Intrinsic Properties of Large CP Violation in the Complex Two-Higgs-Doublet Model

TL;DR

This work maps the intrinsic parameter-space structure of the Complex 2HDM with softly broken $Z_2$ symmetry to host large CP violation, under stringent theoretical and experimental constraints including the eEDM bound. It reveals two distinct CPV pathways: Type-I achieves sizable gauge- and Yukawa-CPV only in a near-degenerate $H_2$ with the 125 GeV Higgs and yields a universal, testable lower bound on the electron EDM; Type-II largely suppresses gauge CPV but allows strong Yukawa CPV in the heavy Higgs sector with maximal mixing, while cancellations can suppress EDMs. A striking hidden-CPV phenomenon arises in the Higgs alignment limit, where heavy-Higgs CP mixing persists despite vanishing gauge couplings, and can be probed through cubic interactions involving charged Higgs and $W$ bosons. The results provide concrete predictions for future EDM experiments and HL-LHC searches, offering targeted strategies to test CP violation in both the gauge and Yukawa sectors and to uncover hidden CP structure via heavy-Higgs interactions.

Abstract

We investigate the intrinsic properties of the parameter space capable of supporting large CP violation in the Complex Two-Higgs-Doublet Model with softly broken $Z_{2}$ symmetry, hosting three CP-mixed neutral Higgs mass eigenstates. Using a comprehensive global scan of Type-I and Type-II models -- incorporating all relevant theoretical requirements and collider constraints together with the stringent electron EDM (eEDM) bound -- we identify distinct phenomenological pathways to regions of large CP violation. In Type-I, we find that all viable parameter points predict a strict lower bound on the eEDM, $|d_e| > 10^{-31}\,e\cdot\mathrm{cm}$, placing this scenario within definitive reach of next-generation EDM experiments; moreover, sizable CP violation in the gauge sector emerges only when the 125~GeV state is nearly degenerate with a second neutral Higgs boson. In contrast, Type-II suppresses gauge-sector CP violation but allows maximal CP mixing in the Yukawa sector of the heavy neutral scalars, exhibiting a strong correlation between large fermionic CP violation and the predicted eEDM. Finally, we uncover a phenomenon of ``hidden CP violation'' in the Higgs alignment limit: even as the heavy neutral scalars decouple from gauge bosons, their CP mixing remains entirely unconstrained and becomes increasingly maximal as the Yukawa-sector CP violation increases. We show that this hidden CP violation can be directly probed through the non-vanishing cubic interactions of the heavy neutral scalars to the charged Higgs and $W$ bosons.

Figures (15)

• Figure 1: Viable parameter points in the $(M_{H_2}, M_{H_3})$ plane for the Type-I C2HDM, with the color code of $\xi_V$. Beige points satisfy theoretical requirements and constraints from electroweak precision data, flavor physics, and Higgs collider searches. Gray points represent the subset additionally satisfying the eEDM bound. Colored points highlight the region with large CP violation ($\xi_V > 0.1$), layered by the value of $\xi_V$, with higher values plotted on top. The right panel provides a magnified view focused on the large $\xi_V$ region.
• Figure 2: Viable parameter points in the $(M_{H^\pm},\,t_\beta)$ plane for the Type-I C2HDM. The color bar indicates the CPV measure $\xi_V$. The beige, gray, and colored points follow the same convention as in \ref{['fig-type1-xiv-mh3-mh2']}.
• Figure 3: Viable parameter points in the $(c(H_1VV), c(H_3 VV))$ plane (left) and in the $(c(H_2VV), c(H_3 VV))$ plane (right) for the Type-I C2HDM. The beige, gray, and colored points follow the convention from \ref{['fig-type1-xiv-mh3-mh2']}, where the color bar indicates the value of the CP-violating measure $\xi_V$.
• Figure 4: Viable parameter points in the $(M_{H_2},\,M_{H_3})$ plane (left) and the $(M_{H^\pm},\,t_\beta)$ plane (right) for the Type-I C2HDM. The color bar indicates the value of the CP-violating measure $\zeta_{t,b,\tau}$. The beige and gray points follow the convention from \ref{['fig-type1-xiv-mh3-mh2']}, while the colored points represent the subset with $\zeta_{t,b,\tau} > 0.1$. The inset in the left panel provides a magnified view of the low-mass region.
• Figure 5: Viable parameter points in the $(t_\beta,\,|m_{12}^2|)$ plane for the Type-I C2HDM. The color bar indicates the value of the CPV measure $\xi_V$ (left panel) and $\zeta_{t,b,\tau}$ (right panel). The beige and gray points follow the convention from \ref{['fig-type1-xiv-mh3-mh2']}, while the colored points represent the subset with $\xi_V > 0.1$ (left) and $\zeta_{t,b,\tau} > 0.1$ (right).