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arxiv: 2605.00989 · v1 · submitted 2026-05-01 · ✦ hep-ph · hep-ex

Recognition: unknown

CP violation in neutral kaon mixing in D⁰rightarrow K_SK_S

Yuval Grossman , Guglielmo Papiri , Stefan Schacht
Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:29 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords CP violationneutral kaon mixingD meson decayscharm sectorweak interactions
0
0 comments X

The pith

Neutral kaon mixing contributes to CP violation in D^0 to K_S K_S only through second-order weak interactions at the 10^{-6} level.

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

The paper examines CP violation induced by neutral kaon mixing in the decay D^0 to two short-lived neutral kaons. It demonstrates that this contribution can only arise when accompanied by second-order weak interactions in the D decay. The authors estimate the size of the effect at roughly 10 to the minus six, which places it well below current experimental reach and below the larger CP violation signals expected from the charm sector itself.

Core claim

The contribution from neutral kaon mixing to CP violation in D^0 → K_S K_S arises only in connection with second-order weak interactions in D decays and is estimated to be at the 10^{-6} level, negligible compared to current experimental sensitivity and to the expected contribution from CP violation in the charm sector.

What carries the argument

The linkage of neutral kaon mixing effects exclusively to second-order weak interactions in D decays, which enforces the suppression.

Load-bearing premise

Neutral kaon mixing effects on the CP asymmetry appear only when second-order weak interactions are present in the D decay.

What would settle it

An experimental measurement of a_CP(D^0 → K_S K_S) significantly exceeding 10^{-6} that cannot be accounted for by charm-sector CP violation.

Figures

Figures reproduced from arXiv: 2605.00989 by Guglielmo Papiri, Stefan Schacht, Yuval Grossman.

Figure 1
Figure 1. Figure 1: Diagrams which contribute to the second order weak interactions for the view at source ↗
read the original abstract

We study CP violation induced by neutral kaon mixing in $a_{CP}(D^0 \rightarrow K_S K_S)$. We show that the contribution from neutral kaon mixing arises only in connection with second-order weak interactions in $D$ decays. We estimate this effect to be at the $10^{-6}$ level, and thus negligible compared to current experimental sensitivity and to the expected contribution from CP violation in the charm sector.

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 studies CP violation induced by neutral kaon mixing in the CP asymmetry a_CP for the decay D^0 → K_S K_S. It demonstrates that this contribution can only arise in association with second-order weak interactions in the D decay and estimates the magnitude of the effect to be at the 10^{-6} level. Consequently, the authors conclude that it is negligible compared to current experimental sensitivity and to the anticipated CP violation from the charm sector.

Significance. Assuming the result is correct, this paper offers an important clarification for experimental studies of CP violation in charm decays. It shows that the neutral kaon mixing effect is suppressed by the second-order nature of the process, leading to a small contribution consistent with the weak interaction hierarchy (G_F^2 |ε| scaling). This helps ensure that observed asymmetries can be attributed to charm CP violation or beyond-Standard-Model effects without contamination from kaon mixing. The derivation is direct and does not rely on additional free parameters.

minor comments (2)
  1. The estimate of 10^{-6} would be strengthened by providing the explicit combination of amplitudes and the numerical value of the kaon CP violation parameter |ε| used in the calculation.
  2. Consider expanding the abstract slightly to include the key argument about second-order weak interactions for better context.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and for the recommendation of minor revision. The referee's summary accurately captures our central result: that the contribution to a_CP(D^0 → K_S K_S) from neutral kaon mixing is suppressed by the requirement of second-order weak interactions in the D decay and is therefore O(10^{-6}). We agree that this clarification is useful for experimental analyses of charm CP violation.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central result follows from the structure of the effective weak Hamiltonian in the Standard Model, where neutral-kaon mixing (a ΔS=2 process) can only enter the D^0 → K_S K_S amplitude via two ΔS=1 vertices plus the mixing insertion, producing an O(G_F^2 |ε|) suppression relative to the leading amplitude. This yields the 10^{-6} estimate directly from known weak-interaction hierarchies and CKM factors without any fitted parameter defined in terms of the target observable, without renaming an empirical pattern, and without load-bearing self-citation. The derivation is therefore self-contained and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; full derivation and parameter choices are not visible. The estimate presumably relies on standard-model weak-interaction amplitudes and known kaon-mixing parameters.

axioms (1)
  • standard math Standard Model weak interactions govern D decays and kaon mixing
    The paper invokes second-order weak processes without deriving them from more fundamental principles.

pith-pipeline@v0.9.0 · 5367 in / 1126 out tokens · 21426 ms · 2026-05-09T18:29:30.628384+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

42 extracted references · 31 canonical work pages

  1. [1]

    It is a singly Cabibbo-suppressed (SCS) process

  2. [2]

    It involves the spectator quark

  3. [3]

    The CP asymmetry, aCP (D0 →K SKS)≡ Γ(D0 →K SKS)−Γ( D 0 →K SKS) Γ(D0 →K SKS) + Γ(D 0 →K SKS) ,(2) is particularly interesting

    The CKM-leading amplitude vanishes in the U-spin limit [2]. The CP asymmetry, aCP (D0 →K SKS)≡ Γ(D0 →K SKS)−Γ( D 0 →K SKS) Γ(D0 →K SKS) + Γ(D 0 →K SKS) ,(2) is particularly interesting. The third suppression factor mentioned above, namely the U-spin argument, implies that the CP asymmetry is enhanced by a factor of the order of the inverse of the dimensio...

  4. [4]

    (20, 21)

    and Eqs. (20, 21). The asymmetrya K,D CP does not depend on the parameterϵ, as it should. The reason is that it does not depend on CP violation in the neutral kaon system. It depends solely on the kaon-mixing interference between the final statesK 0K 0 and K 0 K 0 in the final stateK SKS. B. CP asymmetry in neutral kaon oscillations,a K,ϵ CP We now consid...

  5. [5]

    Navaset al.(Particle Data Group), Phys

    S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024, and 2025 update)

    2024

  6. [6]

    M. J. Savage, Phys. Lett. B257, 414 (1991)

    1991

  7. [7]

    Hiller, M

    G. Hiller, M. Jung, and S. Schacht, Phys. Rev. D87, 014024 (2013), arXiv:1211.3734 [hep-ph]. 12

    work page arXiv 2013

  8. [8]

    Nierste and S

    U. Nierste and S. Schacht, Phys. Rev. D92, 054036 (2015), arXiv:1508.00074 [hep-ph]

    work page arXiv 2015

  9. [9]

    Bonviciniet al.(CLEO), Phys

    G. Bonviciniet al.(CLEO), Phys. Rev. D63, 071101 (2001), arXiv:hep-ex/0012054

    work page arXiv 2001

  10. [10]

    Dashet al., Phys

    N. Dashet al., Phys. Rev. Lett.119, 171801 (2017), arXiv:1705.05966 [hep-ex]

    work page arXiv 2017

  11. [11]

    Adachiet al.(Belle, Belle-II), Phys

    I. Adachiet al.(Belle, Belle-II), Phys. Rev. D111, 012015 (2025), arXiv:2411.00306 [hep-ex]

    work page arXiv 2025

  12. [12]

    Adachiet al.(Belle, Belle-II), Phys

    I. Adachiet al.(Belle, Belle-II), Phys. Rev. D112, 012017 (2025), arXiv:2504.15881 [hep-ex]

    work page arXiv 2025

  13. [13]

    Aaijet al.(LHCb), JHEP10, 055 (2015), arXiv:1508.06087 [hep-ex]

    R. Aaijet al.(LHCb), JHEP10, 055 (2015), arXiv:1508.06087 [hep-ex]

    work page arXiv 2015

  14. [14]

    Aaijet al.(LHCb), JHEP11, 048 (2018), arXiv:1806.01642 [hep-ex]

    R. Aaijet al.(LHCb), JHEP11, 048 (2018), arXiv:1806.01642 [hep-ex]

    work page arXiv 2018

  15. [15]

    Aaijet al.(LHCb), Phys

    R. Aaijet al.(LHCb), Phys. Rev. D104, L031102 (2021), arXiv:2105.01565 [hep-ex]

    work page arXiv 2021

  16. [16]

    Aaijet al.(LHCb), JHEP02, 253 (2026), arXiv:2510.14732 [hep-ex]

    R. Aaijet al.(LHCb), JHEP02, 253 (2026), arXiv:2510.14732 [hep-ex]

    work page arXiv 2026

  17. [17]

    Hayrapetyanet al.(CMS), Eur

    A. Hayrapetyanet al.(CMS), Eur. Phys. J. C84, 1264 (2024), arXiv:2405.11606 [hep-ex]

    work page arXiv 2024

  18. [18]

    Tuci on behalf of the LHCb Collaboration, LHC Seminar, CERN, 22 July 2025, https://indico.cern.ch/event/1569705/

    G. Tuci on behalf of the LHCb Collaboration, LHC Seminar, CERN, 22 July 2025, https://indico.cern.ch/event/1569705/

    work page arXiv 2025

  19. [19]

    Ferber,Towards First Physics at Belle II,Acta Phys

    W. Altmannshoferet al.(Belle-II), PTEP2019, 123C01 (2019), [Erratum: PTEP 2020, 029201 (2020)], arXiv:1808.10567 [hep-ex]. [16]Physics case for an LHCb Upgrade II, Tech. Rep. (CERN, Geneva, 2018) arXiv:1808.08865

    work page arXiv 2019

  20. [20]

    I. I. Bigi and A. I. Sanda, Phys. Lett. B625, 47 (2005), arXiv:hep-ph/0506037

    work page arXiv 2005

  21. [21]

    Xing, Phys

    Z.-Z. Xing, Phys. Lett. B353, 313 (1995), [Erratum: Phys.Lett.B 363, 266 (1995)], arXiv:hep- ph/9505272

    work page arXiv 1995

  22. [22]

    F.-S. Yu, D. Wang, and H.-n. Li, Phys. Rev. Lett.119, 181802 (2017), arXiv:1707.09297 [hep-ph]

    work page arXiv 2017

  23. [23]

    Grossman and Y

    Y. Grossman and Y. Nir, JHEP04, 002 (2012), arXiv:1110.3790 [hep-ph]

    work page arXiv 2012

  24. [24]

    Grossman, P

    Y. Grossman, P. Leo, A. Martini, G. Papiri, and A. Rostomyan, (2025), arXiv:2509.07071 [hep-ph]

    work page arXiv 2025

  25. [25]

    Aoki et al., FLAG review 2024, Phys

    Y. Aokiet al.(Flavour Lattice Averaging Group (FLAG)), Phys. Rev. D113, 014508 (2026), arXiv:2411.04268 [hep-lat]

    work page arXiv 2026

  26. [26]

    B- andD-meson leptonic decay con- stants from four-flavor lattice QCD,

    A. Bazavovet al., Phys. Rev. D98, 074512 (2018), arXiv:1712.09262 [hep-lat]

    work page arXiv 2018

  27. [27]

    R. J. Dowdall, C. T. H. Davies, G. P. Lepage, and C. McNeile, Phys. Rev. D88, 074504 (2013), arXiv:1303.1670 [hep-lat]

    work page arXiv 2013

  28. [28]

    Carrascoet al., Phys

    N. Carrascoet al., Phys. Rev. D91, 054507 (2015), arXiv:1411.7908 [hep-lat]

    work page arXiv 2015

  29. [29]

    F K /Fπ from M¨ obius Domain-Wall fermions solved on gradient-flowed HISQ ensembles,

    N. Milleret al., Phys. Rev. D102, 034507 (2020), arXiv:2005.04795 [hep-lat]

    work page arXiv 2020

  30. [30]

    Ratio of kaon and pion leptonic decay constants with Nf=2+1+1 Wilson-clover twisted-mass fermions,

    C. Alexandrouet al.(Extended Twisted Mass), Phys. Rev. D104, 074520 (2021), arXiv:2104.06747 [hep-lat]

    work page arXiv 2021

  31. [31]

    Binosi and L

    D. Binosi and L. Theußl, Comput. Phys. Commun.161, 76 (2004), arXiv:hep-ph/0309015

    work page arXiv 2004

  32. [32]

    JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes

    D. Binosi, J. Collins, C. Kaufhold, and L. Theussl, Comput. Phys. Commun.180, 1709 (2009), arXiv:0811.4113 [hep-ph]. 13

    work page Pith review arXiv 2009

  33. [33]

    Hocker, H

    A. Hocker, H. Lacker, S. Laplace, and F. Le Diberder, Eur. Phys. J. C21, 225 (2001), arXiv:hep-ph/0104062

    work page arXiv 2001

  34. [34]

    T. B. Day, Phys. Rev.121, 1204 (1961)

    1961

  35. [35]

    H. J. Lipkin, Phys. Rev.176, 1715 (1968)

    1968

  36. [36]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev.47, 777 (1935)

    1935

  37. [37]

    Babusciet al.(KLOE-2), JHEP04, 059 (2022), [Erratum: JHEP 04, 169 (2022)], arXiv:2111.04328 [hep-ex]

    D. Babusciet al.(KLOE-2), JHEP04, 059 (2022), [Erratum: JHEP 04, 169 (2022)], arXiv:2111.04328 [hep-ex]

    work page arXiv 2022

  38. [38]

    Buchanan, R

    C. Buchanan, R. Cousins, C. Dib, R. D. Peccei, and J. Quackenbush, Phys. Rev. D45, 4088 (1992)

    1992

  39. [39]

    G. C. Branco, L. Lavoura, and J. P. Silva,CP Violation, Vol. 103 (1999)

    1999

  40. [40]

    Bernabeu, A

    J. Bernabeu, A. Di Domenico, and P. Villanueva-Perez, Nucl. Phys. B868, 102 (2013), arXiv:1208.0773 [hep-ph]

    work page arXiv 2013

  41. [41]

    Bernabeu, A

    J. Bernabeu, A. Di Domenico, and P. Villanueva-Perez, JHEP10, 139 (2015), arXiv:1509.02000 [hep-ph]

    work page arXiv 2015

  42. [42]

    Ambrosinoet al.(KLOE), Phys

    F. Ambrosinoet al.(KLOE), Phys. Lett. B642, 315 (2006), arXiv:hep-ex/0607027. 14

    work page arXiv 2006