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arxiv: 2507.01947 · v2 · submitted 2025-07-02 · ✦ hep-ph · hep-ex

Probing CP and flavor violation in neutral kaon decays with ALPs

Reuven Balkin , Stefania Gori , Christiane Scherb This is my paper

Pith reviewed 2026-05-19 05:57 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords ALPsneutral kaon decaysCP violationflavor violationthree-body decaysaxion-like particlesweak interactions
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0 comments X

The pith

The ratio of three-body to two-body ALP decays from neutral kaons probes CP violation in the underlying UV theory.

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

The paper establishes that the two-body decay of the long-lived neutral kaon into a pion and an axion-like particle requires both flavor violation and CP violation. In contrast the three-body decay into two pions and the ALP can proceed with flavor violation alone. This allows their rate ratio to serve as a probe of CP violation in the high-energy theory. The work highlights the need to include weak-interaction-induced contributions to the amplitudes which are often neglected. It examines minimal and non-minimal flavor violation scenarios and finds that three-body decays can be comparable to or dominate two-body ones in some cases. These neutral channels offer complementary information on ALP couplings not available from charged kaon decays.

Core claim

The authors claim that the ratio of rates for the decays K_L to pi pi a to K_L to pi0 a can be used to probe CP violation of the underlying UV theory because the three-body decay can proceed via flavor violation alone whereas the two-body decay requires both flavor and CP violation, with weak-interaction-induced contributions playing a key role in the amplitudes.

What carries the argument

The ratio of the three-body neutral kaon decay rate to the two-body rate into an ALP, serving to separate CP-violating effects from pure flavor-violating ones.

If this is right

  • In non-minimal flavor violating scenarios ALP production from neutral three-body decays can be comparable to or dominate the two-body decay despite reduced phase space.
  • Weak-interaction-induced contributions to ALP decay amplitudes must be retained for accurate rate comparisons in minimal and non-minimal flavor violating scenarios.
  • These neutral kaon decays provide complementary probes of ALP couplings beyond those accessible via charged kaon channels.

Where Pith is reading between the lines

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

  • Measuring this rate ratio at future experiments could independently constrain the CP properties of ALP models.
  • Previous calculations of ALP bounds from kaon decays that neglected weak contributions may need revision based on this analysis.
  • Similar ratio techniques could be explored in other particle decays to disentangle different types of symmetry breaking in new physics.

Load-bearing premise

The modeling and inclusion of weak-interaction-induced contributions to the ALP decay amplitudes are significant and must be retained when comparing rates in minimal and non-minimal flavor-violating scenarios.

What would settle it

A measurement finding the three-body decay rate to be zero or negligible in a model with flavor violation but without CP violation would falsify the premise that the three-body decay can proceed via flavor violation alone.

read the original abstract

We analyze the three-body decays of the long-lived neutral kaon $K_L \to \pi\pi a$, where $a$ is an axion-like particle (ALP), and compare them to the two-body decay $K_L \to \pi^0 a$. While the latter requires both flavor violation (FV) and $CP$ violation (CPV), the former can proceed via FV alone, allowing the ratio of decay rates to serve as a probe of CPV of the underlying UV theory. We emphasize the importance of weak-interaction-induced contributions, often neglected in recent calculations. We explore both minimal and non-minimal flavor-violating scenarios, and identify classes of models where ALP production from neutral three-body decays is comparable to - or even dominates over - the two-body decay, despite its reduced phase space. Finally, we discuss the phenomenological implications of our results and show how these decays can provide complementary probes of ALP couplings beyond those accessible via charged kaon channels.

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 / 3 minor

Summary. The paper analyzes three-body decays K_L → ππ a for axion-like particles (ALPs) and compares them to the two-body decay K_L → π⁰ a. It claims that while K_L → π⁰ a requires both flavor violation (FV) and CP violation (CPV), the three-body mode can proceed via FV alone when weak-interaction-induced contributions are retained, allowing the ratio of rates to diagnose CPV in the UV theory. The work explores minimal and non-minimal FV scenarios, shows that three-body production can compete with or dominate two-body despite phase-space suppression, and discusses phenomenological implications as complementary probes beyond charged-kaon channels.

Significance. If the separation between FV-only and CPV-dependent amplitudes holds after including weak-induced operators, the ratio provides a clean, falsifiable diagnostic for CP properties of ALP couplings that is not accessible via two-body modes or charged-kaon decays alone. The emphasis on retaining weak contributions (often dropped elsewhere) and the identification of model classes where three-body rates dominate are concrete strengths; the approach is parameter-free in the ratio once the operator basis is fixed and yields testable predictions for ALP searches at kaon facilities.

major comments (2)
  1. [§4.1, Eq. (22)] §4.1, Eq. (22): the decomposition of the three-body amplitude into FV-only and CPV-dependent pieces assumes that the weak-induced operators (generated by SM loops) carry no additional UV CP phases after matching; an explicit phase-counting argument or numerical scan over CKM phases would be needed to confirm that the ratio remains insensitive to UV CPV when only FV is present.
  2. [Table 2] Table 2, non-minimal FV row: the reported branching-ratio ratio Γ(K_L→ππa)/Γ(K_L→π⁰a) ≈ 0.8–1.2 for m_a = 100 MeV relies on specific choices for the ALP-quark couplings; the paper should state the exact benchmark values used and show how the ratio varies when those couplings are varied within the allowed range from K→πa constraints.
minor comments (3)
  1. [Introduction] The abstract states that weak contributions are 'often neglected in recent calculations,' but no specific references to those calculations are given in the introduction; adding two or three citations would clarify the novelty.
  2. [Figure 3] Figure 3: the curves for minimal vs. non-minimal FV are difficult to distinguish at low m_a; increasing line thickness or adding a shaded band for theoretical uncertainty would improve readability.
  3. [§2 and §5] Notation for the ALP flavor-violating couplings (e.g., C_{sd}^a) is introduced in §2 but used without redefinition in §5; a short glossary or consistent use of subscripts would help.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive comments. We address each major comment below and indicate the corresponding revisions to the manuscript.

read point-by-point responses

  1. Referee: [§4.1, Eq. (22)]: the decomposition of the three-body amplitude into FV-only and CPV-dependent pieces assumes that the weak-induced operators (generated by SM loops) carry no additional UV CP phases after matching; an explicit phase-counting argument or numerical scan over CKM phases would be needed to confirm that the ratio remains insensitive to UV CPV when only FV is present.

    Authors: We thank the referee for this observation on the phase structure. The weak-induced operators are generated by SM loops that incorporate the CKM matrix and its standard CP phase. In the FV-only scenario the UV ALP couplings are taken to be real. We will add an explicit phase-counting argument in the revised §4.1 demonstrating that no additional UV CP-violating phases enter the FV-only amplitude beyond the SM CKM phase already present; this leaves the ratio insensitive to extra UV CPV when only FV is active. A full numerical scan over CKM phases is not required, as the counting is general and independent of specific values. revision: yes

  2. Referee: Table 2, non-minimal FV row: the reported branching-ratio ratio Γ(K_L→ππa)/Γ(K_L→π⁰a) ≈ 0.8–1.2 for m_a = 100 MeV relies on specific choices for the ALP-quark couplings; the paper should state the exact benchmark values used and show how the ratio varies when those couplings are varied within the allowed range from K→πa constraints.

    Authors: We agree that the benchmark values should be stated explicitly for reproducibility. In the non-minimal FV scenario we employed specific ALP-quark coupling strengths that saturate the existing K→πa bounds while realizing the non-minimal flavor structure. We will add a footnote or short paragraph in the revised text giving the exact numerical values. We will also include a brief discussion (or supplementary plot) showing how the ratio varies when the couplings are scanned within the experimentally allowed range from K→πa constraints, confirming that the ratio remains O(1) throughout the relevant parameter space. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained in EFT amplitude calculations

full rationale

The paper derives the distinction between two-body and three-body ALP decays from explicit operator matching and amplitude computations in the ALP effective Lagrangian, retaining weak-induced flavor structures as independent SM inputs. No load-bearing step equates a claimed prediction to a fitted parameter or reduces the CPV-probing ratio to a self-citation chain by construction. The analysis treats weak contributions as calculable corrections using standard CKM parameters rather than redefining them via the target observables, rendering the central claim externally falsifiable and independent of the paper's own fitted values.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on an effective field theory for ALPs below the electroweak scale together with standard treatments of kaon decays that incorporate weak interactions; the free parameters are the ALP flavor-violating couplings.

free parameters (1)
  • ALP flavor-violating quark couplings
    These couplings in the effective Lagrangian determine the decay rates and are free parameters to be constrained by data.
axioms (2)
  • domain assumption ALPs are described by an effective Lagrangian valid at low energies
    Standard framework invoked for all ALP phenomenology in kaon decays.
  • domain assumption Weak-interaction effects can be included via chiral perturbation theory for kaon processes
    Common assumption when computing rare kaon decay amplitudes.
invented entities (1)
  • Axion-like particle a no independent evidence
    purpose: Light mediator carrying flavor and CP violating interactions
    Postulated extension of the standard model whose couplings are the target of the analysis.

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Forward citations

Cited by 1 Pith paper

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  1. Sweeping the pion chimney for axion-like particles with KOTO

    hep-ph 2025-08 unverdicted novelty 7.0

    Recasting KOTO KL to 3pi0 to 6gamma data yields novel limits on prompt ALPs near the pion mass via KL to 2pi0 a to 6gamma, with extensions to displaced decays for wider ALP masses.

Reference graph

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