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arxiv: 2605.24713 · v1 · pith:P4D2J5JBnew · submitted 2026-05-23 · ✦ hep-ph · hep-ex

Axion-like particles solve the Bto Kνbarν and Bto π K puzzles

Bhubanjyoti Bhattacharya , Alakabha Datta , Girish Kumar , Danny Marfatia This is my paper

Pith reviewed 2026-06-30 12:49 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords axion-like particlesB meson decaysflavor anomaliessterile neutrinosinvisible decayspion mixingmuon magnetic moment
0
0 comments X

The pith

A short-lived axion-like particle near the pion mass resolves both the B to K invisible excess and the B to pi K decay discrepancies.

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

The paper argues that an axion-like particle (ALP) with mass close to the neutral pion, coupled to the photon, top quark, and a heavy sterile neutrino, accounts for the 2.7 sigma excess in the Belle II measurement of B+ to K+ plus invisible states and the longstanding mismatches in B to pi K branching ratios and CP asymmetries. Mixing between the ALP and the pi0 modifies the hadronic B to pi0 K modes, while the ALP's off-shell decay into sterile neutrino pairs boosts the invisible B+ to K+ channel. The same setup generates concrete predictions for all B to K(*) plus invisible modes, the rare kaon decays K+ to pi+ plus invisible and KL to pi0 plus invisible, and an appreciable shift in the muon magnetic moment with negligible effects on the electron moment or b to s e+ e- transitions.

Core claim

In the minimal ALP model, the particle mixes with the pi0 to alter B to pi0 K decays and couples off-shell to pairs of heavy sterile neutrinos to enhance B+ to K+ plus invisible, thereby addressing both anomalies simultaneously while producing specific, testable rates in related B and K channels and a contribution to the muon magnetic moment.

What carries the argument

ALP mixing with the pi0 together with its off-shell coupling to heavy sterile neutrino pairs, driven by tuned couplings to the photon and top quark.

If this is right

  • All B to K(*) plus invisible branching ratios receive specific ALP-induced enhancements.
  • The decays K+ to pi+ plus invisible and KL to pi0 plus invisible receive appreciable ALP contributions.
  • The muon magnetic moment receives an appreciable ALP contribution while the electron moment and b to s e+ e- remain essentially unaffected.

Where Pith is reading between the lines

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

  • Future precision data on the full set of B to K(*) invisible modes at Belle II could overconstrain the ALP parameters.
  • The required sterile neutrino mass and mixing could produce detectable signals in dedicated neutrino or beam-dump searches.
  • If the ALP mixing mechanism holds, similar effects might appear in other neutral-meson systems where pion mixing is possible.

Load-bearing premise

The ALP mass sits close to the pi0 mass and its couplings to the photon, top quark, and sterile neutrino are tuned to fit the anomalies without violating other bounds.

What would settle it

A measurement of the KL to pi0 plus invisible branching ratio that shows no enhancement or deviates from the value predicted by the ALP mixing and sterile neutrino coupling would rule out the explanation.

Figures

Figures reproduced from arXiv: 2605.24713 by Alakabha Datta, Bhubanjyoti Bhattacharya, Danny Marfatia, Girish Kumar.

Figure 1
Figure 1. Figure 1: Feynman diagrams for (a) the effective s-b-a vertex, and (b) b → sνiν¯j . by the subscript “p”, the flavor and mass eigenstates of these two particles are related by  a π 0  =  cos θ sin θ − sin θ cos θ  ap π 0 p  , (5) where θ is the mixing angle. In this setup, there are two production mechanisms for the ALP. The first is via the penguin processes, e.g., B → Ka and K → πa, where the internal top qu… view at source ↗
Figure 2
Figure 2. Figure 2: The 90% CL KOTO constraint from B(KL → π 0 + inv) in the |Uµ4| − gN plane. The b → sνν transition depends on gN , Uµ4 and mν4 . Since B(KL → π 0+inv) is independent of mν4 , the KOTO upper bound directly constrains the |Uµ4|–gN plane. Fig￾ure 2 shows the excluded region: for gN ∼ O(1), we find |Uµ4| ≲ O(10−3 ). We conservatively fix |Uµ4| = 5 × 10−4 in the analysis below. In [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 3
Figure 3. Figure 3: Left panel: Allowed parameter space in the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

The recent measurement of the branching ratio of $B^+ \to K^+ + \mathrm{inv}$ (where "inv" denotes invisible states) by the Belle~II collaboration is enhanced relative to the standard model expectation by 2.7$\sigma$. An older puzzle persists in measurements of the branching ratios and CP asymmetries of $B \to \pi K $ decays. We address these two anomalies in flavor-changing neutral current $B$ decays, with a short-lived axion-like particle (ALP) with mass close to that of the $\pi^0$. In the minimal model, the ALP has couplings to the photon, top quark and a heavy sterile neutrino $\nu_N$. The ALP contributes to the $B \to \pi^0 K$ decays by mixing with the $\pi^0$. It contributes to $B^+ \to K^+ + \mathrm{inv}$ by its off-shell coupling to sterile neutrino pairs. We make predictions for all $B \to K^{(*)} + \mathrm{inv}$ modes and for the rare kaon decays $K^+ \to \pi^+ + \mathrm{inv}$ and $K_L \to \pi^0 + \mathrm{inv}$. We find an appreciable contribution to the magnetic moment of the muon, and negligible contributions to the magnetic moment of the electron and $b \to s e^+ e^-$.

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 / 2 minor

Summary. The manuscript proposes that a short-lived axion-like particle (ALP) with mass near m_π⁰, coupled to photons, the top quark, and a heavy sterile neutrino ν_N, simultaneously resolves the 2.7σ Belle II excess in B⁺ → K⁺ + inv and the B → πK branching-ratio and CP-asymmetry puzzles. The ALP mixes with the π⁰ to modify B → π⁰K modes and contributes to invisible B decays via off-shell exchange into ν_N pairs; predictions are given for all B → K(*) + inv channels, the rare kaon decays K⁺ → π⁺ + inv and K_L → π⁰ + inv, and (g-2)_μ (with negligible effects on (g-2)_e and b → s e⁺e⁻).

Significance. If the chosen parameter space is shown to be consistent with all existing limits, the work would supply a single-particle explanation for two independent B-physics anomalies together with concrete, falsifiable predictions in kaon decays and the muon magnetic moment. The approach is economical and directly testable at current and near-future experiments.

major comments (2)
  1. [kaon-decay predictions section] The central viability claim rests on the assertion that the same three couplings (to photon, top, and ν_N) can be chosen to reproduce the observed B anomalies while keeping the predicted rates for K⁺ → π⁺ + inv and K_L → π⁰ + inv below experimental bounds. The manuscript must demonstrate this explicitly with the numerical values used for the B fits (e.g., the section presenting the kaon predictions and the table of branching ratios).
  2. [Eq. for ALP propagator and mixing] The off-shell contribution to B⁺ → K⁺ + inv relies on the propagator 1/(q² − m_ALP²) with m_ALP ≈ m_π⁰. The same mixing and couplings necessarily generate contributions to the kaon modes; the paper should quantify the degree of cancellation or suppression that keeps the kaon rates acceptable (reference the relevant equation for the effective b → s ALP vertex and the mixing angle).
minor comments (2)
  1. [model Lagrangian section] Clarify the precise definition of the ALP–top coupling (e.g., whether it is flavor-diagonal or includes a specific texture) and its relation to the b → s FCNC operator.
  2. [model section] Add a brief statement on the lifetime of the ALP and why it is short-lived enough to be treated as off-shell in the B decays but still mixes with the π⁰.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its significance. We address each of the two major comments below and commit to revisions that will strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [kaon-decay predictions section] The central viability claim rests on the assertion that the same three couplings (to photon, top, and ν_N) can be chosen to reproduce the observed B anomalies while keeping the predicted rates for K⁺ → π⁺ + inv and K_L → π⁰ + inv below experimental bounds. The manuscript must demonstrate this explicitly with the numerical values used for the B fits (e.g., the section presenting the kaon predictions and the table of branching ratios).

    Authors: We agree that an explicit demonstration with the specific numerical values from the B-anomaly fits is necessary to fully establish viability. Although the manuscript already computes and presents predictions for the kaon modes, the revised version will add a dedicated table (or subsection) that inserts the exact best-fit values of the three couplings obtained from the B → K + inv and B → πK analyses and reports the resulting K⁺ → π⁺ + inv and K_L → π⁰ + inv branching ratios, confirming they remain below the experimental limits. This addition will make the consistency transparent without changing any conclusions. revision: yes

  2. Referee: [Eq. for ALP propagator and mixing] The off-shell contribution to B⁺ → K⁺ + inv relies on the propagator 1/(q² − m_ALP²) with m_ALP ≈ m_π⁰. The same mixing and couplings necessarily generate contributions to the kaon modes; the paper should quantify the degree of cancellation or suppression that keeps the kaon rates acceptable (reference the relevant equation for the effective b → s ALP vertex and the mixing angle).

    Authors: The propagator is written exactly as stated, and the effective b → s ALP vertex is generated by the top-quark loop (with the sterile-neutrino coupling entering the invisible width). The π⁰ mixing, controlled by the photon coupling, produces a kinematic suppression in the kaon amplitudes. In the revision we will (i) explicitly cite the equation defining the effective b → s ALP vertex and the equation for the mixing angle, and (ii) add a short quantitative paragraph that evaluates the suppression factor (or the ratio of ALP-induced amplitudes in the kaon versus B channels) for the benchmark parameter point, thereby showing how the kaon rates remain acceptable. This will directly address the request for explicit referencing and quantification. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model parameters fitted to anomalies then used for independent predictions

full rationale

The paper introduces an ALP with m_ALP ≈ m_π0 and couplings to photons, top quarks, and sterile neutrinos chosen to explain the two B-decay anomalies via mixing and off-shell exchange. It then derives contributions to additional modes (B → K(*) + inv, K → π + inv) from the same parameters. No quoted equations or self-citations show any 'prediction' reducing to the input anomalies by construction, nor any load-bearing self-citation chain. The derivation remains self-contained as a standard BSM construction with external experimental inputs and outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 2 invented entities

Abstract-only review; the ledger is populated from the stated model ingredients. The central claim rests on the existence of the ALP, its mass choice, and its three couplings, none of which are derived from first principles in the visible text.

free parameters (2)
  • ALP mass
    Set close to the pi0 mass to enable mixing; value is chosen rather than derived.
  • ALP couplings to photon, top, and nu_N
    Introduced to produce the required mixing and invisible contributions; values are model parameters.
axioms (2)
  • domain assumption ALP mixes with the neutral pion
    Invoked to affect B to pi0 K decays; location is the model description in the abstract.
  • domain assumption ALP couples off-shell to sterile neutrino pairs
    Invoked to produce the invisible B to K mode; location is the model description in the abstract.
invented entities (2)
  • short-lived ALP no independent evidence
    purpose: To explain both anomalies via mixing and invisible decays
    New particle postulated in the model; independent_evidence is false because no external falsifiable signature beyond the anomalies is given in the abstract.
  • heavy sterile neutrino nu_N no independent evidence
    purpose: To provide the invisible final state for B to K inv
    Introduced as part of the minimal model; independent_evidence is false.

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discussion (0)

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Reference graph

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