Relaxed constraints on the heavy scalar masses in 2HDM

In the wake of new scalar searches at the LHC in various channels, it is interesting to investigate the sacrosanctity of the constraints on the masses and couplings of the heavier scalars in a two-Higgs-doublet model (2HDM). We consider the effects of new physics beyond a 2HDM encoded in terms of bosonic dim-6 operators. Although these constraints are mostly immune to such new physics, we demonstrate that, for a specific class of bosonic operators, the constraints on the masses of the exotic scalars from cascade decays can get substantially relaxed. We present such effects for both degenerate and hierarchical mass spectra of the heavier scalars in 2HDM. Some decay channels of the new scalars vanish at the alignment limit in the tree-level 2HDM. But the inclusion of dim-6 terms can lead to significant cross sections for such processes. It is also pointed out that the observation of such processes can no longer rule out the alignment limit if such dim-6 operators are present.

Figure 1

The effect of the ${\phi }^4{D}^2$ type of operators for mass spectrum $\mathbf{C}\mathbf{1}$. Only the colored regions are kinematically viable. The gray regions with the dashed and solid boundaries are ruled out from $gg\to A\to ZH(b\overline{b})$ [50] in a 2HDM and $\mathbf{BP}\mathbf{1}$ of 2HDMEFT, respectively. The brown regions with the dashed and solid boundaries are ruled out from $gg\to A\to \tau \overline{\tau }$ [51] in a 2HDM and $\mathbf{BP}\mathbf{1}$ of 2HDMEFT, respectively. The meshed blue region is disfavored from the theoretical constraints, viz. stability, perturbativity, and unitarity.

Figure 2

The effect of the ${\phi }^4{D}^2$ type of operators for mass spectrum $\mathbf{C}\mathbf{2}$. Color coding is the same as in Fig. 1.

Figure 3

The effect of the ${\phi }^4{D}^2$ type of operators for mass spectrum $\mathbf{C}\mathbf{3}$. The gray regions with the dashed and solid boundaries are ruled out from $gg\to H\to ZA(b\overline{b})$ [50] in a 2HDM and $\mathbf{BP}\mathbf{1}$ of 2HDMEFT, respectively. The brown regions with the dashed and solid boundaries are ruled out from $gg\to H\to \tau \overline{\tau }$ [51] in a 2HDM and $\mathbf{BP}\mathbf{1}$ of 2HDMEFT, respectively. The green region is disfavored from the nonobservation of $gg\to H\to ZZ$ [48] in $\mathbf{BP}\mathbf{1}$ of 2HDMEFT, which is absent in the 2HDM at the tree level for $\cos (\beta -\alpha )=0$. The rest of the color coding is the same as in Fig. 1.

Figure 4

The effect of the ${\phi }^4{D}^2$ type of operators for mass spectrum $\mathbf{C}\mathbf{4}$. Color coding is the same as in Fig. 3.

Figure 5

The effect of the ${\phi }^4{D}^2$ type of operators for $\mathbf{C}\mathbf{5}$ in a type-II 2HDM. (a) The blue regions with the dashed and solid boundaries are ruled out from $H\to ZZ$ [48], the pink regions with the dashed and solid boundaries are ruled out from $A\to \tau \tau$ [51], and the purple regions with the dashed and solid boundaries are ruled out from $A\to Zh$ [50] in a 2HDM and $\mathbf{BP}\mathbf{1}$ of 2HDMEFT, respectively. (b) The solid blue (red) line represents $\sigma \times \mathrm{Br}$ for $gg\to H\to ZZ$ [48] ($gg\to A\to Zh$ [50]) at the alignment limit in the presence of the 6-dim operators mentioned in $\mathbf{BP}\mathbf{1}$. The experimental upper limits to the $\sigma \times \mathrm{Br}$ corresponding to the two processes are also shown as dotted lines in the same color.

Figure 6

The effect of the ${\phi }^4{D}^2$ type of operators on the $m_H-\tan \beta$ plane in a type-II 2HDM. The regions are excluded from $gg\to H\to ZZ$ (gray) [48], $gg\to A\to ZH$ (purple) [50], $gg\to A\to Zh$ (red) [50], $gg\to A\to \tau \overline{\tau }$ (green) [51], $b\overline{b}\to A\to \tau \overline{\tau }$ (brown) [51], and $b\overline{b}\to H\to \tau \overline{\tau }$ (blue) [51, 52]. In the case of 2HDMEFT (dashed lines), the bounds from $A\to ZH$ and $H\to ZZ$ are different compared to a 2HDM at tree level (solid lines).

Figure 7

The effect of 6-dim terms in a type-II 2HDM on (a) $\sigma (H^{\pm }t)\mathrm{Br}(H^{\pm }\to h{W}^{\pm })$ for case $\mathbf{C}\mathbf{1}$, (b) $\sigma (H^{\pm }t)\mathrm{Br}(H^{\pm }\to h{W}^{\pm })$ for case $\mathbf{C}\mathbf{4}$, (c) $\sigma (H^{\pm }t)\mathrm{Br}(H^{\pm }\to H{W}^{\pm })$ for case $\mathbf{C}\mathbf{1}$, and (d) $\sigma (H^{\pm }t)\mathrm{Br}(H^{\pm }\to t\overline{b})$ for case $\mathbf{C}\mathbf{1}$. The solid and dotted lines correspond to the same values of $\sigma \times \mathrm{Br}$ in a 2HDM at tree level and in $\mathbf{BP}\mathbf{1}$ of 2HDMEFT, respectively. The density plots depict the values of the corresponding $\sigma \times \mathrm{Br}$ in the log scale at the LHC with $\sqrt{s}=14\mathrm{TeV}$.

Figure 8

The branching ratios of $A$ in various channels for the hierarchical cases for $\cos (\beta -\alpha )=0$ and $\tan \beta =1.5$. Dashed and solid lines represent the case of a 2HDM at tree level and BP1 of 2HDMEFT, respectively.

Figure 9

The branching ratios of $H$ in various channels for the hierarchical case $\mathbf{C}\mathbf{1}$ for $\cos (\beta -\alpha )=0$ and $\tan \beta =1.5$. Dashed and solid lines represent the case of a 2HDM at tree level and BP1 of 2HDMEFT, respectively.

Figure 10

The branching ratios of $H$ and $A$ in various channels which constrain the parameter space on the $\cos (\beta -\alpha )-m_A$ plane in the degenerate case C5 for a type-II 2HDM. In all three figures, the solid and dashed lines represent the corresponding branching ratios in a 2HDM at the tree level and $\mathbf{BP}\mathbf{1}$ of 2HDMEFT, respectively.

Figure 11

$\sigma (H^{\pm }t)\mathrm{Br}(H^{\pm }\to h{W}^{\pm })$ in the alignment limit, in the presence of the 6-dim terms at the LHC with $\sqrt{s}=14\mathrm{TeV}$ in a type-II 2HDM.