arxiv: 2605.00115 · v1 · submitted 2026-04-30 · ✦ hep-ph

Recognition: unknown

Crossing into the m_a > f_a Region for Leptophilic ALPs

Marta F. Zamoro , \'Alvaro Lozano-Onrubia , Luca Merlo , Samuel Rosende Herrero

Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:27 UTC · model grok-4.3

classification ✦ hep-ph

keywords leptophilic ALPsaxion-like particleselectron g-2 anomalyanomalous magnetic momentmuon to electron conversionALP parameter spaceeffective field theory

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The pith

Leptophilic ALPs with m_a exceeding f_a can explain the electron g-2 tension over a wide parameter range.

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

This paper challenges the standard assumption that the ALP mass must be much smaller than its decay constant. It performs a phenomenological analysis of leptophilic axion-like particles specifically in the regime where m_a exceeds f_a. The central finding is that such particles can account for the -3.8 sigma discrepancy in the electron anomalous magnetic moment as measured with caesium. This explanation occupies a substantial portion of the m_a by f_a plane. The scenario remains consistent with existing limits and can be directly tested by upcoming experiments measuring muon to electron conversion in nuclei.

Core claim

Axion-like particles are usually taken to satisfy m_a much less than f_a, but this restriction is conservative and leaves out viable space. For leptophilic ALPs we analyze the couplings to leptons in the previously unexamined region m_a greater than f_a. We find that these particles can resolve the -3.8 sigma tension in the electron anomalous magnetic dipole moment determined from caesium data across a large fraction of the m_a times f_a parameter space.

What carries the argument

The effective ALP-lepton couplings in a shift-symmetric effective field theory, extended to remain valid when the mass term dominates over the decay constant.

If this is right

The ALP-lepton couplings can be chosen to fit the electron g-2 tension while satisfying current bounds in the m_a greater than f_a region.
This opens a complementary slice of parameter space to standard ALP searches that assume m_a much less than f_a.
Near-future studies of muon to electron conversion in nuclei can confirm or exclude the proposed explanation.
The viable region includes cases where the ALP mass is comparable to or larger than the decay constant.

Where Pith is reading between the lines

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

ALP model building should drop the default restriction to m_a much less than f_a and consider the full plane of possibilities.
The same couplings might simultaneously address other lepton-flavor observables if the framework is extended.
Precision flavor experiments could map out the allowed coupling strengths and distinguish this scenario from alternatives.

Load-bearing premise

The effective field theory for leptophilic ALPs stays valid and can be tuned to match the observed g-2 tension without violating other experimental constraints even when the ALP mass exceeds its decay constant.

What would settle it

A measurement of the muon-to-electron conversion rate in nuclei that lies outside the range predicted by the ALP-lepton couplings needed to fit the electron g-2 tension.

Figures

Figures reproduced from arXiv: 2605.00115 by \'Alvaro Lozano-Onrubia, Luca Merlo, Marta F. Zamoro, Samuel Rosende Herrero.

**Figure 1.** Figure 1: ma × fa parameter space for the texture 3a), having fixed all the Lagrangian coefficients to c L = −c R = 1 (left) and to c L ii = −c R ii = 1 and c L ij = −c R ij = 0.1 (right). The darker (lighter) blue region denotes the parameter space excluded by present experimental constraints (future prospects), at 3σ. The red line represents the condition ma = fa. The gray region is excluded by the theoretical con… view at source ↗

**Figure 2.** Figure 2: ma × fa parameter space for the textures 2a) on the left and 2b) on the right, having fixed all the Lagrangian coefficients to c L = −c R = 1. The darker (lighter) blue region denotes the parameter space excluded by present experimental constraints (future prospects), at 3σ. The red line represents the condition ma = fa. The gray region is excluded by the theoretical consistency condition ma < 4πfa [PITH_… view at source ↗

**Figure 3.** Figure 3: Texture 2a). The c L µe × c R µe parameter space for fixed c L,R ii = 0. fa = 30 GeV in all the plots. ma = 130(180)[230] GeV in the plot on the left (centre) [right]. The coloured regions are excluded at 3σ by the current experimental bounds. To better examine the low scales allowed by this texture, [PITH_FULL_IMAGE:figures/full_fig_p025_3.png] view at source ↗

**Figure 4.** Figure 4: Texture 2b). Top row: c L µe ×c R µe parameter space for fixed c L ii = 1 = −c R ii. Central and lower rows: c L µe × c R µµ parameter space for fixed c L ii = 1 = −c R ij . In all three cases, the chosen values of ma (on top of the plots) increase from left to right. fa = 7 TeV in all the plots. The plots showcase the 3σ exclusion regions for the current (future) experimental bounds in darker (lighter) bl… view at source ↗

**Figure 5.** Figure 5: Texture 3a). Top row: c L µe ×c R µe parameter space for fixed c L ii = 1 = −c R ii. Central and lower rows: c L µe × c R µµ parameter space for fixed c L ii = 1 = −c R ij . In all three cases, the chosen values of ma (on top of the plots) increase from left to right. fa = 10 TeV in all the plots. The plots showcase the 3σ exclusion regions for the current (future) experimental bounds in darker (lighter) b… view at source ↗

**Figure 6.** Figure 6: Texture 3a). c L µe × c L µµ parameter space (for fixed c L ii = 1 = −c R ii). Top row: c R = −1 and fa = 10 TeV. Bottom row: c R = 0 and fa = 5 TeV. In all three cases, the chosen values of ma (on top of the plots) increase from left to right. The plots showcase the 3σ exclusion regions for the current (future) experimental bounds in darker (lighter) blue. Texture 3b) Adopting the same coupling structure … view at source ↗

**Figure 7.** Figure 7: Texture 3c). Top row: c L τµ×c R τµ parameter space. Bottom row: c L τµ×c R ττ parameter space. While the couplings that appear in the axes that are kept free, those ones that refer to the electron are fixed to c L = 10−4 = −c R and the rest are fixed to c L = 1 = −c R. fa = 250 GeV in all the plots. ma = 200(250)[300] GeV in the left (centre) [right] column. The plots showcase the 3σ exclusion regions for… view at source ↗

**Figure 8.** Figure 8: Texture 3d). Top row: c L τe×c R τe parameter space. Bottom row: c L τe×c R ττ parameter space. While the couplings that appear in the axes that are kept free, those ones that refer to the muon are fixed to c L = 10−4 = −c R and the rest are fixed to c L = 1 = −c R. fa = 250 GeV in all the plots. ma = 200(250)[300] GeV in the left (centre) [right] column. The plots showcase the 3σ exclusion regions for the… view at source ↗

**Figure 9.** Figure 9: ma × fa parameter space. The orange region identifies the parameter space where the Caesium anomaly can be solved at 3σ, with the black line representing the best fit values. The left plot refers to the texture 2a), while the right plot to the texture 3d). The darker (lighter) blue regions are excluded by the present experimental bound (by the future prospects) at 3σ. The red line represents the condition … view at source ↗

read the original abstract

Axion-like particles (ALPs) are typically identified as pseudoscalars whose couplings are shift-symmetry invariant with the exception of their couplings to gauge bosons and their mass term. Additionally, the ALP mass $m_a$ is usually assumed to be (much) smaller than the ALP decay constant $f_a$. The latter condition is conservative, at best, and excludes part of the ALP parameter space that is presently viable. We revisit the interpretation of the $m_a\ll f_a$ and perform an analysis focussing on leptophilic ALPs. In particular, we explore regions of the parameter space still uninvestigated, where $m_a>f_a$, thus providing a phenomenological study of the ALP-lepton couplings complementary to the existing literature. We point out that a leptophilic ALP may explain the $-3.8\sigma$ tension in the anomalous magnetic dipole moment of the electron for the Caesium determination in a large region of the $m_a\times f_a$ parameter space, testable in the near future through studies on $\mu\to e$ conversion in nuclei.

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.

Desk Editor's Note private letter to a colleague

The paper usefully scans leptophilic ALPs past the usual m_a << f_a limit and ties a slice to the electron g-2 tension, but the EFT justification in the m_a > f_a region is thin.

read the letter

The main point is that leptophilic ALPs can fit the electron g-2 tension from the Caesium data across a sizable m_a times f_a region even when the mass exceeds the decay constant, and that this slice can be tested soon with mu to e conversion searches. That is the practical takeaway for anyone tracking light pseudoscalars and lepton anomalies. The authors drop the standard m_a much less than f_a assumption, which they correctly note is conservative and leaves out viable space. They then run a focused analysis on the leptophilic couplings and show how the model can accommodate the -3.8 sigma discrepancy without immediate clashes with other bounds. This is the genuinely new element: an explicit look at the m_a > f_a regime for this class of ALPs, presented as complementary to prior work that stayed in the lighter-mass limit. They handle the phenomenological side cleanly by linking the parameter space directly to a near-term experimental channel. The connection to muon conversion experiments gives the claim a clear testability angle that the field can use. The soft spot is the effective theory itself. The usual Lagrangian with derivative couplings and a quadratic mass term assumes the mass is a small explicit breaking of the shift symmetry. Once m_a exceeds f_a the ratio is order one or larger, so higher-order operators in the potential or the lepton couplings are expected to enter at the same scale. These terms would modify the one-loop g-2 contribution and the conversion rate. The paper proceeds with the standard setup and treats m_a and f_a as independent inputs without showing that the cutoff stays well above the relevant momenta or that the results survive matching to a UV completion. That assumption carries the quantitative fit, and it needs explicit support. This is the sort of paper that ALP and BSM phenomenology groups will want to read, especially those following the g-2 anomalies and lepton-flavor searches. A reader who wants to see how the allowed space expands beyond the textbook limit will get something concrete from it. It deserves a serious referee. The core idea is straightforward, the experimental tie-in is timely, and the gap in the literature is real. A referee can press on the EFT validity and ask for the details of the fits and cutoff checks, but the work is worth the time. I would send it for peer review.

Referee Report

2 major / 1 minor

Summary. The manuscript performs a phenomenological study of leptophilic axion-like particles (ALPs) by relaxing the conventional m_a ≪ f_a assumption and exploring the m_a > f_a regime. It claims that in this extended parameter space a leptophilic ALP can account for the -3.8σ electron g-2 tension (Caesium determination) over a large region of m_a × f_a while satisfying other constraints, with near-term testability via μ → e conversion in nuclei.

Significance. If the effective-theory treatment remains valid, the result would be significant: it opens a previously excluded swath of parameter space for leptophilic ALPs to address the electron g-2 anomaly and supplies concrete, falsifiable predictions for upcoming μ → e conversion searches. The work is a useful complement to the existing literature that has focused on the m_a ≪ f_a limit.

major comments (2)

[§2] §2 (Effective Lagrangian): The standard shift-symmetric derivative couplings plus explicit mass term m_a² a²/2 with lepton couplings ∼ m_ℓ/f_a are applied directly for m_a/f_a > 1 without demonstrating that the EFT cutoff remains above the relevant scales or that higher-order operators in the potential and couplings remain negligible. This assumption is load-bearing for both the g-2 loop integral and the predicted μ → e conversion rate.
[§3] §3 (g-2 and conversion calculations): The quantitative fit to the -3.8σ tension and the exclusion plots treat m_a and f_a as independent inputs; no explicit matching to a UV completion or cutoff estimate is provided to justify that the one-loop results survive when m_a > f_a, which directly affects the size of the viable region claimed in the abstract.

minor comments (1)

[Abstract] Abstract: the sentence beginning 'We revisit the interpretation of the m_a ≪ f_a and perform an analysis' is grammatically incomplete and should be clarified.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We appreciate the positive assessment of the significance of exploring the m_a > f_a regime for leptophilic ALPs. Below we provide point-by-point responses to the major comments, with clarifications on the EFT assumptions and calculations.

read point-by-point responses

Referee: [§2] §2 (Effective Lagrangian): The standard shift-symmetric derivative couplings plus explicit mass term m_a² a²/2 with lepton couplings ∼ m_ℓ/f_a are applied directly for m_a/f_a > 1 without demonstrating that the EFT cutoff remains above the relevant scales or that higher-order operators in the potential and couplings remain negligible. This assumption is load-bearing for both the g-2 loop integral and the predicted μ → e conversion rate.

Authors: We thank the referee for raising this key point on EFT validity. Our analysis is a phenomenological study that adopts the standard leading-order ALP Lagrangian with explicit mass term and derivative couplings to leptons. The cutoff Λ is implicitly taken to lie above the relevant process scales (m_μ, m_e, and momentum transfers in μ→e conversion). Shift symmetry suppresses higher-dimensional operators in the couplings, while potential terms are suppressed by additional powers of 1/Λ. For the parameter space of interest, where f_a remains above ~100 MeV to satisfy existing bounds, the one-loop g-2 and conversion results are reliable within this EFT. We will add a dedicated paragraph in §2 estimating the cutoff (e.g., Λ ≳ 4π f_a) and discussing the regime of validity to make this explicit. revision: partial
Referee: [§3] §3 (g-2 and conversion calculations): The quantitative fit to the -3.8σ tension and the exclusion plots treat m_a and f_a as independent inputs; no explicit matching to a UV completion or cutoff estimate is provided to justify that the one-loop results survive when m_a > f_a, which directly affects the size of the viable region claimed in the abstract.

Authors: We agree that an explicit UV completion would strengthen the justification. As a phenomenological exploration, however, we follow the standard approach in the ALP literature of treating m_a and f_a as independent parameters within the EFT, without assuming a specific UV model. The one-loop g-2 integral and tree-level conversion rate are computed directly from the effective Lagrangian, and the viable region is presented under the assumption that the EFT remains valid. We will incorporate a brief cutoff estimate in the revised §3 (and cross-reference §2) to better delineate where the results hold, without altering the main conclusions or the size of the reported parameter space. revision: partial

Circularity Check

0 steps flagged

No circularity; direct parameter-space scan from standard EFT

full rationale

The paper applies the conventional shift-symmetric ALP Lagrangian (with explicit mass term) to compute the one-loop contribution to (g-2)_e and the μ→e conversion rate, then scans the m_a–f_a plane to identify viable regions that accommodate the Caesium anomaly. This is a standard phenomenological exercise whose outputs are not algebraically identical to its inputs; the g-2 tension is an external experimental datum, not a fitted parameter renamed as a prediction. No self-definitional equations, load-bearing self-citations, or ansätze imported from the authors’ prior work are required for the central claim.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities. The claim implicitly rests on standard ALP effective-field-theory assumptions whose validity in the m_a > f_a regime is precisely the point being revisited.

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discussion (0)

Reference graph

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