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REVIEW 3 major objections 3 minor 86 references

Concurrent Exploration of Axion-Like Particle Interactions with Gauge Bosons at the LHC

T0 review · 3 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper derives expected and observed 95% CL limits on axion-like particle couplings to gluons and W bosons using pp to ZZa, pp to WWa, and V-plus-jets channels, claiming access to previously unexplored parameter space.

desk verdict A competent ALP simulation study undone by an internal contradiction: the (cWW, cGG) contours lie in parameter space already excluded by the paper's own cγγ bound. read the letter →

arxiv 2505.21305 v2 pith:26EXPIB6 submitted 2025-05-27 hep-ph

Shirin Chenarani , Mojtaba Mohammadi Najafabadi This is my paper
classification hep-ph
keywords axion-likeparticleALPeffectiveLagrangianmissingtransverseenergyLHCsearchesHL-LHCprospectsZplusjetsrecastWtwo-dimensionalexclusionlimits
verification ladder T0 review T1 audit T2 compute T3 formal

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 paper argues that a 1 MeV axion-like particle that escapes an LHC detector as missing energy can be probed simultaneously for its couplings to gluons and to W bosons using two complementary production modes: associated production with a ZZ or WW pair, and associated production with a single Z or W plus jets. The authors generate signal and background events with detector simulation, train a boosted decision tree to separate them, and produce expected 95% confidence level exclusion contours in the two-dimensional ($c_{WW}/f_a$, $c_{GG}/f_a$) plane for the HL-LHC. They also recast CMS differential cross section measurements for Z+jets and W+jets to obtain observed limits from 13 TeV data. If these results hold, a large region of ALP coupling space not covered by earlier single-coupling searches becomes testable at the LHC.

What carries the argument

The central object is the dimension-5 effective ALP Lagrangian with couplings to gluons ($c_{GG}$), W bosons ($c_{WW}$), and hypercharge ($c_{BB}$), plus a Yukawa-type term; after electroweak symmetry breaking, $c_{WW}$ and $c_{BB}$ combine into the physical couplings that appear in $ZZa$ production. The mechanism is the long-lived ALP signature: because the 1 MeV ALP decays dominantly to photons with a width scaling as the third power of its mass, it escapes the detector and shows up as missing energy, so $VV+a$ and $V$+jets final states are searched as missing-energy-plus-dilepton or diboson topologies. The discriminator is a boosted decision tree over kinematic variables, with limits derived by the CLs method on its output; for $V$+jets the signal is overlaid on CMS differential transverse momentum distributions and constrained by a chi-squared fit. The paper deliberately restricts the signal to diagrams with three effective ALP vertices, arguing that the single-coupling $q\bar{q}\to ZZa$ subprocess contributes less than one percent of the signal rate and would bias the two-dimensional interpretation.

What would settle it

Regenerate the $ZZa$ signal with the $q\bar{q}\to ZZa$ subprocess included and only $c_{WW}$ non-zero, run the same boosted decision tree and CLs pipeline, and compare the resulting contour with Fig. 7; if the acceptance in the high-$m_{ZZ}$ signal region is not below about one percent of the signal, the claimed two-dimensional exclusions move and the central claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the two channels constrain $c_{WW}$ and $c_{GG}$ together rather than one at a time, and that doing so opens previously unexplored parts of the ALP parameter space. For a 1 MeV ALP, the decay length is so large that the particle appears as missing transverse energy, and pp to ZZa and pp to WWa production via gluon fusion with three effective ALP vertices provide clean multilepton or semileptonic final states. A boosted decision tree trained on missing energy, lepton invariant masses, transverse momentum sums, and related variables separates signal from Standard Model backgrounds, and the CLs procedure yields 95% CL expected exclusion contours at integrated luminosities of 138 $fb^{{-1}}$ and 3 $ab^{{-1}}$. Reinterpreting CMS Z+jets and W+jets differential transverse momentum measurements with a chi-squared fit gives observed constraints, with Z+jets the more sensitive of the two; the paper concludes that a significant region of previously unprobed parameter space becomes accessible.

Load-bearing premise

The exclusion contours assume that the single-coupling $q\bar{q}\to ZZa$ subprocess can be dropped and that signal event kinematics do not depend on the values of $c_{WW}$ and $c_{GG}$; if either assumption fails, the contours would not equal the true 95% CL limits of the full ALP model.

Editorial extensions

If this is right

  • Expected 95% CL exclusion contours in the $(c_{WW}/f_a, c_{GG}/f_a)$ plane are provided for $ZZa$ with fully leptonic and semi-leptonic final states and for $WWa$ with the fully leptonic final state, at 138 fb^{-1} and 3 ab^{-1}.
  • Observed limits from CMS Z+jets and W+jets differential cross sections constrain the same two couplings with 13 TeV data, and projected HL-LHC fits reach ALP couplings of order $10^{-3}\ \mathrm{TeV}^{-1}$.
  • The Z+jets channel is more sensitive than W+jets for these couplings, mainly because its fiducial region has a larger ALP signal fraction, more integrated luminosity, and cleaner muon-based observables.
  • The results are almost unchanged for sub-MeV ALP masses, so the contours effectively cover lighter ALPs produced in these topologies.
  • Both analyses constrain $c_{WW}$ and $c_{GG}$ simultaneously, so they complement single-coupling searches and can be combined to tighten the overall bounds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the neglected $q\bar{q}\to ZZa$ subprocess is included with only $c_{WW}$ non-zero, the low-coupling end of the exclusion contours could narrow toward a single-coupling band; testing this would clarify how model-dependent the two-dimensional interpretation is.
  • The same CMS differential distributions could be refit for ALP masses above 1 MeV to map where the missing-energy interpretation breaks down as prompt decays become important.
  • A combined fit of the $VV+a$ expected limits and the $V$+jets observed limits into one contour would quantify how much the two channels tighten the bound in their overlap region.
  • The paper's assumption that signal kinematics are independent of the coupling values could be checked by comparing boosted decision tree responses generated at different $(c_{GG}, c_{WW})$ points; differences would change the acceptance correction and shift the contours.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The manuscript studies a 1 MeV axion-like particle in the dimension-5 ALP effective field theory of Eq. (6). It generates pp -> ZZa and pp -> WWa events with two non-zero couplings, cWW and cGG, applies Delphes fast simulation with the CMS card, and uses a BDT to separate signal from SM backgrounds. It derives expected 95% CL exclusion contours in the (cWW/fa, cGG/fa) plane for integrated luminosities of 138 fb^-1 and 3 ab^-1, and also interprets CMS Z+jets and W+jets differential cross sections to obtain observed constraints and HL-LHC projections. The paper claims that the VVa and V+jets channels are complementary and that together they make a significant region of previously unexplored ALP parameter space accessible.

Significance. If the limits were correct, the paper would be a useful addition to the ALP search program: it provides a complete Monte Carlo chain (FeynRules/MadGraph/Delphes/TMVA/RooStats) and reinterprets public CMS measurements, which is a reproducible and low-cost way to constrain ALP couplings to gluons and W bosons simultaneously. The two-channel complementarity is a genuine strength. However, two load-bearing assumptions currently invalidate the presented contours as limits on the full ALP EFT: the assumed cBB=0 scenario is inconsistent with the paper's own cγγ bound, and the neglected q qbar -> ZZa subprocess dominates in the low-coupling region that the limits claim to reach. The central numerical results therefore need to be rederived under a consistent parameter-space definition before the claimed sensitivity can be accepted.

major comments (3)
  1. [Section 2, Eq. (8), and Section 4.1 / Figs. 7 and 10] The analysis assumes two non-zero coefficients, cWW and cGG, with cBB=0. With cBB=0, Eq. (8) gives cγγ/fa = sin^2(theta_W) cWW/fa, numerically about 0.23 cWW/fa. Section 2 quotes the experimental bound cγγ/fa < 1e-9 TeV^-1 for ma=1 MeV, which implies cWW/fa below about 4.3e-9 TeV^-1. The contours in Figs. 7 and 10 extend to cWW/fa values of order 1e-3 and above, i.e., many orders of magnitude above this bound. For those points the ALP is not long-lived: the lower bound of Eq. (13) no longer applies, the missing-energy interpretation of the signal fails (or the invisible-ALP rate is suppressed by the decay probability), and the region is already excluded by ALP-photon searches. The abstract's claim of access to 'previously unexplored parameter space' is therefore not supported for the cBB=0 scenario. The authors should impose the cγγ constraint explicitly, for example by allowing cBB = -tan^2(theta_W) cWW to cancel cγγ, or restrict the limits to the allowed region, and recompute the contours accordingly.
  2. [Section 3] The exclusion of the q qbar -> ZZa subprocess is justified only by a benchmark comparison at cGG = cWW = 0.5 TeV^-1, where the retained three-vertex process has 2.27 pb and the omitted process has 0.0122 pb. The scaling quoted in the same paragraph, |M|^2 ∝ c_GG^4 c_WW^2 for the retained process and ∝ c_WW^2 for the omitted one, shows that the omitted process dominates at the smaller couplings that the limits actually reach. For example, at cWW = cGG = 0.1 TeV^-1 the retained rate is suppressed by (0.2)^6 relative to the benchmark while the omitted rate is suppressed only by (0.2)^2, making them comparable; at cWW/fa = 1e-3, which Section 7 cites as the reach of the V+jets analysis, the omitted process exceeds the retained one by several orders of magnitude. Thus Figs. 7 and 10 are not limits on the full ALP model of Eq. (6), but only on a subset of diagrams, and the low-coupling parts of the contours are not robust.
  3. [Section 5] The limit derivation assumes that signal event kinematics do not depend on the values of the non-zero Wilson coefficients, but no closure test is presented. The BDT response distributions in Fig. 6 and the efficiencies in Table 1 are obtained for a single benchmark with cWW = cGG = 0.1, while the contours in Fig. 7 scan a wide range of coupling values and ratios. The squared matrix element contains terms with different coupling scalings and different Lorentz structures, so the shapes of /ET, mZZ, and pT^ZZ can vary across the plane; this would change BDT efficiencies and hence the effective signal yield at each point. A quantitative check of the BDT efficiency at several points in the (cWW, cGG) plane is needed before these contours can be interpreted as 95% CL limits over the full shown range.
minor comments (3)
  1. [References] Reference [81] appears corrupted: 'ZZa L. Moneta' should presumably read 'A. L. Moneta'.
  2. [Section 4.2] The EFT validity condition is written as '2/EmaxT < fa'; the use of the slash for missing transverse energy makes the inequality hard to parse. Please clarify the notation, e.g., as 2 E_T^max < f_a if that is the intended condition.
  3. [Table 1 and author line] Table 1 has a formatting problem: the signal row labels run together with the first background column (e.g., 'ZZa(SR1)ZZ'), making the table difficult to read. The author line also contains a spacing error ('andMojtaba').

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the expected and observed limits are independent Monte Carlo projections and public-data recasts; the cγγ/cWW inconsistency is a physical-consistency flaw, not a circular reduction.

full rationale

The central derivation is self-contained. The Section 5 limits come from Monte Carlo event generation (FeynRules/MadGraph/Pythia/Delphes) followed by a CLs likelihood using simulated signal and background yields, not from fitting the ALP couplings to the same observable being predicted. The Section 6 limits are a recast of public CMS Z+jets and W+jets differential measurements using the quoted chi-squared statistic, which is a standard reinterpretation and not circular. Self-citations (Refs. [31-36]) appear only in general parameter-space reviews or as comparison bounds (e.g., Ref. [35] for ttbar/tW limits) and are not load-bearing for the new contours; no fitted parameter is relabeled as a prediction, and no uniqueness theorem or ansatz is imported from prior work by the same authors. There is, however, a non-circular internal-consistency problem: with cBB=0, Eq. (8) gives cγγ/fa = s_theta^2 cWW/fa ≈ 0.23 cWW/fa, so the cited exclusion cγγ/fa > 1e-9 TeV^-1 (Section 2) already rules out cWW/fa above about 4e-9 TeV^-1, while the presented contours and the text quote sensitivity down to cWW/fa around 1e-3 TeV^-1. This undermines the abstract and Section 7 claim of a 'significant region of previously unexplored parameter space' and is a serious correctness risk, but it is not a case of the prediction being equivalent to its input by construction.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The results rest on a standard ALP EFT, an invisibility assumption carried over from prior experimental bounds, and several simplifying choices: a restricted amplitude set, a one-coupling-at-a-time signal grid in the recast, leading-order normalization, and a flat or omitted theory uncertainty. These are inputs the reader must accept before the quoted contours can be taken at face value.

free parameters (4)
  • Overall systematic uncertainty = 10% on signal and background yields
    Chosen by hand in Section 5 to cover detector effects; removing it changes limits by 5-10%.
  • ALP mass = 1 MeV
    Benchmark mass chosen in Sections 3-6; authors argue limits are approximately mass-independent for sub-GeV ALPs.
  • EFT validity cut factor = sqrt(s-hat) < 2 Emax_T (printed as 2/Emax_T)
    Hand-chosen proxy in Section 4.2 for the condition sqrt(s-hat) < fa; as written the formula is dimensionally inconsistent.
  • BDT output threshold = not specified
    Section 5 defines the signal region by a threshold on the BDT output but does not state the threshold value or how it is chosen.
assumptions (7)
  • domain assumption The effective Lagrangian in Eq. (6) (from Ref. [23]) is the correct description of ALP interactions with SM fields.
    All signal predictions are made with this EFT; no alternative model is considered.
  • domain assumption For ma=1 MeV, the ALP is invisible at the LHC because the prior bound cγγ/fa < 1e-9 TeV^-1 forces a decay length above 1e23 m.
    Section 2 uses Eq. (13) and the bound to define the MET signature; if the bound is evaded, the analysis would not target the right final states.
  • ad hoc to paper Only cGG and cWW are non-zero; cBB and caPhi are set to zero in the limit extraction.
    The 2D limits in Figs. 7 and 10 are derived under this assumption; the paper argues cBB is weakly constrained and caPhi is Yukawa-suppressed.
  • ad hoc to paper The subset of signal diagrams with three effective ALP vertices is a complete and gauge-invariant representation of the signal.
    Section 3 excludes the single-coupling qq->ZZa process without demonstrating the gauge invariance or completeness of the remaining set.
  • ad hoc to paper Signal kinematic distributions do not depend on the values of the non-zero Wilson coefficients.
    Explicitly assumed in Section 5 so one BDT can be applied over the whole coupling grid.
  • domain assumption Leading-order event generation without k-factors is adequate for signal and background yields.
    Section 4.1 generates everything at LO; no scale or PDF uncertainty is propagated to the limits.
  • domain assumption In the V+jets recast, CMS measurements are background-only and the ALP signal adds linearly without interference; no theory uncertainty on the SM prediction is included.
    Section 6 equation (14) builds the chi-square this way and uses only CMS uncertainties for delta_i.

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Pith. "Pith review of Concurrent Exploration of Axion-Like Particle Interactions with Gauge Bosons at the LHC." pith.science (2026). https://pith.science/paper/26EXPIB6

@misc{pith2026250521305,
  author       = {Pith},
  title        = {Pith review of: Concurrent Exploration of Axion-Like Particle Interactions with Gauge Bosons at the LHC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/26EXPIB6}},
  note         = {Machine review of arXiv:2505.21305}
}
abstract

Axion-like particles (ALPs) are pseudo Nambu-Goldstone bosons associated with spontaneously broken global symmetries incorporated in the Standard Model (SM) Lagrangian in many models beyond the SM. The existence of a light ALP is plausible due to the long-standing problems that the SM has not been able to address, such as the dark matter (DM) problem and the observed matter-antimatter asymmetry. There are many proposals in recent decades considering the ALP as a solution to some of these shortcomings. Motivated by such potential, we search for ALPs with a mass of 1 MeV at the LHC in a model-independent fashion. We explore two complementary production modes: ALP production in association with a pair of electroweak gauge bosons ($ZZ$ or $WW$) and ALP production in association with a single gauge boson ($W$ or $Z$) plus jets. For the $VV+a$ final state, signal and dominant SM backgrounds are generated, and a realistic detector response simulation is performed. A multivariate analysis is employed to discriminate the $VV+a$ signal from background processes, and the expected $95\%$ confidence level (CL) exclusion limits in two-dimensional parameter spaces involving the ALP couplings are subsequently derived. The $V$+jets channel is interpreted using LHC measurements in regimes where the ALP escapes detection, appearing as missing energy. The two analyses are complementary: both the $VV+a$ and the $V$+jets channels probe simultaneously the ALP couplings to gluons and to electroweak gauge bosons. While the $VV+a$ channel offers clean multi-lepton final states and direct reconstruction of the $ZZ$ or $WW$ system, the $V$+jets channel benefits from larger production cross sections, enabling stronger constraints in certain regions of the parameter space.

Figures

Figures reproduced from arXiv: 2505.21305 by the authors.

Figure 1
Figure 1. Representative Feynman diagrams contributing to the associated production of an ALP with two electroweak gauge bosons, WW or ZZ, at the leading order at a proton-proton collider. where ⃗pa is the ALP three-momentum. Based on the current experimental limits, the parameter space region cγγ/fa > 1 × 10−9 TeV−1 has been experimentally excluded for an ALP of mass 1 MeV [29, 46]. Using Eq. 12 and the upper limit on cγγ/fa… view at source ↗
Figure 2
Figure 2. Leading-order cross sections of the processes pp → WW a (left) and pp → ZZa (right) as a function of cWW assuming √ s = 14 TeV, ma = 1 MeV and two non-zero Wilson coefficients at a time. study. The production cross section for the process pp → ZZa exhibits a dependence on the Wilson coefficient cBB, as detailed in Eqs. 7 and 8 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Leading-order production cross section of the pp → ZZa as a function of cWW and cBB assuming cGG = 0.5 TeV−1 and ma = 1 MeV. weaker compared to cWW . This can be attributed to the specific coupling structure inherent to the interaction terms, particularly the presence of a suppression factor proportional to sin2 θW (denoted s 2 θ ) in the cBB contribution to cZZ. In contrast, the cWW contribution involves a factor o… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Distributions of the discriminating variables for the signal and background processes obtained for the SR1 signal region in the ZZa analysis. The signal and the total background distributions are normalized to unity. power for the ZZa SR1 analysis. The discriminating v…
Figure 5
Figure 5. Figure 5: Distributions of the discriminating variables for the signal and background processes obtained in the WW a analysis. The signal and the total background distributions are normalized to unity. signal from background in both the WW a and ZZa analyses. The only source of …
Figure 6
Figure 6. Figure 6: shows the obtained results for the ZZa SR1, ZZa SR2 and WW a analyses. As seen, (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Expected 95% CL limits in the cWW -cGG plane corresponding to ma = 1 MeV obtained in the ZZa SR1, ZZa SR2 and WW a analyses assuming an overall uncertainty of 10% on the signal and background event selection efficiencies. The presented limits are based on the integrate…
Figure 8
Figure 8. Figure 8: Representative leading order Feynman diagrams for production of an ALP in association with Z+jets (top) and W+jets (bottom) at the LHC. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Left: The measured differential cross section as a function of the Z boson pT for Z+jets with the SM expectation and theoretical prediction of Z+jets+ALP where ALP escape detection and appears as missing transverse momentum. Right: Differential cross section measuremen…
Figure 10
Figure 10. Figure 10: Observed 95% CL limits in the cWW -cGG plane corresponding to √ s = 13 TeV and ma = 1 MeV obtained from the measurement of the CMS experiment on Z+jets and W+jets taken from Refs.[88, 89]. The projected bounds corresponding to Lint. = 3 ab−1 for the HL-LHC are display…

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