arxiv: 2511.21874 · v2 · submitted 2025-11-26 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Model-independent probes of CP violation in the heavy scalar sector at muon colliders

Qianxi Li , Ying-nan Mao , Kechen Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-17 04:08 UTC · model grok-4.3

classification ✦ hep-ph

keywords CP violationheavy scalarmuon collidervector boson fusionHiggs sectormodel-independentZ h1 decay

0 comments

The pith

Observing one vector-boson-fusion process at a muon collider establishes CP violation in the scalar sector.

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

The paper proposes a model-independent test for CP violation by considering a heavy neutral scalar h2 that couples at tree level to both vector-boson pairs and to the combination of the 125 GeV Higgs and a Z boson. At future muon colliders the authors focus on vector-boson fusion production of this heavy scalar followed by its decay into Z h1. A sympathetic reader would care because the appearance of this single process would require both couplings to be nonzero, which cannot occur in a CP-conserving theory and therefore directly signals CP violation without additional assumptions about the underlying model.

Core claim

In an extended scalar sector containing a heavy neutral scalar h2, the observation of the process VV → h2 → Z h1 at a muon collider implies that the h2VV and h2h1Z couplings are both present at tree level. These two couplings cannot coexist for any CP eigenstate scalar; their simultaneous presence is therefore sufficient to establish CP violation in the scalar sector. The authors simulate the signal and backgrounds at 3 TeV and 10 TeV muon colliders with the stated luminosities and map the expected discovery reach in the (c2, c12) coupling plane for several mass hypotheses of h2.

What carries the argument

The single process VV → h2 → Z h1, whose observation forces both the h2VV and h2h1Z couplings to be nonzero and thereby establishes CP violation.

If this is right

Observation of the process directly confirms CP violation without measuring separate CP-odd observables.
The test remains valid across a range of masses for the heavy scalar h2.
Projected discovery sensitivities are given for the coupling parameters at the two collider energies and luminosities considered.
The method applies model-independently to any extended Higgs sector that allows the required tree-level vertices.

Where Pith is reading between the lines

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

The same signature could be searched for at other high-energy lepton colliders if sufficient luminosity is available.
Absence of the signal would place upper limits on the size of CP-violating couplings in multi-Higgs models.
Angular distributions in the final state could provide additional confirmation once the basic process is observed.

Load-bearing premise

A heavy neutral scalar h2 exists with tree-level couplings to both VV and to h1Z, and backgrounds can be controlled well enough for the signal to be observable in the simulated muon-collider environments.

What would settle it

A simulation in which the VV → h2 → Z h1 signal remains unobservable above background for all values of the couplings c2 and c12 at both 3 TeV and 10 TeV would show that the proposed signature cannot establish CP violation.

read the original abstract

We propose a model-independent test of CP violation in the scalar sector. We consider a heavy neutral scalar $h_2$ with tree-level couplings at the $h_2 V V$ and $h_2 h_1 Z$ vertices (with $V=W^{\pm},Z$), alongside the 125~GeV SM-like Higgs boson $h_1$. At future muon colliders (MuC), we exploit vector-boson-fusion (VBF) production of $h_2$ followed by the decay $h_2 \to Z h_1$. In our framework, observing the single process $V V \to h_2 \to Z h_1$ implies both relevant couplings are nonzero, which is sufficient to establish CP violation in the scalar sector. We simulate signal and backgrounds at $\sqrt{s}=3~(10)$~TeV with integrated luminosity $L=0.9~(10)~\mathrm{ab}^{-1}$. We then present the expected discovery sensitivities across the $(c_2,c_{12})$ parameter space (with the coupling parameters $c_{2}$ and $c_{12}$ defined in the text) for multiple $m_{h_2}$ hypotheses.

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.

Desk Editor's Note private letter to a colleague

Muon collider VBF search for a heavy scalar decay chain offers a concrete handle on CP violation but the central claim needs explicit justification that both couplings cannot appear together without it.

read the letter

The paper puts forward a model-independent test: at a muon collider, vector boson fusion can produce a heavy neutral scalar h2 that then decays to Z plus the 125 GeV Higgs. Seeing that single chain would require nonzero h2VV and h2h1Z couplings at tree level, which the authors argue is enough to establish CP violation in the scalar sector. They simulate the process at 3 and 10 TeV with the stated luminosities and show expected reach in the (c2, c12) plane for several mass hypotheses. That combination of collider mode and decay signature is the clearest new element here, and the simulation setup gives a practical starting point for estimating sensitivity. The work is aimed squarely at people already thinking about muon collider phenomenology and extended Higgs sectors, so those readers could extract useful benchmark numbers even if they later adjust the assumptions. The main soft spot is that the abstract does not derive or reference why a CP-conserving theory forbids a single neutral scalar from carrying both couplings at once; possible loopholes such as additional fields or higher-dimensional operators are not addressed in the visible text. Background modeling and efficiency numbers are also absent, which makes it difficult to judge how robust the discovery projections actually are. On the evidence shown, the logic is internally consistent within the stated framework but rests on an unshown step that a referee would want spelled out. I would send this to peer review so the authors can supply the missing derivation and quantitative details; the topic is timely enough that a careful check is worthwhile.

Referee Report

1 major / 1 minor

Summary. The paper proposes a model-independent test of CP violation in the scalar sector at future muon colliders. It posits a heavy neutral scalar h2 with tree-level couplings to both VV (V = W, Z) and to h1Z (where h1 is the 125 GeV SM-like Higgs), and argues that observing vector-boson-fusion production of h2 followed by decay to Zh1 at MuC energies of 3 or 10 TeV would require both couplings to be nonzero and thereby establish CP violation. Signal and background simulations are mentioned for luminosities of 0.9 and 10 ab^{-1}, with expected discovery sensitivities presented in the (c2, c12) parameter space for various mh2 hypotheses.

Significance. If the central logical step holds, the approach would furnish a clean, model-independent signature of CP violation in extended scalar sectors that relies only on the existence of the two specified tree-level vertices rather than on specific model assumptions or loop-induced effects. The collider simulation component could translate this into concrete experimental targets for muon collider searches, potentially complementing other CP probes in the Higgs sector.

major comments (1)

Abstract: The assertion that 'observing the single process VV → h2 → Zh1 implies both relevant couplings are nonzero, which is sufficient to establish CP violation' is stated without any derivation, explicit mapping of the couplings to CP eigenstates, or discussion of why a CP-conserving scalar sector (e.g., via CP-even or CP-odd assignments, additional scalars, or higher-dimensional operators) cannot simultaneously accommodate tree-level h2VV and h2h1Z vertices for a single neutral scalar. This step is load-bearing for the model-independence claim and must be substantiated in the manuscript.

minor comments (1)

Abstract: No quantitative results (e.g., signal efficiencies, background rejection factors, or expected significances) are reported despite the mention of simulations; including even summary numbers would improve clarity of the discovery sensitivities.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and for recognizing the potential significance of our proposed model-independent probe of CP violation. We address the single major comment below and will revise the manuscript to strengthen the presentation of the central logical step.

read point-by-point responses

Referee: Abstract: The assertion that 'observing the single process VV → h2 → Zh1 implies both relevant couplings are nonzero, which is sufficient to establish CP violation' is stated without any derivation, explicit mapping of the couplings to CP eigenstates, or discussion of why a CP-conserving scalar sector (e.g., via CP-even or CP-odd assignments, additional scalars, or higher-dimensional operators) cannot simultaneously accommodate tree-level h2VV and h2h1Z vertices for a single neutral scalar. This step is load-bearing for the model-independence claim and must be substantiated in the manuscript.

Authors: We agree that the abstract presents the key implication concisely without an accompanying derivation. In the revised version we will add a short dedicated paragraph (likely in Section 2) that explicitly maps the tree-level vertices to CP transformation properties. We will show that, for a single neutral scalar, a CP-even assignment permits a tree-level h2VV coupling but forbids a tree-level h2 h1 Z coupling when h1 is CP-even, while a CP-odd assignment permits the h2 h1 Z vertex but forbids the h2VV coupling. Consequently, the simultaneous presence of both vertices at tree level requires the scalar to be a CP mixture, which is possible only in a CP-violating theory. We will also note briefly why additional scalars or higher-dimensional operators within a strictly CP-conserving framework do not circumvent this for a single neutral state. This addition will make the model-independence argument self-contained while preserving the paper’s focus on the collider phenomenology. revision: yes

Circularity Check

0 steps flagged

No circularity: claim rests on general coupling logic without self-referential reduction

full rationale

The available abstract presents a framework in which observation of the single process VV → h2 → Z h1 is said to imply nonzero tree-level couplings at both h2VV and h2h1Z vertices, which is asserted to establish CP violation. No equations, parameter fits, self-citations, or internal definitions are supplied that would reduce this implication to a tautology or fitted input by construction. The argument is framed as model-independent and relies on external theoretical considerations about scalar CP properties rather than any load-bearing self-reference or renaming of known results. The derivation chain is therefore self-contained against the presented inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the central claim rests on the existence of h2 and its couplings plus standard collider simulation assumptions.

free parameters (2)

c2
Coupling parameter scanned across the parameter space to determine discovery sensitivity.
c12
Coupling parameter scanned across the parameter space to determine discovery sensitivity.

axioms (2)

domain assumption A heavy neutral scalar h2 exists with tree-level couplings to VV and to h1Z
Invoked to define the signal process VV → h2 → Z h1
standard math h1 behaves as the 125 GeV SM-like Higgs boson
Used to identify the decay product in the proposed channel

invented entities (1)

heavy neutral scalar h2 no independent evidence
purpose: To host the CP-violating couplings under test
Postulated beyond-Standard-Model particle whose existence and couplings are assumed for the probe

pith-pipeline@v0.9.0 · 5492 in / 1526 out tokens · 74443 ms · 2026-05-17T04:08:21.754780+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

observing the single process VV → h2 → Z h1 implies both relevant couplings are nonzero, which is sufficient to establish CP violation in the scalar sector
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

L ⊃ (g²v/2 W⁺μW⁻μ + …) (c1 h1 + c2 h2) + c12 g²/cW Zμ (h1 ∂μ h2 − h2 ∂μ h1)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

107 extracted references · 107 canonical work pages · 57 internal anchors

[1]

Observation of Large CP Violation in the Neutral B Meson System

J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay,Evidence for the2πDecay of the K 0 2 Meson,Phys. Rev. Lett.13(1964) 138. [2]Bellecollaboration,Observation of large CP violation in the neutralBmeson system, Phys. Rev. Lett.87(2001) 091802 [hep-ex/0107061]. [3]BaBarcollaboration,Observation of CP violation in theB 0 meson system,Phys. Rev. Lett.87(2...

work page internal anchor Pith review Pith/arXiv arXiv 1964
[2]

Khalil and S

S. Khalil and S. Moretti,Standard Model Phenomenology, CRC Press (6, 2022). [6]Particle Data Groupcollaboration,Review of particle physics,Phys. Rev. D110(2024) 030001. [7]LHCbcollaboration,Observation of charge–parity symmetry breaking in baryon decays, Nature643(2025) 1223 [2503.16954]

work page arXiv 2022
[3]

Kobayashi and T

M. Kobayashi and T. Maskawa,CP Violation in the Renormalizable Theory of Weak Interaction,Prog. Theor. Phys.49(1973) 652

work page 1973
[4]

Cabibbo,Unitary Symmetry and Leptonic Decays,Phys

N. Cabibbo,Unitary Symmetry and Leptonic Decays,Phys. Rev. Lett.10(1963) 531

work page 1963
[5]

Nir,Cp violation in meson decays, inLes Houches, vol

Y. Nir,Cp violation in meson decays, inLes Houches, vol. 84, pp. 79–145, Elsevier (2006). [11]HFLA Vcollaboration,Averages of b-hadron, c-hadron, andτ-lepton properties as of 2021, Phys. Rev. D107(2023) 052008 [2206.07501]

work page arXiv 2006
[6]

Cohen, D.B

A.G. Cohen, D.B. Kaplan and A.E. Nelson,Spontaneous baryogenesis at the weak phase transition,Phys. Lett. B263(1991) 86

work page 1991
[7]

Progress in Electroweak Baryogenesis

A.G. Cohen, D.B. Kaplan and A.E. Nelson,Progress in electroweak baryogenesis,Ann. Rev. Nucl. Part. Sci.43(1993) 27 [hep-ph/9302210]

work page internal anchor Pith review Pith/arXiv arXiv 1993
[8]

Electroweak baryogenesis

D.E. Morrissey and M.J. Ramsey-Musolf,Electroweak baryogenesis,New J. Phys.14(2012) 125003 [1206.2942]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[9]

Lee,CP Nonconservation and Spontaneous Symmetry Breaking,Phys

T.D. Lee,CP Nonconservation and Spontaneous Symmetry Breaking,Phys. Rept.9(1974) 143

work page 1974
[10]

Weinberg,Gauge Theory of CP Violation,Phys

S. Weinberg,Gauge Theory of CP Violation,Phys. Rev. Lett.37(1976) 657

work page 1976
[11]

Georgi,A Model of Soft CP Violation,Hadronic J.1(1978) 155

H. Georgi,A Model of Soft CP Violation,Hadronic J.1(1978) 155

work page 1978
[12]

Bento, G.C

L. Bento, G.C. Branco and P.A. Parada,A Minimal model with natural suppression of strong CP violation,Phys. Lett. B267(1991) 95

work page 1991
[13]

Theory and phenomenology of two-Higgs-doublet models

G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva,Theory and phenomenology of two-Higgs-doublet models,Phys. Rept.516(2012) 1 [1106.0034]. – 16 – [20]ACMEcollaboration,Improved limit on the electric dipole moment of the electron,Nature 562(2018) 355

work page internal anchor Pith review Pith/arXiv arXiv 2012
[14]

Roussy et al.,An improved bound on the electron’s electric dipole moment,Science381 (2023) adg4084 [2212.11841]

T.S. Roussy et al.,An improved bound on the electron’s electric dipole moment,Science381 (2023) adg4084 [2212.11841]

work page arXiv 2023
[15]

Abel et al.,Measurement of the Permanent Electric Dipole Moment of the Neutron, Phys

C. Abel et al.,Measurement of the Permanent Electric Dipole Moment of the Neutron, Phys. Rev. Lett.124(2020) 081803 [2001.11966]

work page arXiv 2020
[16]

Reduced Limit on the Permanent Electric Dipole Moment of $^{199}$Hg

B. Graner, Y. Chen, E. Lindahl and B. Heckel,Reduced Limit on the Permanent Electric Dipole Moment of Hg199,Phys. Rev. Lett.116(2016) 161601 [1601.04339]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[17]

Electric dipole moments as probes of new physics

M. Pospelov and A. Ritz,Electric dipole moments as probes of new physics,Annals Phys. 318(2005) 119 [hep-ph/0504231]

work page internal anchor Pith review Pith/arXiv arXiv 2005
[18]

Electric Dipole Moments of Nucleons, Nuclei, and Atoms: The Standard Model and Beyond

J. Engel, M.J. Ramsey-Musolf and U. van Kolck,Electric Dipole Moments of Nucleons, Nuclei, and Atoms: The Standard Model and Beyond,Prog. Part. Nucl. Phys.71(2013) 21 [1303.2371]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[19]

Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation

N. Yamanaka, B.K. Sahoo, N. Yoshinaga, T. Sato, K. Asahi and B.P. Das,Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation,Eur. Phys. J. A53(2017) 54 [1703.01570]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[20]

Search for New Physics with Atoms and Molecules

M.S. Safronova, D. Budker, D. DeMille, D.F.J. Kimball, A. Derevianko and C.W. Clark, Search for New Physics with Atoms and Molecules,Rev. Mod. Phys.90(2018) 025008 [1710.01833]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[21]

Electric Dipole Moments of the Atoms, Molecules, Nuclei and Particles

T. Chupp, P. Fierlinger, M. Ramsey-Musolf and J. Singh,Electric dipole moments of atoms, molecules, nuclei, and particles,Rev. Mod. Phys.91(2019) 015001 [1710.02504]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[22]

Yamaguchi and N

Y. Yamaguchi and N. Yamanaka,Large long-distance contributions to the electric dipole moments of charged leptons in the standard model,Phys. Rev. Lett.125(2020) 241802 [2003.08195]

work page arXiv 2020
[23]

Yamaguchi and N

Y. Yamaguchi and N. Yamanaka,Quark level and hadronic contributions to the electric dipole moment of charged leptons in the standard model,Phys. Rev. D103(2021) 013001 [2006.00281]

work page arXiv 2021
[24]

Consistency of the Two Higgs Doublet Model and CP violation in top production at the LHC

A.W. El Kaffas, W. Khater, O.M. Ogreid and P. Osland,Consistency of the two Higgs doublet model and CP violation in top production at the LHC,Nucl. Phys. B775(2007) 45 [hep-ph/0605142]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[25]

Determining the CP parity of Higgs bosons at the LHC in their tau decay channels

S. Berge, W. Bernreuther and J. Ziethe,Determining the CP parity of Higgs bosons at the LHC in their tau decay channels,Phys. Rev. Lett.100(2008) 171605 [0801.2297]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[26]

Impact of a CP Violating Higgs: from LHC to Baryogenesis

J. Shu and Y. Zhang,Impact of a CP Violating Higgs Sector: From LHC to Baryogenesis, Phys. Rev. Lett.111(2013) 091801 [1304.0773]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[27]

Lightness of Higgs Boson and Spontaneous CP Violation in Lee Model

Y.-n. Mao and S.-h. Zhu,Lightness of Higgs boson and spontaneous CP violation in the Lee model,Phys. Rev. D90(2014) 115024 [1409.6844]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[28]

C.-Y. Chen, S. Dawson and Y. Zhang,Complementarity of LHC and EDMs for Exploring Higgs CP Violation,JHEP06(2015) 056 [1503.01114]. – 17 –

work page internal anchor Pith review Pith/arXiv arXiv 2015
[29]

CP Violating Two-Higgs-Doublet Model: Constraints and LHC Predictions

V. Keus, S.F. King, S. Moretti and K. Yagyu,CP Violating Two-Higgs-Doublet Model: Constraints and LHC Predictions,JHEP04(2016) 048 [1510.04028]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[30]

Probing CP-violating $h\bar{t}t$ coupling in $e^{+}e^{-}\rightarrow h \gamma$

G. Li, H.-R. Wang and S.-h. Zhu,Probing CP-violatingh¯ttcoupling ine +e− →hγ,Phys. Rev. D93(2016) 055038 [1506.06453]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[31]

Anomalous Higgs-top Coupling Pollution on Triple Higgs Coupling Extraction at Future High-Luminosity Electron-Positron Collider

C. Shen and S.-h. Zhu,Anomalous Higgs-top coupling pollution of the triple Higgs coupling extraction at a future high-luminosity electron-positron collider,Phys. Rev. D92(2015) 094001 [1504.05626]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[32]

Large pseudoscalar Yukawa couplings in the complex 2HDM

D. Fontes, J.C. Rom˜ao, R. Santos and J.P. Silva,Large pseudoscalar Yukawa couplings in the complex 2HDM,JHEP06(2015) 060 [1502.01720]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[33]

Higgs pair productions in the CP-violating two-Higgs-doublet model

L. Bian and N. Chen,Higgs pair productions in the CP-violating two-Higgs-doublet model, JHEP09(2016) 069 [1607.02703]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[34]

Lightness of a Higgs Boson and Spontaneous CP-violation in the Lee Model: An Alternative Scenario

Y.-n. Mao and S.-h. Zhu,Lightness of a Higgs Boson and Spontaneous CP-violation in the Lee Model: An Alternative Scenario,Phys. Rev. D94(2016) 055008 [1602.00209]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[35]

CP-Violation in the Two Higgs Doublet Model: from the LHC to EDMs

C.-Y. Chen, H.-L. Li and M. Ramsey-Musolf,CP-Violation in the Two Higgs Doublet Model: from the LHC to EDMs,Phys. Rev. D97(2018) 015020 [1708.00435]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[36]

Spontaneous CP-violation in the Simplest Little Higgs Model and its Future Collider Tests: the Scalar Sector

Y.-n. Mao,Spontaneous CP-violation in the Simplest Little Higgs Model and its Future Collider Tests: the Scalar Sector,Phys. Rev. D97(2018) 075031 [1703.10123]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[37]

X. Chen, G. Li and X. Wan,Probe CP violation inH→γZthrough forward-backward asymmetry,Phys. Rev. D96(2017) 055023 [1705.01254]

work page arXiv 2017
[38]

Wan and Y.-K

X. Wan and Y.-K. Wang,Probing the CP violatingHγγcoupling using interferometry, Chin. Phys. C43(2019) 073101 [1712.00267]

work page arXiv 2019
[39]

Mao,Spontaneous CP-violation in the Simplest Little Higgs Model,PoSICHEP2018 (2019) 003 [1810.03854]

Y.-n. Mao,Spontaneous CP-violation in the Simplest Little Higgs Model,PoSICHEP2018 (2019) 003 [1810.03854]

work page arXiv 2019
[40]

Cheung, A

K. Cheung, A. Jueid, Y.-n. Mao and S. Moretti,Two-Higgs-doublet model with soft CP violation confronting electric dipole moments and colliders,Phys. Rev. D102(2020) 075029 [2003.04178]

work page arXiv 2020
[41]

Cao, K.-P

Q.-H. Cao, K.-P. Xie, H. Zhang and R. Zhang,A New Observable for Measuring CP Property of Top-Higgs Interaction,Chin. Phys. C45(2021) 023117 [2008.13442]

work page arXiv 2021
[42]

Azevedo, R

D. Azevedo, R. Capucha, E. Gouveia, A. Onofre and R. Santos,Light Higgs searches inttϕ production at the LHC,JHEP04(2021) 077 [2012.10730]

work page arXiv 2021
[43]

Azevedo, R

D. Azevedo, R. Capucha, A. Onofre and R. Santos,Scalar mass dependence of angular variables int tϕproduction,JHEP06(2020) 155 [2003.09043]

work page arXiv 2020
[44]

Antusch, O

S. Antusch, O. Fischer, A. Hammad and C. Scherb,Testing CP Properties of Extra Higgs States at the HL-LHC,JHEP03(2021) 200 [2011.10388]

work page arXiv 2021
[45]

Kanemura, M

S. Kanemura, M. Kubota and K. Yagyu,Testing aligned CP-violating Higgs sector at future lepton colliders,JHEP04(2021) 144 [2101.03702]

work page arXiv 2021
[46]

Low, N.R

I. Low, N.R. Shah and X.-P. Wang,Higgs alignment and novel CP-violating observables in two-Higgs-doublet models,Phys. Rev. D105(2022) 035009 [2012.00773]

work page arXiv 2022
[47]

Enomoto, S

K. Enomoto, S. Kanemura and Y. Mura,Electroweak baryogenesis in aligned two Higgs doublet models,JHEP01(2022) 104 [2111.13079]. – 18 –

work page arXiv 2022
[48]

Enomoto, S

K. Enomoto, S. Kanemura and Y. Mura,New benchmark scenarios of electroweak baryogenesis in aligned two Higgs double models,JHEP09(2022) 121 [2207.00060]

work page arXiv 2022
[49]

J. Liu, Y. Nakai, Y. Shigekami and M. Song,Probing CP violation in dark sector through the electron electric dipole moment,JHEP02(2024) 082 [2312.03340]

work page arXiv 2024
[50]

Cheung, Y.-n

K. Cheung, Y.-n. Mao, S. Moretti and R. Zhang,Testing CP-violation in a heavy Higgs sector at CLIC,Eur. Phys. J. C85(2025) 700 [2304.04390]

work page arXiv 2025
[51]

W.-S. Hou, G. Kumar and S. Teunissen,Discovery prospects for electron and neutron electric dipole moments in the general two Higgs doublet model,Phys. Rev. D109(2024) L011703 [2308.04841]

work page arXiv 2024
[52]

R. Boto, L. Lourenco, J.C. Romão and J.P. Silva,Large pseudoscalar Yukawa couplings in the complex 3HDM,JHEP11(2024) 106 [2407.19856]

work page arXiv 2024
[53]

Biekötter, D

T. Biekötter, D. Fontes, M. Mühlleitner, J.C. Romão, R. Santos and J.a.P. Silva,Impact of new experimental data on the C2HDM: the strong interdependence between LHC Higgs data and the electron EDM,JHEP05(2024) 127 [2403.02425]

work page arXiv 2024
[54]

Enomoto, S

K. Enomoto, S. Kanemura and S. Taniguchi,The electric dipole moment in a model for neutrino mass, dark matter and baryon asymmetry of the Universe,JHEP06(2025) 036 [2403.13613]

work page arXiv 2025
[55]

M. Aiko, M. Endo, S. Kanemura and Y. Mura,Electroweak baryogenesis in 2HDM without EDM cancellation,JHEP07(2025) 236 [2504.07705]

work page arXiv 2025
[56]

Dávila, A

J.M. Dávila, A. Karan, E. Passemar, A. Pich and L. Vale Silva,The Electric Dipole Moment of the electron in the decoupling limit of the aligned two-Higgs doublet model, JHEP10(2025) 053 [2504.16700]

work page arXiv 2025
[57]

Boto, J.A.C

R. Boto, J.A.C. Matos, J.C. Romão and J.P. Silva,Surveying the complex three Higgs doublet model with Machine Learning,2510.02445. [65]ATLAScollaboration,Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,Phys. Lett. B716(2012) 1 [1207.7214]. [66]CMScollaboration,Observation of a New Boson at ...

work page arXiv 2012
[58]

Schmidt and M.E

C.R. Schmidt and M.E. Peskin,A Probe of CP violation in top quark pair production at hadron supercolliders,Phys. Rev. Lett.69(1992) 410

work page 1992
[59]

Angular Correlations in Top Quark Pair Production and Decay at Hadron Colliders

G. Mahlon and S.J. Parke,Angular correlations in top quark pair production and decay at hadron colliders,Phys. Rev. D53(1996) 4886 [hep-ph/9512264]

work page internal anchor Pith review Pith/arXiv arXiv 1996
[60]

Probing the CP nature of the Higgs bosons by top-pair production at photon linear colliders

E. Asakawa and K. Hagiwara,Probing the CP nature of the Higgs bosons by t anti-t production at photon linear colliders,Eur. Phys. J. C31(2003) 351 [hep-ph/0305323]

work page internal anchor Pith review Pith/arXiv arXiv 2003
[61]

Determining the CP properties of the Higgs boson

P.S. Bhupal Dev, A. Djouadi, R.M. Godbole, M.M. Muhlleitner and S.D. Rindani, Determining the CP properties of the Higgs boson,Phys. Rev. Lett.100(2008) 051801 [0707.2878]. – 19 –

work page internal anchor Pith review Pith/arXiv arXiv 2008
[62]

Probing Higgs Boson $CP$ Properties with $t\bar{t}H$ at the LHC and the 100 TeV $pp$ Collider

X.-G. He, G.-N. Li and Y.-J. Zheng,Probing Higgs bosonCPProperties witht¯tHat the LHC and the 100 TeVppcollider,Int. J. Mod. Phys. A30(2015) 1550156 [1501.00012]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[63]

Lab-frame observables for probing the top-Higgs interaction

F. Boudjema, R.M. Godbole, D. Guadagnoli and K.A. Mohan,Lab-frame observables for probing the top-Higgs interaction,Phys. Rev.D92(2015) 015019 [1501.03157]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[64]

Boosting the Direct CP Measurement of the Higgs-Top Coupling

M.R. Buckley and D. Goncalves,Boosting the Direct CP Measurement of the Higgs-Top Coupling,Phys. Rev. Lett.116(2016) 091801 [1507.07926]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[65]

Probing CP violation in $e^{+}e^{-}$ production of the Higgs boson and toponia

K. Hagiwara, K. Ma and H. Yokoya,Probing CP violation ine+e− production of the Higgs boson and toponia,JHEP06(2016) 048 [1602.00684]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[66]

Probing the CP nature of the Higgs coupling in $t{\bar t}h$ events at the LHC

S. Amor Dos Santos et al.,Probing the CP nature of the Higgs coupling int¯thevents at the LHC,Phys. Rev. D96(2017) 013004 [1704.03565]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[67]

CP tests of Higgs couplings in $t\bar{t}h$ semileptonic events at the LHC

D. Azevedo, A. Onofre, F. Filthaut and R. Goncalo,CP tests of Higgs couplings int¯th semileptonic events at the LHC,Phys. Rev. D98(2018) 033004 [1711.05292]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[68]

CP-violating top quark couplings at future linear $e^+e^-$ colliders

W. Bernreuther, L. Chen, I. Garc´ia, M. Perell´o, R. Poeschl, F. Richard et al.,CP-violating top quark couplings at future lineare+e− colliders,Eur. Phys. J. C78(2018) 155 [1710.06737]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[69]

Probing the CP properties of top Yukawa coupling at an $e^+e^-$ collider

K. Hagiwara, H. Yokoya and Y.-J. Zheng,Probing the CP properties of top Yukawa coupling at ane+e− collider,JHEP02(2018) 180 [1712.09953]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[70]

Ma,EnhancingCPMeasurement of the Yukawa Interactions of Top-Quark ate −e+ Collider,Phys

K. Ma,EnhancingCPMeasurement of the Yukawa Interactions of Top-Quark ate −e+ Collider,Phys. Lett. B797(2019) 134928 [1809.07127]

work page arXiv 2019
[71]

Higgs Physics at the HL-LHC and HE-LHC

M. Cepeda et al.,Report from Working Group 2: Higgs Physics at the HL-LHC and HE-LHC,CERN Yellow Rep. Monogr.7(2019) 221 [1902.00134]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[72]

Faroughy, J.F

D.A. Faroughy, J.F. Kamenik, N. Koˇsnik and A. Smolkoviˇc,Probing theCPnature of the top quark Yukawa at hadron colliders,JHEP02(2020) 085 [1909.00007]

work page arXiv 2020
[73]

Barger, K

V. Barger, K. Hagiwara and Y.-J. Zheng,CP-violating top-Higgs coupling in SMEFT,Phys. Lett. B850(2024) 138547 [2310.10852]

work page arXiv 2024
[74]

Cassidy, Z

M.E. Cassidy, Z. Dong, K. Kong, I.M. Lewis, Y. Zhang and Y.-J. Zheng,Probing the CP structure of the top quark Yukawa at the future muon collider,JHEP05(2024) 176 [2311.07645]

work page arXiv 2024
[75]

Esmail, A

W. Esmail, A. Hammad, A. Jueid and S. Moretti,Boosting probes of CP violation in the top Yukawa coupling with Deep Learning,2405.16499

work page arXiv
[76]

Hammad and A

A. Hammad and A. Jueid,Progress inCPviolating top-Higgs coupling at the LHC with Machine Learning,2504.11791

work page arXiv
[77]

Probing the CP nature of the Higgs boson at linear colliders with tau spin correlations; the case of mixed scalar--pseudoscalar couplings

K. Desch, A. Imhof, Z. Was and M. Worek,Probing the CP nature of the Higgs boson at linear colliders with tau spin correlations: The Case of mixed scalar - pseudoscalar couplings,Phys. Lett. B579(2004) 157 [hep-ph/0307331]

work page internal anchor Pith review Pith/arXiv arXiv 2004
[78]

Measuring CP Violation in $h \to \tau^+ \tau^-$ at Colliders

R. Harnik, A. Martin, T. Okui, R. Primulando and F. Yu,Measuring CP Violation in h→τ +τ − at Colliders,Phys. Rev. D88(2013) 076009 [1308.1094]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[79]

Higgs CP properties using the tau decay modes at the ILC

S. Berge, W. Bernreuther and H. Spiesberger,Higgs CP properties using theτdecay modes at the ILC,Phys. Lett. B727(2013) 488 [1308.2674]. – 20 –

work page internal anchor Pith review Pith/arXiv arXiv 2013
[80]

Determination of the Higgs CP mixing angle in the tau decay channels at the LHC including the Drell-Yan background

S. Berge, W. Bernreuther and S. Kirchner,Determination of the Higgs CP-mixing angle in the tau decay channels at the LHC including the Drell–Yan background,Eur. Phys. J. C74 (2014) 3164 [1408.0798]

work page internal anchor Pith review Pith/arXiv arXiv 2014

Showing first 80 references.