Scrutinizing the alignment limit in two-Higgs-doublet models: $m_h=125\mathrm{GeV}$

In the alignment limit of a multidoublet Higgs sector, one of the Higgs mass eigenstates aligns 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 lighter of the two $CP$-even Higgs bosons, $h$, is the SM-like state observed at 125 GeV. In particular, we focus on the 2HDM parameter regime where the coupling of $h$ to gauge bosons approaches that of the SM. We review the theoretical structure and analyze the phenomenological implications of the regime of the alignment limit without decoupling, in which the other Higgs scalar masses are not significantly larger than $m_h$ and thus do not decouple from the effective theory at the electroweak scale. 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, the latest constraints from the measurements of the 125 GeV Higgs signal at the LHC, as well as the most recent limits coming from searches for heavy Higgs-like states. We contrast these results with the alignment limit achieved via the decoupling of heavier scalar states, where $h$ is the only light Higgs scalar. Implications for Run 2 at the LHC, including expectations for observing the other scalar states, are also discussed.

Figure 1

$|c_{\beta -\alpha }|$ vs $m_H$ in Type I (left) and Type II (right) with ${\log }_{10}|Z_6|$ color code. Points are ordered from high to low ${\log }_{10}|Z_6|$ values.

Figure 2

$m_H$ vs $m_A$ in Type I (left) and Type II (right) with the color code indicating the value of ${\log }_{10}|c_{\beta -\alpha }|$. Points are ordered from high to low ${\log }_{10}|c_{\beta -\alpha }|$. The dashed lines are isolines of $Z_5=4$ (upper line), 0 (middle line), and $-4$ (lower line) for $|c_{\beta -\alpha }|=0.015$ (varying $|c_{\beta -\alpha }|$ from 0 to 0.14 has no visible effect on them).

Figure 3

$m_H$ vs $m_A$ in Type I (left) and Type II (right) with the color code indicating the value of $m_{H^{\pm }}$. Points are ordered from high to low $m_{H^{\pm }}$.

Figure 4

$|c_{\beta -\alpha }|$ vs $C_F^h$ in Type I (left) and $|c_{\beta -\alpha }|$ vs $C_U^h$ in Type II (right) with $m_H$ color code. Points are ordered from low to high $m_H$. The points with $C_U^h\approx 1$ and $|c_{\beta -\alpha }|>0.03$ are the points for which $C_D^h\approx -1$, i.e., the opposite-sign Yukawa coupling points; see Fig. 5.

Figure 5

$|c_{\beta -\alpha }|$ vs $C_D^h$ in Type II with the $m_H$ color code for the full $C_D^h$ range (left) and zooming in on the $C_D^h>0$ region (right). Points are ordered from low to high $m_H$.

Figure 6

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

Figure 7

$|c_{\beta -\alpha }|$ vs $C_{\gamma }^h$ in Type I (left) and Type II (right) with the $m_H$ color code. Points are ordered from low to high $m_H$.

Figure 8

$|c_{\beta -\alpha }|$ vs the reduced triple Higgs coupling $C_{hhh}$ in Type I (left) and Type II (right) with the $m_H$ color code. Points are ordered from high to low $m_H$ values.

Figure 9

$|c_{\beta -\alpha }|$ vs the triple Higgs coupling $g_{Hhh}$ in Type I (left) and Type II (right) with the $m_H$ color code. Points are ordered from high to low $m_H$ values.

Figure 10

Signal strengths in Type I for the 125.5 GeV state, for $gg\to h\to \gamma \gamma$ (left) and $gg\to h\to Z{Z}^{*}$ (right) with the $m_H$ color code. Points are ordered from low to high $m_H$ values. Points with ${\mu }_{gg}^h(Z{Z}^{*})<0.92$ are ones for which $h\to AA$ decays are present, so that the total $h$ width is increased, which suppresses this particular channel’s rate.

Figure 11

Signal strength for $gg\to h\to Z{Z}^{*}$ in Type I for the 125.5 GeV state with the $C_F^h$ (left) and $\tan \beta$ (right) color code. Points are ordered from low to high $C_F^h$ and $\tan \beta$ values.

Figure 12

Signal strengths in Type II for the 125.5 GeV state with the $m_H$ (left) and $|C_D^h|$ color code. Points are ordered from low to high $m_H$ and $|C_D^h|$ values.

Figure 13

Correlations of signal strengths in Type I, on the left illustrating the dependence on $m_H$ and on the right illustrating the dependence in $|c_{\beta -\alpha }|$. Points are ordered from low to high $m_H$ values (left) and high to low $|c_{\beta -\alpha }|$ values (right).

Figure 14

Correlations of signal strengths in Type II, on the left illustrating the dependence on $m_H$, on the right illustrating the dependence in $|c_{\beta -\alpha }|$. Points are ordered from low to high $m_H$ values (left) and high to low $|c_{\beta -\alpha }|$ values (right).

Figure 15

$\sigma (b\overline{b}X)$ vs $\sigma (gg\to X)$ for $X=A$ (left) and $X=H$ (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. (80) are within 5% and 2% of the SM predictions (in red and dark red, respectively). The dashed lines indicate $\sigma (b\overline{b}X)=\sigma (gg\to X)$.

Figure 16

As in Fig. 15 but for Type II.

Figure 17

Cross sections in Type I (left) and Type II (right) for $gg\to X$ at the 13 TeV LHC as functions of $m_X$ for $X=A$ (upper row) and $X=H$ (lower row) with the $\tan \beta$ color code. In all four plots, points are ordered from low to high $\tan \beta$.

Figure 18

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

Figure 19

Cross section times branching ratio 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), $Y=\tau \tau$ (middle panels), and $Y=t\overline{t}$ (lower panels) with $\tan \beta$ color code. Points are ordered from low to high $\tan \beta$.

Figure 20

Cross sections times branching ratio in Type I (left) and in Type II (right) for $gg\to X\to Y$ at the 13 TeV LHC as functions of $m_X$ for $X,Y=A,Zh$ (upper panel) and $X,Y=H,hh$ (lower panel) with $\tan \beta$ color code. Points are ordered from low to high $\tan \beta$.

Figure 21

Cross sections times branching ratio in Type I (left) and in Type II (right) for Higgs-to-Higgs signatures at the 13 TeV LHC, in the upper panel $gg\to A\to ZH$ with the $m_H$ color code and in the middle and lower panels for $gg\to H\to ZA$ and $gg\to H\to AA$, respectively, with the $m_A$ color code. Points are ordered from high to low $m_A$ or $m_H$.