pith. sign in

arxiv: 2410.17313 · v4 · submitted 2024-10-22 · ✦ hep-ph

Electron EDM and Gamma(μ to e γ) in the 2HDM

Wolfgang Altmannshofer , Beno\^it Assi , Joachim Brod , Nick Hamer , J. Julio , Patipan Uttayarat , Daniil Volkov This is my paper

Pith reviewed 2026-05-23 18:57 UTC · model grok-4.3

classification ✦ hep-ph
keywords two Higgs doublet modelelectron electric dipole momentlepton flavor violationmu to e gammatwo-loop calculationCP violationtau decays
0
0 comments X

The pith

The unconstrained two-Higgs-doublet model receives its first complete two-loop calculation of the electron electric dipole moment and lepton-flavor-violating decay rates.

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

This paper delivers the first full two-loop results for the electron's electric dipole moment and the branching fractions of mu to e gamma and tau to lepton gamma decays inside the most general two-Higgs doublet model. The authors incorporate every possible Yukawa coupling between the Higgs fields and the standard model fermions up to quadratic order together with arbitrary phases in the scalar potential. They supply a public Python package that evaluates the new expressions. These observables are sensitive probes of CP violation and lepton flavor violation that current and future experiments can measure to high precision. The work therefore supplies the necessary theoretical tools to translate experimental limits into constraints on the parameters of the two-Higgs-doublet model.

Core claim

We present the first complete two-loop calculation of the electric dipole moment of the electron, as well as the rates of the lepton-flavor violating decays μ → e + γ and τ → e/μ + γ, in the unconstrained two-Higgs doublet model. We include the most general Yukawa interactions of the Higgs doublets with the Standard Model fermions up to quadratic order, and allow for generic phases in the Higgs potential. A python implementation of our results is provided via a public git repository.

What carries the argument

Two-loop Feynman diagrams generated by the most general Yukawa interactions of the two Higgs doublets with SM fermions up to quadratic order together with generic phases in the Higgs potential.

If this is right

  • Predictions for the electron EDM can now be compared directly with experimental bounds without missing higher-order terms.
  • The rates for μ → eγ and τ → ℓγ receive both one-loop and two-loop contributions that must be included simultaneously.
  • The parameter space of the general 2HDM can be scanned for consistency with all current EDM and LFV data using the supplied code.
  • Future improvements in experimental sensitivity will directly test the two-loop predictions derived here.

Where Pith is reading between the lines

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

  • The same computational framework could be applied to other precision observables such as the muon anomalous magnetic moment.
  • Regions of parameter space that survive current bounds may become accessible to next-generation EDM searches.
  • The results highlight the importance of including two-loop effects when deriving limits on CP-violating phases in extended Higgs sectors.

Load-bearing premise

The most general Yukawa interactions of the Higgs doublets with SM fermions up to quadratic order together with generic phases in the Higgs potential fully capture the relevant physics at two-loop order.

What would settle it

An independent two-loop calculation that yields different numerical values for the electron EDM in a benchmark point of the general 2HDM would falsify the completeness of this result.

Figures

Figures reproduced from arXiv: 2410.17313 by Beno\^it Assi, Daniil Volkov, J. Julio, Joachim Brod, Nick Hamer, Patipan Uttayarat, Wolfgang Altmannshofer.

Figure 1
Figure 1. Figure 1: One-loop contributions to the EDM and anomalous magnetic moment of the electron (left panel), and to µ → eγ (center and right panels). Solid lines denote charged leptons (labelled by ℓ = e, µ, τ ) and the corresponding neutrinos, and dashed lines denote Higgs bosons (labelled by hk and H±). Diagrams with charged Higgs bosons do not contribute to the electron EDM at one loop. servables are of the order of t… view at source ↗
Figure 2
Figure 2. Figure 2: Representative two-loop diagrams contributing to the electron EDM. where here and below we define the mass ratios xa b = M2 a /M2 b . This result is obtained by per￾forming the matching to leading-logarithmic and next-to-leading logarithmic order, expanding up to second order in the external momenta, but keeping only a linear power in the electron mass. The Dirac equation has been used to eliminate contrib… view at source ↗
Figure 3
Figure 3. Figure 3: Representative two-loop diagrams contributing to the electron EDM with vertices arising from the Higgs potential. Here, ℓ denotes either an electron, e, or an electron neutrino, νe. f8e(x, y) = log2 (x) x 3y(3 − y) + 3x 2y 2 − x(3y 2 + 4y + 1) + y 2 + y 2x 3 + log(x) log(y) x 3y(y 2 − 4y + 3) − 3x 2y 2 (y − 1) + xy2 (3y + 1) − y 3 2x 3(y − 1) + log(x) y − xy − x x 2 + log(y) x 2 (1 + 7y − 2y 2 ) + xy(4y + … view at source ↗
Figure 4
Figure 4. Figure 4: Counterterm diagrams that contribute to the electron EDM in the HV scheme. hk , H± γ, Z, W± f ′ i fi γ, Z, W± hk , H± γ f ′ i fi [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Counterterm insertions whose divergent parts contribute to the electron EDM in the HV scheme. diagrams is needed.6 In these calculations it is of crucial importance to keep all “evanescent” contributions (i.e., terms of order ϵ as well as terms proportional to components of momenta in the “parallel space”, µ > 3) in intermediate stages of the calculation. After inclusion of all these terms we recover the r… view at source ↗
read the original abstract

We present the first complete two-loop calculation of the electric dipole moment of the electron, as well as the rates of the lepton-flavor violating decays $\mu \to e + \gamma$ and $\tau \to e/\mu + \gamma$, in the unconstrained two-Higgs doublet model. We include the most general Yukawa interactions of the Higgs doublets with the Standard Model fermions up to quadratic order, and allow for generic phases in the Higgs potential. A python implementation of our results is provided via a public git repository.

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

0 major / 2 minor

Summary. The manuscript claims to present the first complete two-loop calculation of the electron electric dipole moment together with the rates for the lepton-flavor-violating decays μ → eγ and τ → e/μγ in the unconstrained two-Higgs-doublet model. The calculation incorporates the most general Yukawa interactions of the two Higgs doublets with Standard Model fermions (up to quadratic order) and generic CP-violating phases in the Higgs potential. Analytic results are implemented in a publicly released Python package.

Significance. If the two-loop computation is complete and correct, the work supplies a missing ingredient for precision phenomenology in the general 2HDM: explicit, diagram-by-diagram results for EDM and LFV observables that can be used to constrain CP phases and flavor-violating Yukawa matrices. The public code release is a concrete strength that permits direct verification and reuse, raising the practical impact of the results beyond a purely analytic paper.

minor comments (2)
  1. The title refers only to the electron EDM and Γ(μ → eγ), yet the abstract and the stated scope also include τ → e/μγ rates; a modest title adjustment would improve accuracy and discoverability.
  2. The abstract states that the Python implementation is provided via a public git repository, but the manuscript does not specify the repository URL or commit hash; adding this information in the text or a footnote would facilitate immediate access.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; direct perturbative computation

full rationale

The manuscript performs an explicit two-loop calculation of the electron EDM and LFV decay rates in the general 2HDM, including all relevant diagrams, counterterms, and the most general CP-violating Yukawa matrices. No parameters are fitted to a data subset and then relabeled as predictions; the analytic results are derived from the Lagrangian and supplied via public code for external verification. No self-citation chains, uniqueness theorems, or ansatze are invoked to force the central result. The derivation is self-contained against the model Lagrangian and standard renormalization procedures.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The computation is performed inside the established 2HDM framework; no new particles or forces are introduced and no parameters are fitted to data within the paper itself.

axioms (2)
  • domain assumption Two-Higgs-doublet model with the most general Yukawa interactions of the Higgs doublets with the Standard Model fermions up to quadratic order
    Explicitly stated as the setting for the calculation in the abstract.
  • domain assumption Generic phases allowed in the Higgs potential
    Included in the model definition given in the abstract.

pith-pipeline@v0.9.0 · 5638 in / 1288 out tokens · 30725 ms · 2026-05-23T18:57:31.162966+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

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

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.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Towards a Unified Framework for Pseudo-Nambu-Goldstone Dark Matter and Electroweak Baryogenesis

    hep-ph 2025-09 unverdicted novelty 6.0

    The cS2HDM unifies a pseudo-Nambu-Goldstone dark matter candidate with electroweak baryogenesis in a two-Higgs-doublet plus complex singlet setup, featuring naturally suppressed DM-nucleon scattering and CP-violating ...

  2. Novel probes for electron-muon flavor violation from exotic Higgs decays

    hep-ph 2025-08 unverdicted novelty 6.0

    Novel multilepton signatures from Higgs decays to a light pseudoscalar decaying to e-mu pairs in type-III 2HDM can set stronger limits on LFV couplings than low-energy experiments.

Reference graph

Works this paper leans on

44 extracted references · 44 canonical work pages · cited by 2 Pith papers · 17 internal anchors

  1. [1]

    CP violation and baryogenesis

    W. Bernreuther,CP violation and baryogenesis,Lect. Notes Phys.591(2002) 237–293, [hep-ph/0205279]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  2. [2]

    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

  3. [3]

    V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov,On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe,Phys. Lett. B155(1985) 36

    work page 1985

  4. [4]

    N. G. Deshpande and E. Ma,Pattern of Symmetry Breaking with Two Higgs Doublets, Phys. Rev. D18(1978) 2574

    work page 1978

  5. [5]

    S. J. Huber, M. Pospelov and A. Ritz,Electric dipole moment constraints on minimal electroweak baryogenesis,Phys. Rev. D75(2007) 036006, [hep-ph/0610003]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  6. [6]

    Electroweak Baryogenesis and the Standard Model Effective Field Theory

    J. de Vries, M. Postma, J. van de Vis and G. White,Electroweak Baryogenesis and the Standard Model Effective Field Theory,JHEP01(2018) 089, [1710.04061]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  7. [7]

    De Vries, M

    J. De Vries, M. Postma and J. van de Vis,The role of leptons in electroweak baryogenesis,JHEP04(2019) 024, [1811.11104]. 6We checked explicitly that no finite contribution to the counterterm insertion leads to a non-vanishing con- tribution to the results in the limitd→4. 19

    work page arXiv 2019

  8. [8]

    Fuchs, M

    E. Fuchs, M. Losada, Y. Nir and Y. Viernik,CPviolation fromτ,tandbdimension-6 Yukawa couplings - interplay of baryogenesis, EDM and Higgs physics,JHEP05(2020) 056, [2003.00099]

    work page arXiv 2020

  9. [9]

    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) 21–74, [1303.2371]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  10. [10]

    Altmannshofer, S

    W. Altmannshofer, S. Gori, N. Hamer and H. H. Patel,Electron EDM in the complex two-Higgs doublet model,Phys. Rev. D102(2020) 115042, [2009.01258]

    work page arXiv 2020

  11. [11]

    T. S. Roussy et al.,An improved bound on the electron’s electric dipole moment,Science 381(2023) adg4084, [2212.11841]. [12]MEGcollaboration, A. M. Baldini et al.,Search for the lepton flavour violating decay µ+ →e +γwith the full dataset of the MEG experiment,Eur. Phys. J. C76(2016) 434, [1605.05081]. [13]MEG IIcollaboration, K. Afanaciev et al.,A search...

    work page arXiv 2023

  12. [12]

    Basis-independent methods for the two-Higgs-doublet model

    S. Davidson and H. E. Haber,Basis-independent methods for the two-Higgs-doublet model,Phys. Rev.D72(2005) 035004, [hep-ph/0504050]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  13. [13]

    H. E. Haber and D. O’Neil,Basis-independent methods for the two-Higgs-doublet model. II. The Significance of tanβ,Phys. Rev. D74(2006) 015018, [hep-ph/0602242]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  14. [14]

    R. Boto, T. V. Fernandes, H. E. Haber, J. C. Rom˜ ao and J. a. P. Silva, Basis-independent treatment of the complex 2HDM,Phys. Rev. D101(2020) 055023, [2001.01430]

    work page arXiv 2020

  15. [15]

    S. L. Glashow and S. Weinberg,Natural Conservation Laws for Neutral Currents,Phys. Rev. D15(1977) 1958

    work page 1977

  16. [16]

    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) 119–169, [hep-ph/0504231]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  17. [17]

    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

  18. [18]

    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

  19. [19]

    Y. Ema, T. Gao and M. Pospelov,Standard Model Prediction for Paramagnetic Electric Dipole Moments,Phys. Rev. Lett.129(2022) 231801, [2202.10524]. 20

    work page arXiv 2022

  20. [20]

    Mu to e gamma in the 2 Higgs Doublet Model: an exercise in EFT

    S. Davidson,µ→eγin the 2HDM: an exercise in EFT,Eur. Phys. J. C76(2016) 258, [1601.01949]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  21. [21]

    Panico, A

    G. Panico, A. Pomarol and M. Riembau,EFT approach to the electron Electric Dipole Moment at the two-loop level,JHEP04(2019) 090, [1810.09413]

    work page arXiv 2019

  22. [22]

    J. Brod, J. M. Cornell, D. Skodras and E. Stamou,Global constraints on Yukawa operators in the standard model effective theory,JHEP08(2022) 294, [2203.03736]

    work page arXiv 2022

  23. [23]

    J. Brod, Z. Polonsky and E. Stamou,A precise electron EDM constraint on CP-odd heavy-quark Yukawas,JHEP06(2024) 091, [2306.12478]

    work page arXiv 2024

  24. [24]

    J. Brod, L. H¨ udepohl, E. Stamou and T. Steudtner,MaRTIn – Manual for the ”Massive Recursive Tensor Integration”,Comput. Phys. Commun.306(2025) 109372, [2401.04033]

    work page arXiv 2025

  25. [25]

    J. A. M. Vermaseren,New features of FORM,math-ph/0010025

    work page internal anchor Pith review Pith/arXiv arXiv

  26. [26]

    A. I. Davydychev and J. Tausk,Two loop selfenergy diagrams with different masses and the momentum expansion,Nucl.Phys.B397(1993) 123–142

    work page 1993

  27. [27]

    Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]

    C. Bobeth, M. Misiak and J. Urban,Photonic penguins at two loops and m(t) dependence of BR[B→X(s)ℓ +ℓ−],Nucl.Phys.B574(2000) 291–330, [hep-ph/9910220]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  28. [28]

    Nogueira,Automatic Feynman graph generation,J

    P. Nogueira,Automatic Feynman graph generation,J. Comput. Phys.105(1993) 279–289

    work page 1993

  29. [29]

    FeynRules 2.0 - A complete toolbox for tree-level phenomenology

    A. Alloul, N. D. Christensen, C. Degrande, C. Duhr and B. Fuks,FeynRules 2.0 - A complete toolbox for tree-level phenomenology,Comput. Phys. Commun.185(2014) 2250–2300, [1310.1921]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  30. [30]

    Brod and M

    J. Brod and M. Gorbahn,TheZPenguin in Generic Extensions of the Standard Model, JHEP09(2019) 027, [1903.05116]

    work page arXiv 2019

  31. [31]

    Application of the Background-Field Method to the electroweak Standard Model

    A. Denner, G. Weiglein and S. Dittmaier,Application of the background field method to the electroweak standard model,Nucl. Phys. B440(1995) 95–128, [hep-ph/9410338]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  32. [32]

    Techniques for the calculation of electroweak radiative corrections at the one-loop level and results for W-physics at LEP200

    A. Denner,Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200,Fortsch. Phys.41(1993) 307–420, [0709.1075]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  33. [33]

    Weinberg,Larger Higgs Exchange Terms in the Neutron Electric Dipole Moment, Phys

    S. Weinberg,Larger Higgs Exchange Terms in the Neutron Electric Dipole Moment, Phys. Rev. Lett.63(1989) 2333

    work page 1989

  34. [34]

    D. A. Dicus,Neutron Electric Dipole Moment From Charged Higgs Exchange,Phys. Rev. D41(1990) 999

    work page 1990

  35. [35]

    S. M. Barr and A. Zee,Electric Dipole Moment of the Electron and of the Neutron, Phys. Rev. Lett.65(1990) 21–24

    work page 1990

  36. [36]

    ’t Hooft and M

    G. ’t Hooft and M. J. G. Veltman,Regularization and Renormalization of Gauge Fields, Nucl. Phys.B44(1972) 189–213. 21

    work page 1972

  37. [37]

    Breitenlohner and D

    P. Breitenlohner and D. Maison,Dimensional Renormalization and the Action Principle, Commun. Math. Phys.52(1977) 11–38

    work page 1977

  38. [38]

    J. C. Collins,Renormalization, vol. 26 ofCambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge, 1986, 10.1017/CBO9780511622656

    work page doi:10.1017/cbo9780511622656 1986

  39. [39]

    J. D. Bjorken and S. Weinberg,A Mechanism for Nonconservation of Muon Number, Phys. Rev. Lett.38(1977) 622

    work page 1977

  40. [40]

    Lepton-Flavor Violation via Right-Handed Neutrino Yukawa Couplings in Supersymmetric Standard Model

    J. Hisano, T. Moroi, K. Tobe and M. Yamaguchi,Lepton flavor violation via right-handed neutrino Yukawa couplings in supersymmetric standard model,Phys. Rev. D53(1996) 2442–2459, [hep-ph/9510309]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  41. [41]

    Two--loop Contributions of Flavor Changing Neutral Higgs Boson to $\mu \to e\gamma$

    D. Chang, W. S. Hou and W.-Y. Keung,Two loop contributions of flavor changing neutral Higgs bosons toµ→eγ,Phys. Rev. D48(1993) 217–224, [hep-ph/9302267]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  42. [42]

    Leigh, S

    R. Leigh, S. Paban and R. Xu,Electric dipole moment of electron,Nucl. Phys. B352 (1991) 45–58

    work page 1991

  43. [43]

    JaxoDraw: A graphical user interface for drawing Feynman diagrams

    D. Binosi and L. Theussl,JaxoDraw: A Graphical user interface for drawing Feynman diagrams,Comput. Phys. Commun.161(2004) 76–86, [hep-ph/0309015]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  44. [44]

    J. A. M. Vermaseren,Axodraw,Comput. Phys. Commun.83(1994) 45–58. 22

    work page 1994