pith. sign in

arxiv: 2606.23580 · v1 · pith:JZJZR4J6new · submitted 2026-06-22 · ✦ hep-ph · hep-ex· hep-th· nucl-ex· nucl-th

Quantification of the Flavor Diagonal Hadronic CP Violation

Nodoka Yamanaka This is my paper

Pith reviewed 2026-06-26 08:07 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-thnucl-exnucl-th
keywords CP violationelectric dipole momentsstrong CP problemhadronic matrix elementslattice QCDneutron opticsbeta decay
0
0 comments X

The pith

Recent progress allows quantification of flavor-diagonal hadronic CP violation contributing to electric dipole moments and other observables.

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

This review examines flavor diagonal CP violation in elementary particle physics and its effects on atomic, nuclear, and nucleon electric dipole moments, T-violating neutron optics, and beta decay angular correlations. It highlights the importance of this CP violation in searches for new physics beyond the standard model. The paper details recent advances in calculating the relevant hadronic matrix elements, enabling better quantification of these contributions. Additionally, it discusses an approach to resolving the strong CP problem that avoids introducing extra interactions or fields.

Core claim

The paper establishes that recent computational and theoretical progress now permits the quantification of hadron-level CP violation effects that feed into experimental observables such as electric dipole moments, thereby tightening constraints on physics beyond the Standard Model and offering a path to address the strong CP problem through existing fields alone.

What carries the argument

Flavor-diagonal hadronic matrix elements of effective CP-violating operators, computed using lattice QCD or other first-principles methods.

Load-bearing premise

The review assumes that the flavor-diagonal hadronic matrix elements and effective operators can be reliably computed or parameterized from first principles or lattice QCD without introducing uncontrolled systematic errors that would invalidate the connection to experimental observables.

What would settle it

A lattice QCD calculation of a key hadronic matrix element that deviates significantly from the parameterized value used in the review, or an experimental measurement of an EDM that cannot be explained by the quantified contributions plus known physics.

Figures

Figures reproduced from arXiv: 2606.23580 by Nodoka Yamanaka.

Figure 1
Figure 1. Figure 1: Leading order χPT contribution to the nucleon EDM (a) and to the one-pion exchange CP-odd nuclear force (b). The yellow blobs denote the CP-odd pion-nucleon interaction (7). Actually, ¯g (1) πNN contributes at the leading order to the CP-odd nuclear force through the diagram shown in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
read the original abstract

The flavor diagonal CP violation of elementary particle physics contributes to the atomic, nuclear, and nucleon electric dipole moments (EDMs), T-violating neutron optics, and to the angular correlations of beta decay. In this contribution, we review the basics and the importance of CP violation in the search for new physics beyond the standard model, the recent progress in the quantification of the hadron level CP violation contributing to the aforementioned observables, and finally the current attempt to solve the strong CP problem without additional interactions and fields.

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 reviews the role of flavor-diagonal hadronic CP violation in contributing to atomic, nuclear, and nucleon electric dipole moments (EDMs), T-violating neutron optics, and beta-decay angular correlations. It covers the basics and importance of CP violation for beyond-Standard-Model searches, recent progress in quantifying the relevant hadron-level matrix elements and effective operators, and an attempt to address the strong CP problem without introducing additional interactions or fields.

Significance. If the quantifications of hadronic CP-violating effects hold, the review would provide useful benchmarks for connecting lattice QCD or other non-perturbative methods to experimental observables in EDM and beta-decay searches. The proposed minimal solution to the strong CP problem, if internally consistent and falsifiable, would be of interest to the field, though its viability rests on the reliability of the hadronic matrix elements discussed.

minor comments (2)
  1. The abstract states that the work reviews 'recent progress in the quantification' but does not specify which lattice QCD calculations or effective-field-theory frameworks are covered in the main text; adding a brief table or section summarizing the key references and their quoted uncertainties would improve clarity for readers.
  2. The claim of solving the strong CP problem 'without additional interactions and fields' is presented as a central element; the manuscript should explicitly state in the introduction or conclusion whether this approach reproduces the observed neutron EDM bound or requires further assumptions on the theta term.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive recommendation of minor revision. The referee's summary correctly identifies the scope of the review, including the quantification of flavor-diagonal hadronic CP violation effects and the discussion of a minimal approach to the strong CP problem. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

Review summary with no derivations or predictions exhibits no circularity

full rationale

The document is explicitly a review article that summarizes existing literature on flavor-diagonal hadronic CP violation, EDMs, and the strong CP problem. No original equations, derivations, fitted parameters, or first-principles predictions are presented in the provided abstract or text. Consequently there are no load-bearing steps that could reduce by construction to inputs, self-citations, or ansatzes. The work is self-contained as an overview of external results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only access prevents enumeration of specific free parameters or invented entities; the paper operates within standard model effective field theory and lattice QCD assumptions typical for hep-ph CP-violation studies.

pith-pipeline@v0.9.1-grok · 5604 in / 1063 out tokens · 19835 ms · 2026-06-26T08:07:51.002940+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

88 extracted references · 31 linked inside Pith

  1. [1]

    L. D. Landau, Nucl. Phys. 3, 127 (1957)

    1957

  2. [2]

    J. H. Christenson et al., Phys. Rev. Lett. 13, 138-140 (1964)

    1964

  3. [3]

    A. D. Sakharov, Pisma Zh. Eksp. Teor. Fiz. 5, 32-35 (1967)

    1967

  4. [4]

    Graner et al

    B. Graner et al. , Phys. Rev. Lett. 116, 161601 (2016) [erratum: Phys. Rev. Lett. 119, 119901 (2017)] [arXiv:1601.04339 [physics.atom-ph]]

    Pith/arXiv arXiv 2016

  5. [5]

    Abel et al

    C. Abel et al. [nEDM Collaboration], Phys. Rev. Lett. 124, 081803 (2020) [arXiv:2001.11966 [hep-ex]]

    arXiv 2020

  6. [6]

    T. S. Roussy et al., Science 381 (2023), 46 [arXiv:2212.11841 [physics.atom-ph]]

    arXiv 2023

  7. [7]

    Analysis of the Electric Dipole Moment in t he R-parity Violating Supersymmetric Standard Model,

    N. Y amanaka, “Analysis of the Electric Dipole Moment in t he R-parity Violating Supersymmetric Standard Model,” Springer, Berlin Germany (2014)

    2014

  8. [8]

    Y amanaka et al., Eur

    N. Y amanaka et al., Eur. Phys. J. A 53, no.3, 54 (2017) [arXiv:1703.01570 [hep-ph]]

    Pith/arXiv arXiv 2017

  9. [9]

    Chupp et al., Rev

    T. Chupp et al., Rev. Mod. Phys. 91, no.1, 015001 (2019) [arXiv:1710.02504 [physics.atom-ph ]]

    Pith/arXiv arXiv 2019

  10. [10]

    Nakabe et al., [arXiv:2509.06542 [nucl-ex]]

    R. Nakabe et al., [arXiv:2509.06542 [nucl-ex]]

    Pith/arXiv arXiv

  11. [11]

    V . P . Gudkov, Phys. Rept.212, 77-105 (1992)

    1992

  12. [12]

    J. D. Bowman and V . Gudkov, Phys. Rev. C 90, no.6, 065503 (2014) [arXiv:1407.7004 [hep-ph]]

    Pith/arXiv arXiv 2014

  13. [13]

    Gudkov and H

    V . Gudkov and H. M. Shimizu, Phys. Rev. C 97, no.6, 065502 (2018) [arXiv:1710.02193 [nucl-th]]

    Pith/arXiv arXiv 2018

  14. [14]

    Huber et al., Phys

    R. Huber et al., Phys. Rev. Lett. 90, 202301 (2003) [arXiv:nucl-ex /0301010 [nucl-ex]]

    2003

  15. [15]

    Soldner et al., Phys

    T. Soldner et al., Phys. Lett. B 581, 49-55 (2004)

    2004

  16. [16]

    H. P . Mumm et al., Phys. Rev. Lett. 107, 102301 (2011) [arXiv:1104.2778 [nucl-ex]]

    Pith/arXiv arXiv 2011

  17. [17]

    Kozela et al., Phys

    A. Kozela et al., Phys. Rev. C 85, 045501 (2012) [arXiv:1111.4695 [nucl-ex]]

    Pith/arXiv arXiv 2012

  18. [18]

    T. E. Chupp et al., Phys. Rev. C 86, 035505 (2012) [arXiv:1205.6588 [nucl-ex]]

    Pith/arXiv arXiv 2012

  19. [19]

    Murata et al., Hyperfine Interact

    J. Murata et al., Hyperfine Interact. 237, no.1, 125 (2016)

    2016

  20. [20]

    Herczeg, Prog

    P . Herczeg, Prog. Part. Nucl. Phys. 46, 413-457 (2001)

    2001

  21. [21]

    Gonz´ alez-Alonso, O

    M. Gonz´ alez-Alonso, O. Naviliat-Cuncic and N. Severi jns, Prog. Part. Nucl. Phys. 104, 165-223 (2019) [arXiv:1803.08732 [hep-ph]]

    Pith/arXiv arXiv 2019

  22. [22]

    Kobayashi and T

    M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652-657 (1973)

    1973

  23. [23]

    B. H. J. McKellar et al., Phys. Lett. B 197, 556-560 (1987)

    1987

  24. [24]

    Buchalla, A

    G. Buchalla, A. J. Buras and M. E. Lautenbacher, Rev. Mod . Phys. 68, 1125-1144 (1996) [arXiv:hep- ph/9512380 [hep-ph]]

    arXiv 1996

  25. [25]

    Y amanaka and E

    N. Y amanaka and E. Hiyama, JHEP 02, 067 (2016) [arXiv:1512.03013 [hep-ph]]

    Pith/arXiv arXiv 2016

  26. [26]

    Y amaguchi and N

    Y . Y amaguchi and N. Y amanaka, Phys. Rev. Lett.125, 241802 (2020) [arXiv:2003.08195 [hep-ph]]

    arXiv 2020

  27. [27]

    Y amaguchi and N

    Y . Y amaguchi and N. Y amanaka, Phys. Rev. D103, no.1, 013001 (2021) [arXiv:2006.00281 [hep-ph]]

    arXiv 2021

  28. [28]

    Jarlskog, Phys

    C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985)

    1985

  29. [29]

    Grzadkowski et al., JHEP 10, 085 (2010) [arXiv:1008.4884 [hep-ph]]

    B. Grzadkowski et al., JHEP 10, 085 (2010) [arXiv:1008.4884 [hep-ph]]

    Pith/arXiv arXiv 2010

  30. [30]

    Isidori, F

    G. Isidori, F. Wilsch and D. Wyler, Rev. Mod. Phys. 96, no.1, 1 (2024) [arXiv:2303.16922 [hep-ph]]

    arXiv 2024

  31. [31]

    R. J. Crewther et al., Phys. Lett. B 88, 123 (1979) [erratum: Phys. Lett. B 91, 487 (1980)]

    1979

  32. [32]

    Mereghetti et al., Phys

    E. Mereghetti et al., Phys. Lett. B 696, 97-102 (2011) [arXiv:1010.4078 [hep-ph]]

    Pith/arXiv arXiv 2011

  33. [33]

    de Vries, E

    J. de Vries, E. Mereghetti and A. Walker-Loud, Phys. Rev . C 92, no.4, 045201 (2015) [arXiv:1506.06247 [nucl-th]]. 7

    Pith/arXiv arXiv 2015

  34. [34]

    de Vries et al., Phys

    J. de Vries et al., Phys. Lett. B 766, 254-262 (2017) [arXiv:1612.01567 [hep-lat]]

    Pith/arXiv arXiv 2017

  35. [35]

    Dobaczewski and J

    J. Dobaczewski and J. Engel, Phys. Rev. Lett. 94, 232502 (2005) [arXiv:nucl-th /0503057 [nucl-th]]

    2005

  36. [36]

    Y amanaka and E

    N. Y amanaka and E. Hiyama, Phys. Rev. C 91, no.5, 054005 (2015) [arXiv:1503.04446 [nucl-th]]

    Pith/arXiv arXiv 2015

  37. [37]

    Y amanaka et al., Phys

    N. Y amanaka et al., Phys. Rev. C 95, no.6, 065503 (2017) [arXiv:1603.03136 [nucl-th]]

    Pith/arXiv arXiv 2017

  38. [38]

    Y amanaka, Int

    N. Y amanaka, Int. J. Mod. Phys. E 26, no.4, 1730002 (2017) [arXiv:1609.04759 [nucl-th]]

    Pith/arXiv arXiv 2017

  39. [39]

    Y amanaka, T

    N. Y amanaka, T. Y amada and Y . Funaki, Phys. Rev. C100, no.5, 055501 (2019) [arXiv:1907.08091 [nucl- th]]

    arXiv 2019

  40. [40]

    Y anase and N

    K. Y anase and N. Shimizu, Phys. Rev. C 102, no.6, 065502 (2020) [arXiv:2006.15142 [nucl-th]]

    arXiv 2020

  41. [41]

    Y anase, Phys

    K. Y anase, Phys. Rev. C 103, no.3, 035501 (2021) [arXiv:2008.03678 [nucl-th]]

    arXiv 2021

  42. [42]

    Froese and P

    P . Froese and P . Navratil, Phys. Rev. C 104, no.2, 025502 (2021) [arXiv:2103.06365 [nucl-th]]

    arXiv 2021

  43. [43]

    Y anase et al., Phys

    K. Y anase et al., Phys. Lett. B 841, 137897 (2023) [arXiv:2210.08498 [nucl-th]]

    arXiv 2023

  44. [44]

    Dutsov et al., Phys

    C. Dutsov et al., Phys. Rev. D 112, no.7, 076031 (2025) [arXiv:2506.13588 [hep-ex]]

    arXiv 2025

  45. [45]

    E. F. Zhou and J. M. Y ao, [arXiv:2511.05984 [nucl-th]]

    arXiv

  46. [46]

    Degrassi et al., JHEP 11, 044 (2005) [arXiv:hep-ph /0510137 [hep-ph]]

    G. Degrassi et al., JHEP 11, 044 (2005) [arXiv:hep-ph /0510137 [hep-ph]]

    2005

  47. [47]

    Hisano, K

    J. Hisano, K. Tsumura and M. J. S. Y ang, Phys. Lett. B 713, 473-480 (2012) [arXiv:1205.2212 [hep-ph]]

    Pith/arXiv arXiv 2012

  48. [48]

    Kley et al., Eur

    J. Kley et al., Eur. Phys. J. C 82, no.10, 926 (2022) [arXiv:2109.15085 [hep-ph]]

    arXiv 2022

  49. [49]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. Lett. 63, 2333 (1989)

    1989

  50. [50]

    Aoki et al

    Y . Aoki et al. [Flavour Lattice Averaging Group (FLAG)], Phys. Rev. D 113, no.1, 014508 (2026) [arXiv:2411.04268 [hep-lat]]

    Pith/arXiv arXiv 2026

  51. [51]

    Y amanaka et al

    N. Y amanaka et al. [JLQCD], Phys. Rev. D 98, no.5, 054516 (2018) [arXiv:1805.10507 [hep-lat]]

    Pith/arXiv arXiv 2018

  52. [52]

    Hasan et al., Phys

    N. Hasan et al., Phys. Rev. D 99, no.11, 114505 (2019) [arXiv:1903.06487 [hep-lat]]

    Pith/arXiv arXiv 2019

  53. [53]

    Harris et al., Phys

    T. Harris et al., Phys. Rev. D 100, no.3, 034513 (2019) [arXiv:1905.01291 [hep-lat]]

    arXiv 2019

  54. [54]

    Horkel et al

    D. Horkel et al. [χQCD], Phys. Rev. D 101, no.9, 094501 (2020) [arXiv:2002.06699 [hep-lat]]

    arXiv 2020

  55. [55]

    Park et al

    S. Park et al. [NME], Phys. Rev. D 105, no.5, 054505 (2022) [arXiv:2103.05599 [hep-lat]]

    arXiv 2022

  56. [56]

    Tsuji et al

    R. Tsuji et al. [P ACS], Phys. Rev. D106, no.9, 094505 (2022) [arXiv:2207.11914 [hep-lat]]

    arXiv 2022

  57. [57]

    G. S. Bali et al. [RQCD], Phys. Rev. D 108, no.3, 034512 (2023) [arXiv:2305.04717 [hep-lat]]

    arXiv 2023

  58. [58]

    J. H. Wang et al., [arXiv:2511.02326 [hep-lat]]

    arXiv

  59. [59]

    Y amanaka et al., Phys

    N. Y amanaka et al., Phys. Rev. D 88, 074036 (2013) [arXiv:1307.4208 [hep-ph]]

    Pith/arXiv arXiv 2013

  60. [60]

    Gupta et al., Phys

    R. Gupta et al., Phys. Rev. Lett. 127, no.24, 24 (2021) [arXiv:2105.12095 [hep-lat]]

    arXiv 2021

  61. [61]

    Agadjanov et al., Phys

    A. Agadjanov et al., Phys. Rev. Lett. 131, no.26, 26 (2023) [arXiv:2303.08741 [hep-lat]]

    arXiv 2023

  62. [62]

    Barca, G

    L. Barca, G. Bali and S. Collins, Phys. Rev. D 111, no.3, L031505 (2025) [arXiv:2412.13138 [hep-lat]]

    arXiv 2025

  63. [63]

    Gubler and D

    P . Gubler and D. Satow, Prog. Part. Nucl. Phys. 106, 1-67 (2019) [arXiv:1812.00385 [hep-ph]]

    Pith/arXiv arXiv 2019

  64. [64]

    J. H. Huang, T. T. Sun and H. Chen, Phys. Rev. D 101, no.5, 054007 (2020) [arXiv:1910.08298 [nucl-th]]

    arXiv 2020

  65. [65]

    Friedman and A

    E. Friedman and A. Gal, Phys. Lett. B 792, 340-344 (2019) [arXiv:1901.03130 [nucl-th]]

    Pith/arXiv arXiv 2019

  66. [66]

    B. L. Huang and J. Ou-Y ang, Phys. Rev. D 101, no.5, 056021 (2020) [arXiv:1911.00846 [nucl-th]]

    arXiv 2020

  67. [67]

    Ikeno et al., PTEP 2023, no.3, 033D03 (2023) [arXiv:2204.09211 [nucl-th]]

    N. Ikeno et al., PTEP 2023, no.3, 033D03 (2023) [arXiv:2204.09211 [nucl-th]]

    arXiv 2023

  68. [68]

    Hoferichter et al., Phys

    M. Hoferichter et al., Phys. Lett. B 843, 138001 (2023) [arXiv:2305.07045 [hep-ph]]

    arXiv 2023

  69. [69]

    Y amanaka et al., Phys

    N. Y amanaka et al., Phys. Rev. D 89, no.7, 074017 (2014) [arXiv:1401.2852 [hep-ph]]

    Pith/arXiv arXiv 2014

  70. [70]

    Y anase et al., Phys

    K. Y anase et al., Phys. Rev. D 99, no.7, 075021 (2019) [arXiv:1805.00419 [nucl-th]]

    Pith/arXiv arXiv 2019

  71. [71]

    B. K. Sahoo, N. Y amanaka and K. Y anase, Phys. Rev. A 108, no.4, 042811 (2023) [arXiv:2306.14441 [hep-ph]]

    arXiv 2023

  72. [72]

    D. A. Demir, M. Pospelov and A. Ritz, Phys. Rev. D 67, 015007 (2003) [arXiv:hep-ph/0208257 [hep-ph]]

    Pith/arXiv arXiv 2003

  73. [73]

    Haisch and A

    U. Haisch and A. Hala, JHEP 11, 154 (2019) [arXiv:1909.08955 [hep-ph]]

    arXiv 2019

  74. [74]

    Y amanaka and E

    N. Y amanaka and E. Hiyama, Phys. Rev. D 103, no.3, 035023 (2021) [arXiv:2011.02531 [hep-ph]]

    arXiv 2021

  75. [75]

    Osamura, P

    N. Osamura, P . Gubler and N. Y amanaka, JHEP 06, 072 (2022) [arXiv:2203.06878 [hep-ph]]

    arXiv 2022

  76. [76]

    Y amanaka and M

    N. Y amanaka and M. Oka, Phys. Rev. D 106, no.7, 075021 (2022) [arXiv:2208.03920 [nucl-th]]

    arXiv 2022

  77. [77]

    H. An, X. Ji and F. Xu, JHEP 02, 043 (2010) [arXiv:0908.2420 [hep-ph]]

    Pith/arXiv arXiv 2010

  78. [78]

    W . Y . Aiet al., Phys. Lett. B 822 (2021), 136616 [arXiv:2001.07152 [hep-th]]

    arXiv 2021

  79. [79]

    Nakamura and G

    Y . Nakamura and G. Schierholz, Nucl. Phys. B 986 (2023), 116063 [arXiv:2106.11369 [hep-ph]]

    arXiv 2023

  80. [80]

    Y amanaka, [arXiv:2212.10994 [hep-th]]

    N. Y amanaka, [arXiv:2212.10994 [hep-th]]

    arXiv

Showing first 80 references.