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arxiv: 2604.07481 · v1 · submitted 2026-04-08 · ✦ hep-ph · hep-ex

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Axion-like Particles and Lepton Flavor Violation in Muonic Atoms

Girish Kumar , Alexey A. Petrov
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:23 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords axion-like particleslepton flavor violationmuonic atomsmuon to electron conversionanomalous magnetic momentMu2emuon decaysALP constraints
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The pith

Laboratory constraints from muon decays and the electron magnetic moment cap the ALP-mediated branching ratio for muon-electron conversion in muonic atoms at O(10^{-20}) in aluminum.

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

The paper calculates the rate for the lepton-flavor-violating process μ⁻ e⁻ → e⁻ e⁻ inside a muonic atom when mediated by an axion-like particle that couples flavor-violatingly to electrons and muons while coupling diagonally to electrons. It shows that lighter ALPs increase the rate parametrically and that the rate grows with the cube of (Z-1), favoring heavier atoms. After folding in all relevant laboratory limits, including those from μ→3e, μ→eγ, muonium conversion, and especially the electron anomalous magnetic moment, the allowed branching ratio drops to at most 10^{-20} in aluminum, with the resonant mass window suppressed even more. A reader would care because this implies that Mu2e is unlikely to see a signal from this mechanism unless the model is extended, while the upcoming Mu3e experiment will test the most promising remaining corner of parameter space.

Core claim

In the simplified ALP framework with flavor-violating e-μ couplings and a flavor-diagonal pseudoscalar electron coupling, the ALP-mediated contribution to the μ⁻ e⁻ → e⁻ e⁻ transition rate in a muonic atom, after all laboratory constraints are applied, yields a branching ratio at most O(10^{-20}) for aluminum; the resonant region 2m_e < m_a < m_μ - m_e is far more suppressed, and Δa_e excludes the largest fraction of the scanned parameter space.

What carries the argument

The ALP-exchange amplitude for the μ⁻ e⁻ → e⁻ e⁻ transition inside the muonic atom, computed at fixed couplings and then subjected to global constraints from muon decays, magnetic moments, and muonium oscillations.

If this is right

  • The branching ratio scales as (Z-1)^3, so searches in heavier nuclei such as lead or gold would be more sensitive at fixed ALP couplings.
  • The largest viable rates remain tied to values of B(μ→3e) near its present experimental limit, placing the most relevant parameter space within reach of the Mu3e experiment.
  • Invisible ALP decays to a dark sector are permitted but do not open new viable regions for the muonic-atom signal once laboratory bounds are imposed.
  • Light mediators enhance the rate at fixed couplings but are already excluded over most of the space by Δa_e and other processes.

Where Pith is reading between the lines

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

  • If the simplified model is correct, precision measurements of the electron magnetic moment will remain the dominant constraint on this class of ALP explanations for lepton flavor violation.
  • Extending the framework to include additional scalar or vector mediators could alter the relative importance of Δa_e versus μ→3e and potentially reopen higher-rate windows.
  • The (Z-1)^3 scaling suggests that dedicated searches in high-Z muonic atoms could be prioritized even if Mu2e on aluminum yields a null result.
  • The suppression of the resonant window implies that off-shell ALP exchange dominates any observable signal, favoring broad searches over narrow mass windows.

Load-bearing premise

The analysis rests on a simplified ALP model that assumes only the stated flavor-violating e-μ and diagonal electron couplings without extra new physics that could change the rates or relax the existing bounds.

What would settle it

An observation of the μ⁻ e⁻ → e⁻ e⁻ branching ratio in aluminum above O(10^{-20}) while remaining consistent with current limits on Δa_e and B(μ→3e) would falsify the claim that laboratory constraints restrict the rate to this level.

Figures

Figures reproduced from arXiv: 2604.07481 by Alexey A. Petrov, Girish Kumar.

Figure 1
Figure 1. Figure 1: ALP-induced µ −e − → e −e − at tree-level. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: ALP mass dependence of branching ratio of µ −e − → e −e − in muonic atom for aluminum and gold target, taking an example benchmark value g S,P eµ = g P ee = 10−6 . gold, τ˜µ = 2.19×10−6 s, ∼ 9×10−7 s, and ∼ 7×10−8 s, respectively. Using Eqs. (3.3)–(3.5), the branching ratio for µ −e − → e −e − is then given by B(µ −e − → e −e −) = ˜τµ Γ(µ −e − → e −e −) = ˜τµ 2 |ψe(0)| 2σ|v1 − v2| , ≃ τ˜µ(Z − 1)3 α 3m3 em2… view at source ↗
Figure 3
Figure 3. Figure 3: Constraints on the LFV couplings g S,P eµ (assuming g S eµ = g P eµ) as a function of the ALP mass. The dashed gray contours indicate B(µ −e − → e −e −) values. The ALP-electron coupling is g P ee = 10−6 in the left plot and g P ee = 10−10 in the right plot. 10−32. For ma > mµ, muonium oscillation, which is insensitive to g P ee and therefore remains unchanged, becomes the leading constraint, allowing maxi… view at source ↗
Figure 4
Figure 4. Figure 4: Scatter plot of B(µ → 3e) vs. B(µ −e − → e −e −) for an aluminum target, with color indicating correlation with ma. The coupling gχχ is assumed to be zero in the left plot and finite in the right plot. See text for scan details. to the current experimental limit on B(µ → 3e). Unlike the constraints shown in [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Heatmap of the fraction of sampled points ruled out by the constraints. Diagonal entries ii show the fraction excluded by each constraint alone. Off-diagonal entries ij show the fraction excluded simultaneously by both constraints i and j. See text for details. visualized in the heatmap in [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
read the original abstract

We explore the potential of the Mu2e experiment to probe the lepton-flavor-violating process $\mu^- e^- \to e^- e^-$ in a muonic atom within a simplified axion-like particle (ALP) framework featuring flavor-violating $e$-$\mu$ couplings and a flavor-diagonal pseudoscalar coupling to electrons, which also allows for possible invisible ALP decays into a dark sector. We compute the ALP-mediated contribution to the transition rate and show that, at fixed couplings, the branching ratio increases for lighter mediators and scales as $(Z-1)^3$, favoring heavier nuclei. We compare the model against constraints from $\mu\to e\gamma$, $\mu\to 3e$, $\mu\to e\gamma\gamma$, $\mu\to e+\mathrm{inv}$, and muonium-antimuonium conversion, as well as from the anomalous magnetic moments of the electron and muon. Additional astrophysical and beam-dump limits on the electron coupling are also discussed. A key result is that $\Delta a_e$ provides one of the most stringent probes of the parameter space and, in the global scan, excludes the largest fraction of sampled points. After applying the laboratory constraints used in the scan, the viable branching ratio for $\mu^- e^- \to e^- e^-$ in aluminum drops to at most $\mathcal{O}(10^{-20})$, while the resonant region $2m_e<m_a<m_\mu-m_e$ is much more heavily suppressed. The highest achievable values are closely tied to $\mathcal{B}(\mu\to 3e)$ near its current limit, indicating that the upcoming Mu3e experiment will explore the most promising region relevant for this muonic-atom signal. Our analysis shows that, although a light ALP can parametrically enhance $\mu^- e^- \to e^- e^-$ at fixed couplings, existing bounds -- especially $\Delta a_e$, $\mu\to 3e$, $\mu\to e\gamma$, and muonium oscillations -- severely limit the observable rate.

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 manuscript claims that within a simplified ALP model with flavor-violating e-μ couplings and a flavor-diagonal pseudoscalar electron coupling (allowing invisible decays), the ALP-mediated branching ratio for μ⁻e⁻ → e⁻e⁻ in muonic atoms scales with mediator mass and nuclear charge as (Z-1)³ at fixed couplings. After a global parameter scan subject to laboratory constraints from μ→eγ, μ→3e, μ→eγγ, μ→e+inv, muonium conversion, Δa_e, Δa_μ, and astrophysical/beam-dump limits, the viable branching ratio in aluminum is at most O(10^{-20}), with the resonant window 2m_e < m_a < m_μ - m_e more suppressed. Δa_e excludes the largest fraction of points and is among the strongest probes; the highest rates remain tied to the current μ→3e limit, so Mu3e will probe the most relevant region for this signal.

Significance. If the central results hold, the work provides a concrete benchmark showing that existing constraints render this particular ALP-mediated LFV signal in muonic atoms unobservably small for Mu2e, while underscoring the complementary power of Mu3e. The parametric study of mass and Z dependence, together with the comprehensive multi-constraint scan that quantifies exclusion fractions, offers a useful reference for ALP model building with LFV. Credit is due for the explicit inclusion of invisible ALP decays and the direct linkage of the muonic-atom rate to near-term experimental sensitivities.

major comments (2)
  1. [Section 4] Section 4 (anomalous magnetic moments): The bound from Δa_e on |g_aee| is applied directly to restrict the flavor-violating coupling g_aeμ in the scan, and this drives the O(10^{-20}) upper limit on the branching ratio. The manuscript does not vary the net Δa_e by allowing additional new-physics contributions that could offset the ALP loop term. This assumption is load-bearing for the suppression claim; a concrete test is to augment the scan with a free offset parameter δ(Δa_e) and recompute the post-constraint distribution of branching ratios.
  2. [Section 3] Section 3 (transition rate): The statement that the branching ratio increases for lighter mediators and scales as (Z-1)³ at fixed couplings is central to identifying heavier nuclei as favorable. The derivation of this Z dependence from the overlap integrals or effective operators should be shown explicitly (including any mass-dependent form factors) to confirm it remains valid through the resonant region 2m_e < m_a < m_μ - m_e.
minor comments (3)
  1. [Section 2] The notation for the three couplings (g_aee, g_aeμ, and any invisible width parameter) should be introduced with a single equation or table in Section 2 to avoid later ambiguity when quoting numerical bounds.
  2. Figure 5 (or equivalent scan plot) would benefit from an additional panel or inset showing the distribution of branching ratios before versus after the Δa_e cut, to make the exclusion power visually quantitative.
  3. [Section 4] A reference to the standard treatment of ALP contributions to (g-2)_e (e.g., the loop integral in the literature) should be added when the Δa_e formula is first written.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We address each major comment below and indicate the revisions we plan to make.

read point-by-point responses

  1. Referee: [Section 4] Section 4 (anomalous magnetic moments): The bound from Δa_e on |g_aee| is applied directly to restrict the flavor-violating coupling g_aeμ in the scan, and this drives the O(10^{-20}) upper limit on the branching ratio. The manuscript does not vary the net Δa_e by allowing additional new-physics contributions that could offset the ALP loop term. This assumption is load-bearing for the suppression claim; a concrete test is to augment the scan with a free offset parameter δ(Δa_e) and recompute the post-constraint distribution of branching ratios.

    Authors: We appreciate the referee highlighting this important assumption. Our analysis is performed within a simplified ALP model in which the ALP is responsible for both the LFV couplings and the contributions to the anomalous magnetic moments. In this minimal framework, there are no additional new physics contributions to offset the ALP term in Δa_e. Introducing a free offset parameter would necessitate specifying the nature of the additional contributions, which lies beyond the scope of the present work. We will revise the manuscript to explicitly discuss this modeling assumption in Section 4 and note that cancellations from unspecified sources could in principle relax the bounds, though such scenarios would require a more complete model. revision: partial

  2. Referee: [Section 3] Section 3 (transition rate): The statement that the branching ratio increases for lighter mediators and scales as (Z-1)³ at fixed couplings is central to identifying heavier nuclei as favorable. The derivation of this Z dependence from the overlap integrals or effective operators should be shown explicitly (including any mass-dependent form factors) to confirm it remains valid through the resonant region 2m_e < m_a < m_μ - m_e.

    Authors: We agree that providing the explicit derivation will improve the clarity of the paper. The scaling with (Z-1)^3 originates from the normalization factors in the muon and electron wave functions for a nucleus with charge Z, combined with the overlap integrals of the effective operators generated by ALP exchange. We will add this derivation to Section 3, including the relevant mass-dependent form factors from the ALP propagator. Furthermore, we confirm that this Z dependence remains valid in the resonant region, as the resonance condition affects the propagator but preserves the nuclear overlap structure at fixed couplings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external constraints and standard formulas

full rationale

The paper derives the ALP-mediated branching ratio for μ⁻e⁻ → e⁻e⁻ from the specified flavor-violating and diagonal couplings using explicit rate formulas, then applies independent laboratory bounds (Δa_e, μ→3e, μ→eγ, muonium conversion, etc.) obtained from external experiments. No quoted step reduces a prediction to a fitted parameter from the same dataset, nor does any central claim rest on a self-citation chain or ansatz imported from the authors' prior work. The suppression to O(10^{-20}) follows directly from intersecting the model with those external limits; the analysis remains self-contained against benchmarks outside the present scan.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The central claim rests on a simplified ALP model with two free couplings (flavor-violating e-μ and flavor-diagonal electron) that are scanned subject to external constraints; the ALP itself is postulated without independent evidence beyond the model assumptions.

free parameters (3)
  • ALP mass m_a
    Scanned over ranges including resonant and non-resonant regions to assess branching ratio enhancement.
  • Flavor-violating coupling g_{a e μ}
    Free parameter in the model, constrained by LFV processes but not fitted to the muonic atom rate.
  • Electron pseudoscalar coupling g_{a e e}
    Free parameter scanned and constrained primarily by Δa_e and other electron-related bounds.
axioms (2)
  • domain assumption ALP is a light pseudoscalar with the specified flavor structure and possible invisible decays
    Invoked throughout the framework to enable the LFV mediation and decay channels.
  • standard math Standard model background processes and nuclear effects are negligible or correctly subtracted in the rate calculation
    Assumed when isolating the ALP contribution to the transition rate.
invented entities (1)
  • Axion-like particle with flavor-violating e-μ couplings no independent evidence
    purpose: To mediate the μ^- e^- → e^- e^- process in muonic atoms
    Postulated in the simplified framework; no independent falsifiable evidence provided beyond consistency with constraints.

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discussion (0)

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