mathrm{BR}(A\to Zh)$ as functions of $m_H$ and $m_A$, respectively, for Type I (left) and Type II (right) 2HDMs. Blue points fulfill all constraints, including the FDOK requirement. Also shown are the points that have Low FD (in orange) and High FD (in red) as defined in Sec. 3c. The black lines show the current limits from the CMS analysis of Ref. [32].

Figure 16

We plot $[\sigma (gg\to H)+\sigma (bbH)]\mathrm{BR}(H\to hh)$ and $[\sigma (gg\to A)+\sigma (bbA)]\mathrm{BR}(A\to Zh)$ as functions of $m_H$ and $m_A$, respectively, for Type I (left) and Type II (right) 2HDMs. For this figure, only FDOK points are shown. Implications of various levels of precision for future $h$ measurements are displayed. Color scheme as in Fig. 7. Values of $\sigma \times \mathrm{BR}$ below ${10}^{-8}$ are not plotted.

Figure 17

Scatterplots of ${\mu }_{\mathrm{ggF}h+\mathrm{bb}h}^{\mathrm{FD}}$ versus ${\mu }_{Zh}^{\mathrm{FD}}$. Top plots illustrate how high the FD fractions can go for postLHC8 points (not imposing any FD limit). The plots in the lower row illustrate how convergence of the $h$ properties to SM-like values would limit the maximum possible FDs. We display only points with ${\mu }_{Zh}^{\mathrm{FD}}\ge {10}^{-3}$—there are many points with much lower values.

Figure 18

Constraints in the planes $\cos (\beta -\alpha )$ versus $\tan \beta$ (top row), $m_H$ versus $\cos (\beta -\alpha )$ (middle row) and $m_H$ versus $m_A$ (bottom row) for $m_h\sim 125.5\mathrm{GeV}$. The blue points are the postLHC8-FDOK points. The orange (red) points are allowed postLHC8, but have Low FD (High FD). Many, but not all, Low FD and High FD points have postLHC8-FDOK points hidden below. Regarding the $m_H$ versus $\cos (\beta -\alpha )$ plots, replacing $m_H$ by $m_A$ or $m_{H^{\pm }}$ gives essentially the same picture.

Figure 19

Constraints on the 2HDM of Type I and Type II in the $\sin (\beta -\alpha )$ versus $\tan \beta$ plane for $m_H\sim 125.5\mathrm{GeV}$. We show points that survive at the preLHC (grey), A-limits (green), postLHC8-FDOK (blue), $\mathrm{SM}\pm 15\%$ (cyan), $\mathrm{SM}\pm 10\%$ (dark green), and $\mathrm{SM}\pm 5\%$ (red) levels. There are no FDOK requirements imposed on the preLHC and A-limits points. The $\mathrm{SM}\pm 15\%$, $\pm 10\%$, $\pm 5\%$ points are subjected to FDOK requirements.

Figure 20

Scatterplots of ${\lambda }_{HHAA}$ in the $m_{H^{\pm }}$ versus $m_A$ and $m_A$ versus $\sin (\beta -\alpha )$ planes for the case of $m_H\sim 125.5\mathrm{GeV}$. The values of ${\lambda }_{HHAA}$ are color coded as indicated by the scales on the right of the plots. The full set of preLHC conditions is satisfied for all points shown.

Figure 21

We plot ${\mu }_{gg}^H(\gamma \gamma )$ as a function of $\sin \alpha$ for points having $gg\to ZZ$ and $VV\to ZZ$ rates within $\pm 15\%$, $\pm 10\%$ or $\pm 5\%$ of the SM predictions.

Figure 22

Constraints in the $m_h$ versus $\sin (\beta -\alpha )$ and $m_A$ versus $\sin (\beta -\alpha )$ planes for the $m_H\sim 125.5\mathrm{GeV}$ scenarios. Results for $m_{H^{\pm }}$ versus $\sin (\beta -\alpha )$ are very similar to those for $m_A$ versus $\sin (\beta -\alpha )$. There are no FDOK requirements imposed on the preLHC and A-limits points. The $\mathrm{SM}\pm 15\%$, $\pm 10\%$, $\pm 5\%$ points are subjected to FDOK requirements.

Figure 23

We plot ${\mu }_{\mathrm{ggF}H+\mathrm{bb}H}^{\mathrm{FD}}$ versus ${\mu }_{ZH}^{\mathrm{FD}}$ illustrating how high FD fractions can go for postLHC8 points for the $m_H\sim 125.5\mathrm{GeV}$ scenarios. Also shown is how convergence of the $H$ properties to SM-like values would limit the maximum possible feed downs. We display only points with ${\mu }_{ZH}^{\mathrm{FD}}\ge {10}^{-4}$—there are many points with much lower values.

Figure 24

We display points in the $\mathrm{sgn}(C_V^H)C_{HHH}$ versus $m_A$ plane for the $m_H\sim 125.5\mathrm{GeV}$ scenario comparing current $H$ fits to the case where future measurements show that all channel rates are within $\pm 15\%,\pm 10\%,\pm 5\%$ of the SM Higgs prediction; FDOK is required in all cases. Color scheme is as for Fig. 19, except that preLHC and A-limits points are not displayed.

Figure 25

${\mu }_{\mathrm{VH}}^h(b\overline{b})$, i.e. $V^{*}\to Vh$ associated production with $h\to b\overline{b}$ relative to the SM, as a function of $m_h$. Note that ${\mu }_{\mathrm{VH}}^h(bb)$ is actually independent of energy and that the ratio also applies to any situation where the subprocess of interest is $V^{*}\to Vh$, including the LEP $Z^{*}\to Zh$ process. There are no FDOK requirements imposed on the preLHC and A-limits points. The $\mathrm{SM}\pm 15\%$, $\pm 10\%$, $\pm 5\%$ points are subjected to FDOK requirements.

Figure 26

$\sigma (gg\to h)\mathrm{BR}(h\to \gamma \gamma )$ for $\sqrt{s}=14\mathrm{TeV}$ with postLHC8-FDOK constraints imposed as well as further limitations imposed by $\mathrm{SM}\pm 15\%,\pm 10\%,\pm 5\%$ constraints. There are no FDOK requirements imposed on the preLHC and A-limits points. The $\mathrm{SM}\pm 15\%,\pm 10\%,\pm 5\%$ points are subjected to FDOK requirements.

Figure 27

Rates (in pb) of pseudoscalar $A$ production at $\sqrt{s}=14\mathrm{TeV}$ as a function of $m_A$ for the $m_H\sim 125.5\mathrm{GeV}$ scenarios, separated into different $A$ decay modes: $A\to \gamma \gamma$ (top), $A\to \tau \tau$ (middle) and $A\to t\overline{t}$ (bottom). In each case, we sum over $gg\to A$ and $gg\to bbA$ production. The values of $\tan \beta$ are color coded as indicated by the scale on the right of the plots.

Figure 28

We plot $[\sigma (gg\to h)+\sigma (bbh)]\mathrm{BR}(h\to \gamma \gamma )$ versus $[\sigma (gg\to A)+\sigma (bbA)]\mathrm{BR}(A\to \tau \tau )$ for $\sqrt{s}=14\mathrm{TeV}$ with postLHC8-FDOK constraints imposed. Colors indicate the value of $\tan \beta$. We have required $|\sin (\beta -\alpha )|<0.1$ so that the rate for $V^{*}\to Vh$ will be at most 0.01 times the SM rate at the same mass.

Figure 29

We plot $[\sigma (gg\to H+bbH)2\mathrm{BR}(H\to hh)]/[\sigma (gg\to H+bbH)2P_{H,2h}+\sigma (gg\to A+bbA)2P_{A,2h}]$ on the $x$ axis and $[\sigma (gg\to A+bbA)\mathrm{BR}(A\to Zh)]/[\sigma (gg\to H+bbH)P_{H,1h}+\sigma (gg\to A+bbA)P_{A,1h}]$ on the $y$ axis. The postLHC8-FDOK points are displayed in blue. The cyan, green and red points obey FDOK constraints and have all the channel rates of Eq. (6) within $\mathrm{SM}\pm 15\%$, $\mathrm{SM}\pm 10\%$ and $\mathrm{SM}\pm 5\%$, respectively; cf. Fig. 7.

Figure 30

For Type II 2HDM, we plot $v^2{g}_{H{H}^{+}{H}^{-}}\mathrm{sgn}(C_V^H)/m_{H^{\pm }}^2$ versus $C_D^H$ (left) and $C_{\gamma }^H$ versus $C_D^H$ (right). We show FDOK points consistent at the postLHC8 level (blue) and after presumed LHC measurements showing SM consistency at the $\pm 15\%$ (cyan) and $\pm 10\%$ (dark green) level. No points survive if SM consistency is demonstrated at the $\pm 5\%$ level.

Figure 31

For Type I 2HDM, we plot: Left, $v^2{g}_{H{H}^{+}{H}^{-}}\mathrm{sgn}(C_V^H)/m_{H^{\pm }}^2$ versus $C_D^H$ (left) and $C_{\gamma }^H$ versus $C_D^H$ (right), showing FDOK points consistent at the postLHC8 level (blue) and after presumed LHC measurements showing SM consistency at the $\pm 15\%$ (cyan), $\pm 10\%$ (dark green) and $\pm 5\%$ (red) levels.

Figure 32

We plot $C_g^H$ versus $C_U^H$ for Type I (right) and Type II (left). We show FDOK points consistent at the postLHC8 level (blue) and after presumed LHC measurements showing SM consistency at the $\pm 15\%$ (cyan) and $\pm 10\%$ (dark green) levels. Points consistent with the SM (red points) at the $\pm 5\%$ level are only present in the $C_U^H<0$ branch of the Type I model.