Restricting the parameter space of type-II two-Higgs-doublet models with $CP$ violation

We explore the parameter space of the type-II two-Higgs-doublet model with softly broken $Z_2$ symmetry, allowing for $CP$ violation in the scalar potential. Imposing theory-motivated and experimentally-driven constraints, we show that as the $CP$-violating phases are increased, only small regions of parameter space survive, including regions slightly away from the alignment limit. Electroweak oblique parameters and electric dipole moments emerge as most restrictive constraints. We show that imposing these constraints (as well as theoretical bounds such as perturbativity) the masses of the charged and heavy neutral Higgs, unlike in the $CP$ conserving case, are bound from above and below. In particular, the heavy neutral Higgs masses are almost degenerate. In this parameter space region we highlight the relevant decay signals of the heavy neutral Higgs, involving both $Zh$ and $WW/ZZ$, indicative of $CP$ violation in the model.

Figure 1

Allowed parameter space for the 2HDM with $CP$ violation from LHC-Higgs data. We show restrictions on the parameter space coming from varying $\tan \beta$ and $\cos (\beta -\alpha )$. Each plot has a fixed value of ${\alpha }_b$ (measuring the amount of $CP$-violating admixture within the SM-like Higgs boson). Top left: ${\alpha }_b=0$ ($CP$-conserving SM-like Higgs), top right: ${\alpha }_b=0.05$, middle left: ${\alpha }_b=0.1$, middle right: ${\alpha }_b=0.2$, bottom left: ${\alpha }_b=0.3$, bottom right: ${\alpha }_b=0.4$. We included all CMS and ATLAS data at $36{\mathrm{fb}}^{-1}$, as well as data on the Higgs production and diboson decays at $140{\mathrm{fb}}^{-1}$ as in the latest lilith software [56].

Figure 2

Contours of the signal strengths for the three Higgs channels $gg\to h\to ZZ$ (red-thick), $Vh\to (h\to b\overline{b})$ (green-light) and $gg\to h\to \gamma \gamma$ (black-thin), using the upper and lower bounds from the ATLAS detector obtained with $36{\mathrm{fb}}^{-1}$ (dashed, dot-dashed and dotted respectively) and with $139{\mathrm{fb}}^{-1}$ (all solid) of integrated luminosity. The white regions are points in parameter space that individually lie within the $b\overline{b}$, the $ZZ$ and the $\gamma \gamma$ bounds using the $139{\mathrm{fb}}^{-1}$ of luminosity from ATLAS. The gray regions represent points that are outside of either of the bounds, i.e., these regions do not represent a combination of bounds. We take ${\alpha }_b=0.1$ in the left panel and ${\alpha }_b=0.3$ in the right panel. In both cases the individually allowed regions from each of the three Higgs signals is located in between their respective contour curves and clearly shrink when going from $36{\mathrm{fb}}^{-1}$ to $139{\mathrm{fb}}^{-1}$ of integrated luminosity (although note that the upper bound from $b\overline{b}$ at $36{\mathrm{fb}}^{-1}$ does not appear in the plot).

Figure 3

Restrictions for the $CPV$ 2HDM on the parameter space in $M_{H^{\pm }}-M_{H_2}$ plane from oblique parameters and EDMs. We show plots for different values of $\sin {\alpha }_b$. Top left: ${\alpha }_b=0.1$, top right: ${\alpha }_b=0.2$, bottom left: ${\alpha }_b=0.3$, bottom right: ${\alpha }_b=0.4$. The black dotted region is populated by points that pass all experimental and theoretical bounds, except for precision electroweak tests and EDMs. The rainbow-colored region contains points passing all tests described in Sec. 3.

Figure 4

Restrictions for the 2HDM with $CP$ violation on the parameter space for $M_{H_3}$ and $M_{H_2}$ plane from oblique parameters. We show plots for different values of $\sin {\alpha }_b$. Top left: ${\alpha }_b=0.1$, top right: ${\alpha }_b=0.2$, bottom left: ${\alpha }_b=0.3$, bottom right: ${\alpha }_b=0.4$. The black dots are points that pass all experimental and theoretical bounds, except for precision electroweak tests and EDMs. The rainbow-colored dots are points that pass all tests described in Sec. 3.

Figure 5

Constraints on $\Im {\lambda }_5$, a source of CPV in the Lagrangian of the 2HDM, versus $M_{H_2}$ from oblique parameters. We show plots for different values of ${\alpha }_b$. Top left: ${\alpha }_b=0.1$, top right: ${\alpha }_b=0.2$, bottom left: ${\alpha }_b=0.3$, bottom right: ${\alpha }_b=0.4$. The rainbow colored dots are points that pass all tests described in Sec. 3, including precision tests and EDM bounds.

Figure 6

${\sigma }_{g{g}_{H_2}}$ times branching ratios versus $M_{H_2}$, in pb, allowed by both STU and EDM constraints for different values of $\sin {\alpha }_b$. Top left: ${\alpha }_b=0.1$, top right: ${\alpha }_b=0.2$, bottom left: ${\alpha }_b=0.3$, bottom right: ${\alpha }_b=0.4$. We plot, in each panel, the $M_{H_2}$ region and ${\alpha }_c$ range surviving the constraints for the chosen values of ${\alpha }_b$ and $\cos (\beta -\alpha )$, consistent with the allowed ones in Fig. 3.

Figure 7

${\sigma }_{g{g}_{H_3}}$ times branching ratios versus $M_{H_3}$, in pb, allowed by both STU and EDM constraints, for different values of $\sin {\alpha }_b$. Top left: ${\alpha }_b=0.1$, top right: ${\alpha }_b=0.2$, bottom left: ${\alpha }_b=0.3$, bottom right: ${\alpha }_b=0.4$. We plot, in each panel, the $M_{H_3}$ region and ${\alpha }_c$ range surviving the constraints for the chosen values of ${\alpha }_b$ and $\cos (\beta -\alpha )$, consistent with the allowed ones in Fig. 3.