Scrutinizing the alignment limit in two-Higgs-doublet models. II. $m_H=125\mathrm{GeV}$

In the alignment limit of a multidoublet Higgs sector, one of the Higgs mass eigenstates aligns in field space with the direction of the scalar field vacuum expectation values, and its couplings approach those of the Standard Model (SM) Higgs boson. We consider $CP$-conserving two-Higgs-doublet models (2HDMs) of type I and type II near the alignment limit in which the heavier of the two $CP$-even Higgs bosons, $H$, is the SM-like state observed with a mass of 125 GeV, and the couplings of $H$ to gauge bosons approach those of the SM. We review the theoretical structure and analyze the phenomenological implications of this particular realization of the alignment limit, where decoupling of the extra states cannot occur given that the lighter $CP$-even state $h$ must, by definition, have a mass below 125 GeV. For the numerical analysis, we perform scans of the 2HDM parameter space employing the software packages 2hdmc and lilith, taking into account all relevant pre-LHC constraints, constraints from the measurements of the 125 GeV Higgs signal at the LHC, as well as the most recent limits coming from searches for other Higgs-like states. Implications for Run 2 at the LHC, including expectations for observing the other scalar states, are also discussed.

Figure 1

$|s_{\beta -\alpha }|$ versus $m_h$ in type I (left) and type II (right) with ${\log }_{10}|Z_6|$ color code. Points are plotted in the order of high to low ${\log }_{10}|Z_6|$ values.

Figure 2

$m_{H^{\pm }}$ versus $m_A$ in type I (left) and type II (right) with $m_h$ color code. Points are ordered from high to low $m_h$ values. The right plot shows the whole parameter space scanned over for type II, with the horizontal line indicating the updated limit on the charged Higgs mass, $m_{H^{\pm }}>480\mathrm{GeV}$.

Figure 3

$|s_{\beta -\alpha }|$ versus reduced fermionic coupling $C_F^H$ in type I (left) and $C_U^H$ in type II (right). In the upper two panels, the color code shows the dependence on $m_h$; in the lower two panels the dependence on $m_A$, with points ordered from high to low $m_h$ and $m_A$ values, respectively. Note that the color scales for $m_A$ are different for type I and type II because of the very different allowed ranges of $m_A$.

Figure 4

In the left panel, we exhibit $|s_{\beta -\alpha }|$ versus $C_D^H$ in type II. The color code shows the dependence on $m_h$, with points ordered from high to low $m_h$ values. In the right panel, we exhibit $s_{\beta -\alpha }$ vs $\tan \beta$ with the color code showing $C_D^H$ ordered from high to low values.

Figure 5

Fermionic couplings versus $\tan \beta$ in type I (upper panel) and type II (lower panels) with $|s_{\beta -\alpha }|$ color code. Points are ordered from high to low $|s_{\beta -\alpha }|$.

Figure 6

$|s_{\beta -\alpha }|$ versus $C_{\gamma }^H$ in type I (left) and type II (right) with $m_h$ color code (upper panels) and with $m_{H^{\pm }}$ color code (lower panels). Points are ordered from high to low $m_h$ in the upper panels and from low to high $m_{H^{\pm }}$ in the lower panels.

Figure 7

As for Fig. 6 but showing the dependence of $C_{\gamma }^H$ on $\overline{m}\equiv \mathrm{sgn}{\overline{m}}^2\sqrt{|{\overline{m}}^2|}$. Points are ordered from high to low $\overline{m}$.

Figure 8

Reduced triple Higgs coupling $C_{HHH}$ in type I (left) and type II (right), in the top panels with $m_h$ and in the bottom panels with $m_A$ color coding. Points are ordered from high to low $\overline{m}$, $m_h$ or $m_A$ values.

Figure 9

As in Fig. 8 but with $\tan \beta$ color coding. Points are ordered from high to low $\tan \beta$ values.

Figure 10

Signal strengths in type I.

Figure 11

Signal strengths in type II. The horizontal bars near $|s_{\beta -\alpha }|\approx 0.1$ arise from the opposite-sign $C_D^H$ solution.

Figure 12

Examples of correlations between signal strengths in type I. The top panels show ${\mu }_{\mathrm{VBF}}^H(\gamma \gamma )$ vs ${\mu }_{gg}^H(\gamma \gamma )$, the upper middle panels show ${\mu }_{\mathrm{VBF}}^H(Z{Z}^{*})$ vs ${\mu }_{gg}^H(Z{Z}^{*})$, the lower middle panels show ${\mu }_{gg}^H(Z{Z}^{*})$ vs ${\mu }_{gg}^H(\gamma \gamma )$ and the bottom panels show ${\mu }_{gg}^H(\tau \tau )$ vs ${\mu }_{gg}^H(\gamma \gamma )$. The color code indicates, from left to right, the dependence on $|s_{\beta -\alpha }|$, $m_h$ and $m_A$. Points are ordered from high to low $|s_{\beta -\alpha }|$, $m_h$ and $m_A$ values.

Figure 13

Examples of correlations between signal strengths in type II. The top panels shows ${\mu }_{\mathrm{VBF}}^H(\gamma \gamma )$ vs ${\mu }_{gg}^H(\gamma \gamma )$, the upper middle panels show ${\mu }_{\mathrm{VBF}}^H(Z{Z}^{*})$ vs ${\mu }_{gg}^H(Z{Z}^{*})$, the lower middle panels show ${\mu }_{gg}^H(Z{Z}^{*})$ vs ${\mu }_{gg}^H(\gamma \gamma )$ and the bottom panels show ${\mu }_{gg}^H(\tau \tau )$ vs ${\mu }_{gg}^H(\gamma \gamma )$. The color code indicates, from left to right, the dependence on $|s_{\beta -\alpha }|$, $m_h$ and $m_A$. Points are ordered from high to low $|s_{\beta -\alpha }|$, $m_h$ and $m_A$ values. Note that the correlations look the same in the first two rows of plots (i.e. for VBF vs $gg$ production in $\gamma \gamma$ or $Z{Z}^{*}$ final state) but the actual $\mu$ values are different. The opposite-sign $C_D^H$ solution is visible as a separate narrow line with: $|s_{\beta -\alpha }|\approx 0.1$ (left-hand panels), $m_h\gtrsim 65\mathrm{GeV}$ (middle panels) and $m_A\in [420,630]\mathrm{GeV}$ (right-hand panels).

Figure 14

$\sigma (b\overline{b}X)$ versus $\sigma (gg\to X)$ for $X=h$ (left) and $X=A$ (right) in type I at the 13 TeV LHC for points satisfying all present constraints (in beige) as well as points for which the signals strengths from Eq. (67) are within 5% and 2% of the SM predictions (in red and dark red, respectively). The dashed lines indicate ${\sigma }_{13}(b\overline{b}X)={\sigma }_{13}(gg\to X)$.

Figure 15

As in Fig. 14 but for type II.

Figure 16

Cross sections in type I (left) and type II (right) for $gg\to X$ as functions of $m_X$ for $X=h$ (upper panels) and $X=A$ (middle panels) with $\tan \beta$ color code. The bottom panels depict the cross sections for $b\overline{b}A$ production as function of $m_A$ with $\tan \beta$ color code. In all six plots, points are ordered from high to low $\tan \beta$.

Figure 17

Cross sections times branching ratios in type I (left) and in type II (right) for $gg\to h\to Y$ at the 13 TeV LHC as functions of $m_h$ for $Y=\gamma \gamma$ (upper panels) and $Y=\tau \tau$ (lower panels) with $\tan \beta$ color code. Points are ordered from high to low $\tan \beta$.

Figure 18

Cross sections times branching ratios in type I (left) and in type II (right) for $A\to Y$ signatures at the 13 TeV LHC as functions of $m_A$ with $Y=\gamma \gamma$ (upper panels), $Y=\tau \tau$ (middle panels) and $Y=t\overline{t}$ (lower panels) with $\tan \beta$ color code. Points are ordered from high to low $\tan \beta$.

Figure 19

Cross sections times branching ratios in type I (left) and in type II (right) at the 13 TeV LHC as functions of $m_A$ for $gg\to A\to Zh$ (upper panels) and for $gg\to A\to ZH$ (lower panels) with $\tan \beta$ color code. Points are ordered from low to high $\tan \beta$.

Figure 20

Projection of the scan points in the plane $\tan \beta$ vs $m_A$, on the left for type I, on the right for type II. The red points are consistent with all constraints used in this paper, while the underlying black points are those which are excluded by the CMS $A\to Zh$ ($Z\to \ell \ell$, $h\to b\overline{b},\tau \tau$) limit [17] after all other constraints have been applied.

Figure 21

As in Fig. 20 but in the plane $|s_{\beta -\alpha }|$ vs $C_F^H$ for type I (left) and $|s_{\beta -\alpha }|$ vs $C_U^H$ for type II (right). To be compared to Fig. 3.

Figure 22

As in Fig. 20 but in the plane $|s_{\beta -\alpha }|$ vs $C_D^H$ for type II. To be compared to the left panel of Fig. 4. Note that the figure shows only the positive $C_D^H$ region, the opposite-sign solution not being affected by the CMS $A\to Zh$ constraint.

Figure 23

As in Fig. 20 but in the plane $|s_{\beta -\alpha }|$ vs $C_{\gamma }^H$. To be compared to Fig. 6.

Figure 24

As in Fig. 20 but in the plane $|s_{\beta -\alpha }|$ vs $C_{HHH}$. To be compared to Fig. 8.

Figure 25

As in Fig. 20 but in the ${\mu }_{gg}^H(\tau \tau )$ vs ${\mu }_{gg}^H(\gamma \gamma )$ in type I (left panel) and ${\mu }_{VBF}^H(\gamma \gamma )$ vs ${\mu }_{gg}^H(\gamma \gamma )$ in type II (right panel) planes. To be compared to the fourth and first rows of Fig. 12 and Fig. 13 respectively.

Figure 26

As in Fig. 20, but showing cross sections $\sigma (b\overline{b}X)$ versus $\sigma (gg\to X)$ for $X=h$ (left) and $X=A$ (right) in type II at the 13 TeV LHC. To be compared to Fig. 15. The effect on the analogous type I results is very small.

Figure 27

As in Fig. 20, but showing cross section times branching ratio as function of $m_A$ in type I (left) and in type II (right) for $gg\to A\to Zh$ at the 13 TeV LHC. To be compared to the upper row of plots of Fig. 19. The strip of red points with $m_A>400\mathrm{GeV}$ and high cross section corresponds to the red points in the bottom-right corners of Fig. 20; the CMS $A\to Zh$ limit is evaded because of a light $h$, $m_h\lesssim 40\mathrm{GeV}$.