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arxiv: 2512.17002 · v2 · pith:B4G3XXOMnew · submitted 2025-12-18 · ✦ hep-ph · hep-ex

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

Soojin Lee , A. Hammad , Dongjoo Kim , Jeonghyeon Song This is my paper

Pith reviewed 2026-05-21 16:59 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords complex two-Higgs-doublet modelCP violationelectron electric dipole momentHiggs alignment limitType-I and Type-IIhidden CP violationneutral Higgs mixing
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0 comments X

The pith

Distinct structures in the complex two-Higgs-doublet model enable large CP violation under experimental constraints.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper maps viable regions of the complex two-Higgs-doublet model with softly broken Z2 symmetry, where the 125 GeV Higgs is the lightest neutral state, that support large CP violation while satisfying theoretical, collider, and electron EDM bounds. Global scans show Type-I models achieve peak gauge-sector CP violation when the 125 GeV boson is nearly degenerate with a second neutral scalar, typically producing electron EDMs above 10 to the minus 31 e cm. Type-II models suppress gauge CP violation but permit near-maximal Yukawa-sector CP violation through destructive interference that keeps electron EDMs as low as 10 to the minus 35 e cm. The analysis also identifies hidden CP violation in the near-alignment limit arising from mixing among heavy neutral Higgs states.

Core claim

In the complex two-Higgs-doublet model with softly broken Z2 symmetry and the lightest neutral Higgs identified as the 125 GeV state, global scans reveal distinct structures supporting large CP violation. Type-I models maximize CP violation in the gauge sector near degeneracy of the 125 GeV boson with a second neutral scalar, yielding predicted electron EDM values typically above 10^{-31} e cm. Type-II models suppress gauge CPV but allow nearly maximal Yukawa CPV with electron EDMs down to O(10^{-35}) e cm due to destructive interference. Hidden CPV emerges in the near-alignment limit through CP-violating mixing of heavy neutral Higgs bosons governed by the angle alpha3, accessible via CP-vi

What carries the argument

Parameter space structures identified in global scans that support large CP violation, including near-degeneracy of neutral scalars in Type-I, destructive interference in Type-II electron EDM contributions, and alpha3-driven mixing of heavy neutral Higgs bosons in the near-alignment limit.

If this is right

  • Next-generation electron EDM experiments can probe most viable Type-I points because predicted values exceed 10^{-31} e cm.
  • Type-II realizations remain consistent with current EDM bounds while still allowing near-maximal Yukawa CP violation.
  • Hidden CPV in the alignment limit can be tested through CP-odd observables in H2 and H3 decays and the H2-H3-Z coupling at future colliders.
  • The robust H2-H3-Z coupling provides a direct experimental handle on hidden CPV independent of other mixing angles.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These structures suggest that searches for additional Higgs bosons at the LHC should target specific mass hierarchies to enhance sensitivity to CP-violating signals.
  • Hidden CPV implies that the alignment limit does not eliminate all observable CP-violating effects, opening new channels for collider probes beyond standard Higgs coupling measurements.
  • The separation of gauge and Yukawa CPV in the two types may connect to model-building efforts addressing the baryon asymmetry through Higgs-sector sources.

Load-bearing premise

The global scan fully captures the viable parameter space without selection biases introduced by identifying the 125 GeV boson as the lightest neutral Higgs under the softly broken Z2 symmetry.

What would settle it

A precision measurement showing an electron electric dipole moment well below 10^{-31} e cm in a confirmed Type-I realization, or the absence of CP-violating effects in H2 and H3 Yukawa couplings and the H2-H3-Z interaction at a future collider, would falsify the reported structures for large CP violation.

Figures

Figures reproduced from arXiv: 2512.17002 by A. Hammad, Dongjoo Kim, Jeonghyeon Song, Soojin Lee.

Figure 1
Figure 1. Figure 1: Viable parameter points in the (MH2 , MH3 ) plane for the Type-I C2HDM, with the color code of ξV . 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 (ξV > 0.1), layered by the value of … view at source ↗
Figure 2
Figure 2. Figure 2: Viable parameter points in the (MH± , tβ) plane for the Type-I C2HDM. The color bar indicates the CPV measure ξV . The beige, gray, and colored points follow the same convention as in [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Viable parameter points in the (c(H1V V ), c(H3V V )) plane (left) and in the (c(H2V V ), c(H3V V )) plane (right) for the Type-I C2HDM. The beige, gray, and colored points follow the convention from [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Viable parameter points in the (MH2 , MH3 ) plane (left) and the (MH± , tβ) plane (right) for the Type-I C2HDM. The color bar indicates the value of the CP-violating measure ζt,b,τ . The beige and gray points follow the convention from [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Viable parameter points in the (tβ, |m2 12|) plane for the Type-I C2HDM. The color bar indicates the value of the CPV measure ξV (left panel) and ζt,b,τ (right panel). The beige and gray points follow the convention from [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Viable parameter points in the (MH2 , MH3 ) plane for the Type-II C2HDM. The color bar indicates the value of the CP-violating measure ζt (left panel) and ζb,τ (right panel). The beige and gray points follow the convention from [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Viable parameter points in the (MH± , tβ) plane for the Type-II C2HDM. The color bar indicates the value of the CP-violating measure ζt (left panel) and ζb,τ (right panel). The beige and gray points follow the convention from [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Viable parameter points in the (tβ, |m2 12|) plane for the Type-II C2HDM. The color bar indicates the value of the CP-violating measure ζt (left panel) and ζb,τ (right panel). The beige and gray points follow the convention from [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The eEDM prospect of the viable parameter points as a function of [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Branching ratios of H2 in the Near-Degenerate CPV Scenario where MH2 ∈ [126, 128] GeV and ξV > 0.1 in Type-I C2HDM. The decay modes into b ¯b, τ +τ −, cc, γγ ¯ are shown in the left panel; W+W−, gg, ZZ, Zγ in the middle; and H±W∓ in the right panel. In the H±W∓ panel, the color bar indicates MH± . These branching ratios are obtained using C2HDM HDECAY [42], which evaluates Higgs decay rates via the anyHde… view at source ↗
Figure 11
Figure 11. Figure 11: Signal strengths µ decay production of H1 and H2 in the Near-Degenerate CPV Scenario: MH2 ∈ [126, 128] GeV and ξV > 0.1 in Type-I C2HDM. Shown are decay modes into ZZ, W +W−, b ¯b, and τ +τ − for gluon fusion (top) and VBF (bottom) productions. The color code denotes ξV [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Signal strengths of H1 and H2 for the decay modes into γγ and Zγ in the Near-Degenerate CPV Scenario (MH2 ∈ [126, 128] GeV, ξV > 0.1). Results for gluon fusion are shown in the top panels, and for VBF in the bottom. The color code denotes ξV . MH2 − MH1 ≲ 3 GeV typically results in the two states appearing as a single, broadened resonance. Moreover, other mass-insensitive channels, which roughly span the … view at source ↗
Figure 13
Figure 13. Figure 13: Viable parameter points in the (α H1 t , κ H1 t ) plane (left) and (α H1 τ , κH1 τ ) plane (right) for the Type-II C2HDM. Gray points represent the full set of viable parameter points, while colored points indicate the subset satisfying the large CP violation condition: ζt > 0.1 (left) and ζb,τ > 0.1 (right). The color code denotes the magnitude of ζt and ζb,τ , respectively. The solid black curve in the … view at source ↗
Figure 14
Figure 14. Figure 14: Viable parameter points in the (αt , κt) (left panels) and (ατ , κτ ) (right panels) planes for H2 (upper panels) and H3 (lower panels) in the Type-II C2HDM. Gray points represent the full viable space; colored points satisfy the large CP violation conditions (ζt > 0.1 left, ζb,τ > 0.1 right). The color code indicates the magnitude of ζt and ζb,τ . to uncover this Yukawa-sector CP violation. The situation… view at source ↗
Figure 15
Figure 15. Figure 15: Viable parameter points in the (δH-align, α3) plane for Type-I (left panel) and Type-II (right panel) C2HDM, where δH-align is the Higgs alignment measure. Beige points satisfy theoreti￾cal 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 satisfy the condition ζ… view at source ↗
read the original abstract

We investigate the parameter space supporting large CP violation (CPV) in the complex two-Higgs-doublet model with softly broken $Z_{2}$ symmetry, where the 125~GeV Higgs boson is identified as the lightest neutral Higgs boson $H_1$. Through a comprehensive global scan of Type-I and Type-II models under theoretical, collider, and eEDM constraints, we identify distinct structures that facilitate large CPV. In Type-I, gauge-sector CPV is maximized when the 125~GeV Higgs boson is nearly degenerate with a second neutral scalar. For the ensemble of physically viable points, the predicted eEDM values typically exceed $10^{-31}\,e\cdot\mathrm{cm}$, placing the model largely within the sensitivity of next-generation experiments. Conversely, Type-II models strongly suppress gauge-sector CPV while allowing for nearly maximal CPV in the Yukawa sector. Destructive interference among various contributions allows for $|d_e|$ values as low as $O(10^{-35})\,e\cdot\mathrm{cm}$, resulting in no phenomenologically relevant lower bound. Finally, we uncover the phenomenon of ``hidden CPV'' in the near-alignment limit, characterized by CP-violating mixing between the heavy neutral Higgs bosons governed by the angle $\alpha_3$. We demonstrate that this hidden CPV can be experimentally probed at future colliders via CP-violating Yukawa interactions of $H_2$ and $H_3$, as well as the robust $H_2$-$H_3$-$Z$ coupling.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates large CP violation in the complex two-Higgs-doublet model with softly broken Z2 symmetry, where the 125 GeV Higgs is identified as the lightest neutral scalar H1. Through global scans of Type-I and Type-II realizations under theoretical, collider, and eEDM constraints, it reports distinct structures enabling large CPV: near-degeneracy of H1 with a second neutral scalar maximizing gauge-sector CPV in Type-I; strong suppression of gauge CPV but nearly maximal Yukawa CPV (with |de| down to O(10^{-35}) e cm) in Type-II; and hidden CPV in the near-alignment limit via alpha3-governed mixing between heavy neutral scalars H2 and H3, which can be probed via CP-violating Yukawa couplings and the H2-H3-Z interaction.

Significance. If the scan-based structures are robust, the work offers concrete guidance on how large CPV can arise in the C2HDM while remaining consistent with existing bounds, with direct implications for next-generation eEDM searches (Type-I) and collider probes of hidden CPV (via H2/H3 Yukawas and H2-H3-Z). The explicit separation of gauge versus Yukawa CPV sectors and the identification of the alpha3-driven hidden mechanism are potentially useful for model-building and experimental prioritization.

major comments (2)
  1. [Global scan section] The abstract and the section describing the global scan report outcomes from a comprehensive scan but supply no information on the scan algorithm, prior ranges for the CP-violating phases and mixing angles (including alpha3), convergence criteria, sampling density, or the precise post-scan cuts applied under the theoretical, collider, and eEDM constraints. This is load-bearing for the central claim, because the reported maximization, suppression, and hidden-CPV structures are extracted from the ensemble of viable points; without these details the numerical support cannot be assessed and possible selection effects remain unquantified.
  2. [Model setup and scan description] The analysis enforces that the 125 GeV boson is the lightest neutral Higgs H1 together with the softly broken Z2 symmetry. These choices restrict the sampled space; the manuscript does not examine or test whether regions with different mass orderings or exact Z2 symmetry exhibit qualitatively different CPV patterns. This assumption is load-bearing for the claim that the identified structures are intrinsic to the model rather than artifacts of the selection.
minor comments (2)
  1. [Hidden CPV discussion] Clarify the precise definition of the angle alpha3 and its relation to the CP-violating phases in the potential when discussing hidden CPV in the alignment limit.
  2. [Results sections] Ensure that any tables or figures summarizing viable-point ensembles explicitly state which constraints were active at each stage.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript to improve transparency and completeness.

read point-by-point responses

  1. Referee: [Global scan section] The abstract and the section describing the global scan report outcomes from a comprehensive scan but supply no information on the scan algorithm, prior ranges for the CP-violating phases and mixing angles (including alpha3), convergence criteria, sampling density, or the precise post-scan cuts applied under the theoretical, collider, and eEDM constraints. This is load-bearing for the central claim, because the reported maximization, suppression, and hidden-CPV structures are extracted from the ensemble of viable points; without these details the numerical support cannot be assessed and possible selection effects remain unquantified.

    Authors: We agree that a detailed description of the scan procedure is necessary to allow assessment of the robustness of the reported structures. In the revised manuscript we have added a new subsection to the global scan section that specifies the algorithm used, the prior ranges for all CP-violating phases and mixing angles (including α₃), convergence criteria, sampling density, and the exact post-scan cuts applied under the theoretical, collider, and eEDM constraints. These additions make the numerical support for the identified CPV patterns fully transparent. revision: yes

  2. Referee: [Model setup and scan description] The analysis enforces that the 125 GeV boson is the lightest neutral Higgs H1 together with the softly broken Z2 symmetry. These choices restrict the sampled space; the manuscript does not examine or test whether regions with different mass orderings or exact Z2 symmetry exhibit qualitatively different CPV patterns. This assumption is load-bearing for the claim that the identified structures are intrinsic to the model rather than artifacts of the selection.

    Authors: We acknowledge that the study is performed under the phenomenologically motivated choice that the 125 GeV state is the lightest neutral Higgs H₁ in the softly broken Z₂ C2HDM. While we did not perform additional scans for alternative mass orderings or the exact Z₂ limit, we maintain that the reported structures follow directly from the model’s theoretical consistency and current experimental constraints rather than from selection artifacts. In the revised manuscript we have added a concise discussion of the rationale for these choices and note that a systematic exploration of other regimes is an interesting avenue for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity: structures identified via scan, not reduced by construction

full rationale

The paper's central results are empirical patterns extracted from a global numerical scan of the c2HDM parameter space under explicit theoretical, collider, and eEDM constraints, with the 125 GeV state fixed as the lightest neutral Higgs H1 and softly broken Z2 symmetry. These are model-definition choices that delimit the sampled domain; the reported structures (near-degeneracy maximizing gauge CPV in Type-I, Yukawa-sector dominance with low de in Type-II, and hidden CPV via alpha3 mixing in the alignment limit) are outputs of that scan rather than quantities shown to equal the inputs by algebraic identity or by renaming a fitted parameter. No load-bearing self-citation, ansatz smuggling, or uniqueness theorem imported from prior work appears in the provided text, and the derivation chain does not contain any step that reduces a claimed prediction to a tautological re-expression of the scan priors. The analysis is therefore self-contained as a phenomenological survey.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model is built on the standard complex 2HDM with softly broken Z2; the central claims rest on numerical sampling of its free parameters rather than new axioms or entities.

free parameters (2)
  • CP-violating phases in potential and Yukawas
    Complex parameters scanned to generate large CPV while satisfying constraints.
  • Higgs mixing angles including alpha3
    Angles that control CP-violating mixing between neutral scalars, especially in the hidden-CPV regime.
axioms (2)
  • domain assumption Softly broken Z2 symmetry
    Invoked to define the model while still permitting CP violation.
  • domain assumption 125 GeV Higgs identified as lightest neutral scalar H1
    Standard phenomenological assumption stated in the abstract.

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