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Axion-like particles at colliders reduce to one shift-symmetric effective field theory, and this review lays out the full chain: operators, production, decay, lifetimes, and the current bounds on the ALP-photon coupling.

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A pedagogical review of the ALP effective field theory, production and decay at colliders, indirect search strategies, and a summary of current bounds on the ALP-photon coupling.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection A solid, clearly-written ALP collider review whose only real blemish is a units inconsistency between the Lagrangian definition of gaγγ and the headline figure axes. the 1 major comments →

arxiv 2508.19358 v1 pith:LK2M2CFL submitted 2025-08-26 hep-ph

Axions and Axion-like particles: collider searches

Anke Biek\"otter , Ken Mimasu This is my paper
classification hep-ph PACS 14.80.Va
keywords axion-like particlesALP effective field theorycollider phenomenologyshift symmetrypseudo-Nambu-Goldstone bosonsALP-photon couplingdisplaced searchesSMEFT interference
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This review aims to give a newcomer a working map of how to search for axion-like particles at high-energy colliders. It argues that the whole subject can be organized by a single ALP effective field theory in which the ALP is a shift-symmetric pseudo-Nambu-Goldstone boson whose derivative couplings are suppressed by a decay constant f. From that Lagrangian the review derives the production channels (gluon fusion, vector-boson fusion, associated production, decays of Z and Higgs), the decay widths and lifetime regimes (prompt, displaced, invisible), and the indirect probes (off-shell energy growth and ALP-SMEFT interference). The payoff is a set of collider bounds on the ALP-photon coupling, presented with the caveat that they assume only one coupling is present. A sympathetic reader would take the paper's central claim to be that this EFT-based, single-coupling picture is the right starting point, and that a global multi-coupling analysis is the necessary next step.

Core claim

The paper's central contribution is a self-contained presentation of ALP collider phenomenology built on the ALP-EFT of Eq. (11). The structural claim is that the ALP's shift symmetry forces its leading interactions to be derivative, with gauge couplings carrying an alpha/(4 pi) loop normalization and all couplings suppressed by 1/f; after electroweak symmetry breaking the two Wilson coefficients cBB and cWW produce four mass-basis couplings--ga gamma gamma, ga gamma Z, ga ZZ, ga WW--so the phenomenological couplings cannot be turned on independently. The review shows why production amplitudes grow with energy (similar to s/f^2 for the main 2-to-2 processes), why fermionic couplings are supp

What carries the argument

The engine is the ALP-EFT Lagrangian at dimension <= 6 written in the derivative basis: a SM-singlet pseudoscalar a with approximate shift symmetry a -> a + c, whose leading couplings are (a/f) F F-tilde gauge terms (with alpha/(4 pi) loop normalization) and derivative fermion currents, plus the dimension-six (partial a)^2 H-dagger H term. Field redefinitions show the redundant operator O_H can be removed while anomaly-induced shifts connect bases; this basis choice, the RG equations, and the effective couplings C_eff defined from on-shell three-point amplitudes carry the phenomenology. The specific mechanism that makes colliders powerful is the momentum-dependent a-X-X' vertex: amplitudes g

Load-bearing premise

The whole summary, especially the headline bound plots, assumes the Higgs is an ordinary SU(2) doublet (linear electroweak symmetry breaking) and that only the ALP-photon coupling is switched on; if the Higgs sector is non-linear or additional ALP couplings are present, the cross-section rankings and the displayed exclusions would change.

What would settle it

Measure pp -> a+Z in a mass range where the review's single-coupling benchmark fixes sigma(a+Z)/sigma(a+gamma) via Eq. (20); a rate incompatible with that ratio for the same mass and coupling would show the one-coupling assumption behind the headline bounds is violated. Equivalently, a search for a->Zgamma in the 10-100 GeV range that sees a signal where the ga gamma gamma-only plot predicts none would break the single-coupling picture the summary bounds assume.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Colliders are the decisive probes for ALP masses above roughly 100 MeV; the review's mass-dependent cross sections show where hadron, lepton, and ultra-peripheral collision searches each win.
  • Because ALP-gauge amplitudes grow with energy, a+gamma, a+Z, and vector-boson-fusion searches become more sensitive at higher centre-of-mass energies, so future colliders would extend the LHC-type bounds.
  • The ga gamma gamma summary bounds are conditional: a comparable ALP-gluon coupling would suppress the diphoton branching fraction by roughly alpha_s^2/alpha_EM^2 times the colour factor, making hadronic final states the relevant search channel instead.
  • Off-shell, virtual, and RG-mixed effects constrain ALP couplings even without direct production--top-philic ALPs are bounded by top-pair precision data in the intermediate mass window, and electroweak precision observables such as the W mass can bound cBB.
  • Because RG running turns a high-scale top coupling into a low-scale lepton coupling at roughly ten percent of its value, constraints on lepton couplings indirectly constrain otherwise inaccessible couplings.

Where Pith is reading between the lines

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

  • The single-coupling excluded regions in the bound plots are best read as benchmarks; a global fit over the full ALP parameter space would shift them, as the review's own caveats imply.
  • The photophobic limit cBB = -cWW is the natural test case for colliders: photon-based bounds vanish there, so a+Z, h->Za, and neutral VBF become the primary discovery modes.
  • The lifetime classification (prompt/displaced/invisible) could be turned into a systematic coverage map for future forward and far detectors, optimising search strategies over the (ma, ga gamma gamma) plane rather than relying on individual experiments' wedges.
  • The energy-growth argument implies a future 1 TeV lepton collider would test the a+gamma and neutral-VBF channels beyond LHC reach even where direct resonance searches are background-limited.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 5 minor

Summary. This review aims to provide a pedagogical entry point to ALP collider phenomenology. It motivates ALPs as pseudo-Nambu-Goldstone bosons, constructs the dimension-6 ALP-EFT in the linear electroweak-symmetry-breaking realization, discusses basis changes and renormalization-group evolution, reviews single-ALP production modes (gauge-boson couplings, fermion couplings, VBF, production in Z/H decays), decays and lifetimes in perturbative and chiral regimes, indirect/non-resonant probes and ALP-SMEFT interference, and closes with a summary of collider bounds on the ALP-photon coupling. The paper is explicitly a review: it collects formulas and references and does not present new predictions.

Significance. If the convention issue identified below is fixed, this will be a valuable and reliable review. The EFT definitions, basis-change relations (Eq. (17)), RG formulas (Eqs. (29)-(32)), decay widths (Eq. (44)) and chiral decay widths (Eqs. (45)-(47)) are consistent with the cited literature. The illustrative cross-section plots (Figs. 7, 8 and 10) are clearly computed with stated assumptions and coupling normalizations. The main strengths are the concise collection of formulas, the extensive reference list, and the explicit caveats about single-coupling assumptions and the choice of linear vs non-linear Higgs realization. The one serious defect is the untranslated unit convention in the headline summary plots, which currently prevents a newcomer from mapping the plotted bounds onto the Lagrangian in Eq. (19).

major comments (1)
  1. [Sec. 7; Figs. 1 and 14; Eqs. (19)-(20)] There is an inconsistency in the definition of the quantity plotted as |gaγγ| [GeV^-1]. In Eq. (19) the ALP-photon term is (a/f) gaγγ F F~, and Eq. (20) gives gaγγ = (α/4π)cγγ, i.e. gaγγ is dimensionless; production cross sections (Eqs. (40)-(41)) depend on gaγγ/f. The axes in Figs. 1 and 14, and the discussion in Section 7, instead use |gaγγ| in GeV^-1, which corresponds to the conventional normalization L = -(1/4) g_aγ a F F~ with g_aγ = gaγγ/f. The paper never states this conversion or the value of f used. Please define g_aγ (or relabel the axes and give the mapping g_aγ = gaγγ/f) in Section 7, and ensure the text's 'gaγγ, defined in Eq. (19)' refers to the plotted quantity. Without this, the headline bounds cannot be compared with the EFT Lagrangian.
minor comments (5)
  1. [Table 1] In the third column (N_f = 3, general case), the entries sum to 45 independent parameters (1 + 4 + 45 - 5), not 46 as shown in the 'total' row. Please correct the total or explain any additional redundancy.
  2. [Sec. 4.3] The sentence 'For couplings of order one' is imprecise: the plots use c_x/f = 1 TeV^{-1}, a dimensionful illustrative value. Rephrase to avoid implying c_x itself is unity.
  3. [Eq. (49)] The quantity defined as PDFdecay is a survival probability, not a probability density. Rename it or add a clarifying phrase.
  4. [Sec. 7 / Fig. 14] The experiment named 'PrimeEx' in the text appears as 'PrimEx' in Fig. 14; please unify the spelling.
  5. [References] Ref. [24] is a living online resource; please include an access date so the compiled bounds can be traced to a specific version.

Circularity Check

0 steps flagged

No significant circularity: the review's EFT framework, cross sections, decay rates, and bound summaries are either derived in the paper from first principles or assembled from independent, non-self-cited literature.

full rationale

This is a review article. Its central content is a pedagogical presentation of the ALP-EFT, production and decay formulas, and a compilation of collider bounds. The ALP Lagrangian in Eq. (11) is stated directly, and the subsequent mass-basis couplings, Feynman rules, cross sections, and decay widths follow from standard manipulations (EWSB, field redefinitions, and well-known phase-space calculations) performed in the text. For example, the production amplitude in Eq. (40) is written explicitly in terms of the gaγγ defined in Eq. (19), and the decay widths in Eq. (44) are written in terms of the effective couplings defined in Eq. (33); none of these reduce to a fitted value or to a self-citation. The summary bounds in Figs. 1 and 14 are explicitly adapted from Ref. [24], an external living-summary resource (O'Hare/AxionLimits), not from the authors' own fits. Self-citations occur (e.g., Refs. [23, 51, 62, 131, 141]) but they are not load-bearing: the statements they support are either derived in the paper itself or corroborated by independent works (e.g., Refs. [48, 136, 132, 133]). The ALP-SMEFT mixing discussion in Section 6.2 cites the external calculation [136] and uses Ref. [141] only as an illustrative global-fit application, not as the basis of the review's derivations. The apparent inconsistency between the dimensionless gaγγ in Eq. (19) and the GeV^-1 axes in Fig. 14 is a presentational/convention issue, not a circularity: it does not constitute a prediction that is equivalent to an input by construction. No fitted-input-called-prediction, self-definitional, or uniqueness-imported-from-authors pattern is present. Under the stated hard rules, a review that is self-contained against external benchmarks and whose self-citations are ancillary should receive a low score; here it receives zero.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

No new fitted parameters or invented particles. The ALP is the subject of the review, not introduced here. The only hand-chosen number is the illustrative benchmark cx/f = 1 TeV^-1.

free parameters (1)
  • cx/f (illustrative coupling) = 1 TeV^-1
    Hand-chosen benchmark used to compute the illustrative cross sections in Figs. 7 and 8. Not fitted to data and not a prediction.
axioms (5)
  • domain assumption ALPs are SM-singlet pseudoscalar pNGBs with an approximate shift symmetry and derivative couplings suppressed by a scale f.
    Section 1 and Eq. (11). This is the defining framework of the ALP-EFT reviewed in the paper.
  • domain assumption The review adopts a linear realization of electroweak symmetry breaking (SMEFT-like ALP-EFT), not HEFT.
    Section 1 states the linear realization may be restrictive but is used throughout; the non-linear ALP EFT is mentioned only in passing.
  • domain assumption ALP couplings are assumed CP-even with real Wilson coefficients in the fermion sector.
    Section 3: 'we focus on CP-even ALP couplings, i.e. we consider cF to have real entries only'.
  • domain assumption The summary of collider bounds assumes a single active ALP coupling (gaγγ) with all others set to zero.
    Section 7: 'the limits presented assume an ALP-photon coupling only, with all other ALP couplings set to zero'. The authors note this is not valid for generic ALP models.
  • standard math Perturbative EFT validity and standard QFT results (anomalies, one-loop matching) are taken as given.
    Used throughout Sections 3-6; no derivations are reproduced in the review.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Axions and Axion-like particles: collider searches." pith.science (2026). https://pith.science/paper/LK2M2CFL

@misc{pith2026250819358,
  author       = {Pith},
  title        = {Pith review of: Axions and Axion-like particles: collider searches},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LK2M2CFL}},
  note         = {Machine review of arXiv:2508.19358}
}
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read the original abstract

We give an overview of collider searches for Axion-like particles (ALPs). The intention of this review is to give a pedagogical introduction to collider phenomenology of ALPs, and provide a starting point for newcomers, including suitable references to deepen their knowledge. We motivate how ALPs arise from the breaking of approximate global symmetries and describe their interactions across different scales in an effective field theory framework. We further review the dominant production and decay channels for ALPs at high-energy hadron and lepton colliders as well as indirect ways to probe their interactions via precision measurements of Standard Model processes.

Figures

Figures reproduced from arXiv: 2508.19358 by Anke Biek\"otter, Ken Mimasu.

Figure 1
Figure 1. Figure 1: Summary of bounds on the ALP-photon coupling adapted from Ref. [24]. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: One-loop contributions to the RG running and matching of the ALP-lepton coupling from the ALP-top coupling. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Feynman diagram for fermion-anti–fermion initiated ALP production in association with a SM gauge boson, [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Feynman diagrams depicting ALP production via VBF. (a) Partonic contribution to non-exclusive VBF production. The emitting [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Feynman diagrams for the rare ALP-production modes sensitive to the four-point interactions with gauge bosons that only depend [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Feynman diagrams for ALP production in association with a fermion-anti–fermion pair via an (a) fermion-anti–fermion initial state [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Cross sections in femtobarn for ALP production modes in 13 TeV proton-proton collisions. For each process, a single relevant ALP [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Cross sections in attobarn for ALP production modes in lepton anti-lepton collisions at various center-of-mass energies. For each [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Sample Feynman diagrams contributing to e [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Partial decay widths in individual two-body decay channels of the ALP. Bosonic and fermionic modes are represented by solid and [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Different kinematic regimes relevant for ALP decays, adapted from [127]. where ⃗pa,lab denotes the ALP momentum in the lab frame. The probability density of an ALP decaying after traveling a distance l is given by an exponential function exp(−l/la). For a detector of size Ldet, the probability density is PDFdecay(ma, Ldet) = exp − maLdetΓ tot |⃗pa,lab| ! . (49) In case a single channel contributes to the … view at source ↗
Figure 12
Figure 12. Figure 12: Schematic Feynman diagram for the 2 → 2 scattering of SM gauge bosons mediated by an ALP with momentum-dependent couplings. Since the ALP-fermion couplings are proportional to fermion masses (see Eq. (27)), amplitudes involving two fermions and two gauge bosons will instead scale with (mf p)/ f 2 , and four-fermion amplitudes will tend to a constant ∼ m 2 f / f 2 , like for a Higgs-boson mediated amplitud… view at source ↗
Figure 14
Figure 14. Figure 14: Bounds on the ALP-photon couplings shown in Fig. 1, zooming into the high mass region and focusing on collider experiments, [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗

discussion (0)

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Forward citations

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This paper was first reviewed by deepseek-v4-flash on August 5, 2026.