{"id":"c0ac28bd-59c7-45de-bb6a-b469b75c321f","arxiv_id":"2411.18246","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A TeV-scale model with vector-like leptons and a Peccei-Quinn scalar predicts a GeV ALP with tunable couplings, while resolving the muon g-2 and neutrino-mass puzzles.","lead":"The paper presents a model where a light GeV-scale axion-like particle (ALP) emerges from TeV-scale exotic leptons, while also explaining the muon g-2 anomaly and small neutrino masses. A generalist might read it to see how one model can tie together three open puzzles in particle physics: the muon g-2 discrepancy, neutrino masses, and the origin of a light axion-like particle.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central GeV-ALP prediction rests on three one-loop formulas (Eqs. 5–7) that are stated without derivation; the paper's own caveat about the Mψ=Λ limit makes the leading-order ALP mass uncontrolled in part of the advertised parameter space.","rationale":"The reader identified the validity of the one-loop expressions as the weakest assumption, and my read agrees. The central claim is not internally inconsistent: Eq. (5) is dimensionally consistent, the μ_R dependence is plausible for a one-loop formula, and the quoted benchmark gives m_a of order a few GeV when estimated from the stated ingredients. The concern is therefore not that the paper is wrong on its face, but that the proceedings do not contain enough information to verify the formulas on which the entire claim stands. The paper's own admission that the leading ALP mass vanishes at Mψ=Λ sharpens this: there is a region of the advertised parameter space where the prediction is controlled only by an unstated NLO term. This justifies a conditional verdict and a concrete re-derivation test, but it does not justify rejecting the model. If the parent paper [2] contains the full derivation and the formulas match, the central claim would be established; if not, the GeV-mass window is unsupported.","tokens_in":4647,"tokens_out":22527,"duration_ms":217101,"concrete_test":"Independently re-derive Eq. (5) from the one-loop Coleman-Weinberg potential of the neutral mass matrix Mχ in Eq. (2), keeping full Mψ and Λ dependence, and evaluate m_a at the benchmark Λ=1500 GeV, Mψ=600 GeV, m_V=m_V'=17 GeV, f_a=Mψ√2, for several renormalization scales μ_R between 500 GeV and 2 TeV. If the result differs from Eq. (5) by more than a factor of two, or if the NLO contribution changes m_a by more than O(1) at Mψ=1.1Λ, the proceedings' central prediction is not established. Separately, compute the triangle diagram for Eq. (7) and compare its coefficient, especially the denominator Y_V+(Mψ/Λ)Y_V'.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline claim, 'we obtain a mass of the ALP of O(GeV) for a scale f_a~TeV', is carried entirely by Eq. (5), which is introduced as the result of a Coleman-Weinberg calculation but is not derived in this document. The ALP-muon coupling of Eq. (7), the second phenomenological pillar, is likewise stated as the outcome of an unspecified 'full 1-loop calculation'. The paper's own caveat at the end of §2.2 — 'it vanishes for Mψ=Λ, thus the NLO contribution would be necessary' — shows that the leading expression is not uniformly valid over the parameter space that the figures scan: near the diagonal Mψ≈Λ the entire ALP mass comes from an unspecified higher-order term. Moreover, Eq. (5) is renormalization-scheme dependent through μ_R, and no μ_R choice or error estimate is given, so the numerical contours of Figs. 1 and 2 cannot be reproduced from this document alone. If Eq. (5) or Eq. (7) contains a missing diagram, an incorrect coefficient, or a sign error, the O(GeV) mass window and the 'many orders of magnitude' coupling range would shift or collapse. This is a correctness risk, but it is also a checkable one; nothing internal to the paper forces a contradiction.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This proceedings contribution presents an extension of the Standard Model with two right-handed neutrinos, a vector-like electroweak lepton doublet, and a complex scalar singlet φ carrying a U(1)PQ charge. The authors focus on 'Model B', in which the vector-like mass is generated dynamically from <φ>, while the HNL mass scale Λ remains a free parameter. They claim that explicit PQ-breaking terms in the Lagrangian generate, at one loop, an ALP mass of order GeV for f_a ~ TeV, with an ALP-muon coupling that can span many orders of magnitude. The model is also proposed as a solution to the muon g−2 anomaly and accommodates neutrino masses through the linear seesaw. The paper presents the relevant mass matrices, quotes one-loop formulas for the muon mass, ALP mass, ALP-gauge couplings, and ALP-muon coupling, and shows parameter-space regions satisfying perturbativity, neutrino-mass, and (g−2)_μ constraints, together with existing bounds from ALP searches.","tokens_in":5067,"tokens_out":11542,"duration_ms":108748,"significance":"If the quoted one-loop results are correct, the model is phenomenologically interesting: it connects a GeV-scale ALP with TeV-scale new fermions and a TeV-scale axion-decay constant, producing testable predictions for collider and beam-dump searches. The ALP mass and couplings are derived quantities rather than fits to ALP data, so the 'predicted mass' claim is not circular. The paper also makes good use of existing experimental limits and explicitly flags the caveat that lattice QCD may contradict the (g−2)_μ anomaly. However, the central one-loop formulas are quoted without derivation, and the admitted NLO sensitivity near Mψ=Λ leaves a part of the advertised parameter space uncontrolled; the manuscript is therefore not yet self-contained enough for the headline prediction to be independently validated.","major_comments":[{"comment":"The ALP mass formula is the load-bearing quantity for the headline claim of O(GeV) mass for f_a ~ TeV, but it is stated only as the result of an unspecified Coleman-Weinberg calculation. The expression depends on the renormalization scale μ_R, and the paper gives no choice of μ_R or an estimate of the associated uncertainty, so the contours in Figs. 1 and 2 cannot be reproduced from this text alone. More importantly, the authors note immediately after Eq. (5) that the leading-order result vanishes at Mψ = Λ; in any region of Fig. 1 near that diagonal, the entire ALP mass comes from an unspecified NLO contribution. Since the central claim is a prediction of the mass range, the authors should either provide the derivation or the precise corresponding equations in Ref. [2], specify the μ_R choice, and explain how the NLO region is handled, or restrict the claimed parameter space to where the leading-order expression is controlled.","section":"§2.2, Eq. (5)"},{"comment":"The value of Y_V' used in Eq. (7) is fixed by requiring the muon mass and the (g−2)_μ anomaly, so the plotted 'many orders of magnitude' range of g_{aμμ} is contingent on the anomaly being a real target. The footnote correctly acknowledges that recent lattice results contradict the anomaly, but if those results survive, the model no longer 'solves' (g−2)_μ and the dotted/dashed regions of Fig. 1 acquire a different meaning. The authors should present the allowed parameter space also under the alternative assumption that δaμ is only an upper bound, so that the ALP-coupling prediction is disentangled from the fate of the anomaly.","section":"§3, Fig. 1 and Eq. (7)"},{"comment":"The quoted one-loop muon pole mass contains an explicit dependence on μ_R. A physical pole mass should be renormalization-scale independent at the considered order after all contributions are included; if this expression is instead the running MS-bar mass or an approximation, that should be stated and the chosen scale given. This matters because the relation between m_μ and Y_V' determines a substantial part of the phenomenological analysis.","section":"§2.1, Eq. (4)"},{"comment":"The restriction of the Coleman-Weinberg computation to 'the neutral sector' is asserted but not justified. As printed in Table 1, the charged-sector operator Y_R ψ_L H μ_R in Eq. (1) carries a nonzero PQ charge (μ_R is assigned n_{ψ_L}), so it can in principle contribute to the ALP potential. Please state the PQ charge relations that make the charged sector PQ-invariant or negligible at one loop, or include its contribution in the quoted formula.","section":"§2.2, Eq. (5)"}],"minor_comments":[{"comment":"The notation φ^{(*)} is used without specifying the mapping between the sign of x or y and the choice of φ versus φ^*; please define this explicitly for each of the four realisations.","section":"Eq. (1)"},{"comment":"The definition δ_{x,1} ≡ sgn(x) δ_{|x|,1} is nonstandard: since x ∈ {0, ±1}, this is simply x. The notation invites confusion with an ordinary Kronecker delta and should be simplified or clearly motivated.","section":"End of §2.2"},{"comment":"The statement that recent lattice calculations contradict the (g−2)_μ anomaly is made without a reference; please provide one so that the caveat can be checked.","section":"Footnote 1"},{"comment":"The notation Y_{V,V'} ⊂ [0.05, 0.4] and α_{N,ψ} > 0.5 should use standard set-membership notation (e.g., ∈), and the caption should state whether all constraints are applied simultaneously.","section":"Fig. 2 caption"},{"comment":"The sentence 'the HNLs live in the TeV-scale' is imprecise: Λ is a free TeV-scale mass, but in the benchmark of Fig. 2 Mψ = 600 GeV. Please rephrase to distinguish the two mass scales.","section":"Conclusions"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings contribution that relies heavily on the companion paper [2] (arXiv:2402.14059) for the derivations of Eqs. (4)-(7). If that companion paper has already passed peer review, some of the missing derivation may be acceptable for a proceedings; however, the Editor may wish to confirm the status and availability of [2] before publication. The lattice g−2 caveat should not remain only a footnote, since it directly affects the interpretation of Fig. 1."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: this is a conference proceedings summarizing the authors' own earlier full paper (arXiv:2402.14059). It doesn't claim to add results, and it doesn't. What it does give is a compact statement of a model where a GeV-scale ALP emerges radiatively, with f_a as low as a TeV, from an exotic lepton sector that also addresses the muon g-2 anomaly and neutrino masses.\n\nThe model building is coherent: a complex scalar singlet with a PQ charge, vector-like doublet leptons, and two heavy right-handed neutrinos. The idea that the ALP mass is generated by explicit PQ-breaking terms and can be O(GeV) with f_a ~ TeV is worth knowing about. The paper honestly flags that recent lattice results contradict the g-2 anomaly, and says that if confirmed, g-2 would become a bound rather than a motivation. That is candid. The figures show surviving parameter space, and the message that the model is testable at the TeV scale is clear.\n\nThe soft spot is exactly where the stress test points. The central predictions rest on three one-loop formulas, Eqs. (5)-(7), that are stated with no derivation and no explicit renormalization scale. Eq. (5) vanishes at M_psi = Lambda, so the leading order is not controlled there, and the paper itself says NLO is necessary. That means the O(GeV) mass contours in Fig. 1 cannot be reproduced from this document alone, and any missing diagram or wrong coefficient in the parent paper would shift or collapse the parameter space. None of this is internal contradiction; it is a checkable correctness risk. The proper referee target is the parent paper, not this proceedings.\n\nAlso minor: the muon coupling g_a_mu_mu is promoted as spanning many orders of magnitude, but part of that spread is just the scan over Y_V with Y_V' fixed to fit m_mu and g-2. Not a flaw, just context.\n\nVerdict: for a proceedings, this is an adequate summary. I'd send the full paper [2] to a serious referee; this one deserves a quick consistency check against [2] and publication in the proceedings if that checks out. I would not cite the proceedings in my own work; I'd cite [2].","headline":"A clean proceedings summary of the authors' own full paper; the model is interesting and honestly flagged, but the central loop formulas are asserted, not derived, so the real referee target is the parent paper.","tokens_in":5540,"tokens_out":2332,"would_cite":false,"duration_ms":20871,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A GeV-scale axion-like particle is the predicted consequence of a TeV-scale extension of the Standard Model built from vector-like leptons and explicit Peccei-Quinn breaking.","keywords":["axion-like particle","Peccei-Quinn symmetry","vector-like leptons","muon g-2","linear seesaw","Coleman-Weinberg potential","heavy neutral leptons","collider phenomenology"],"falsifier":"Recompute the ALP mass from the full two-loop effective potential in Model B and check whether $m_a$ stays in the GeV range when $M_\\psi \\approx \\Lambda$; if it does not, the predicted parameter space collapses. Independently, confirmation of the lattice value of the muon $g-2$ would remove the anomaly this model is built to explain, turning the claimed signature into a constraint.","tokens_in":4434,"feed_emoji":"⚛️","tokens_out":4944,"duration_ms":43610,"temperature":0.7,"pith_summary":"This paper tries to establish that a GeV-mass axion-like particle (ALP) is not an add-on but a predicted consequence of a TeV-scale extension of the Standard Model built to explain the muon $g-2$ anomaly and small neutrino masses. In the proposed model, explicit Peccei-Quinn symmetry-breaking terms in an exotic leptonic sector generate a radiative ALP mass that lands at $\\mathcal{O}(\\text{GeV})$ when the ALP decay constant $f_a$ is as low as the TeV scale. Because the ALP couplings to muons and photons are generated at one loop, they can vary over many orders of magnitude, which is unusual for ultraviolet constructions. If correct, the model is testable at current and near-future colliders, since the predicted ALP mass and coupling region has not yet been excluded.","feed_headline":"TeV-scale leptons predict a GeV axion-like particle","feed_subtitle":"Explicit PQ breaking in an exotic lepton sector yields a light ALP with $f_a \\sim$ TeV, testable at colliders.","key_machinery":"The argument is carried by the one-loop Coleman-Weinberg effective potential of the neutral sector, Eq. (5), which converts the explicit Peccei-Quinn breaking into a radiative ALP mass, and by the one-loop triangle diagrams that produce the ALP couplings to photons, $Z$, $W$, and muons, Eqs. (6) and (7). The mass formula vanishes at $M_\\psi = \\Lambda$, so the paper acknowledges that the next-to-leading order contribution becomes necessary there. The relation between $\\delta a_\\mu$ and the muon mass fixes one Yukawa coupling, $Y_V'$, once $Y_V$ is chosen in the $(M_\\psi, \\Lambda)$ parameter space.","core_discovery":"The central claim is that a GeV-scale ALP emerges naturally from a TeV-scale model where two heavy right-handed neutrinos and a vector-like electroweak lepton doublet are added to the Standard Model, together with a complex scalar singlet whose Peccei-Quinn symmetry is spontaneously broken. Explicit $U(1)_{\\rm PQ}$-breaking terms in the heavy lepton sector generate the ALP mass radiatively, with $m_a \\sim \\mathcal{O}(\\text{GeV})$ for $f_a \\sim \\text{TeV}$. The ALP couplings to gauge bosons and to muons are generated at one loop, and the ALP-muon coupling can span several orders of magnitude. The model also provides a linear seesaw origin for active neutrino masses and resolves the muon $g-2$ anomaly through electroweak vector-like lepton contributions, while the ALP contribution to $g-2$ itself is negligible.","pith_inferences":["If the one-loop mass formula survives an independent check, the model predicts a concrete target region ($m_a \\sim \\text{GeV}$, $f_a \\sim \\text{TeV}$) that could be probed by beam-dump or forward-physics experiments, not only by LHC vector-boson-scattering searches.","The continuous span of $g_{a\\mu\\mu}$ means the same model could be tuned to evade current direct searches while still producing visible signatures in loop-induced processes; a dedicated scan over $Y_V$ could reveal whether such tuning is required.","If the lattice value of the muon $g-2$ is confirmed, the model's motivation shifts from explaining an anomaly to being constrained by it, and the ALP parameter space may become a target for exclusion rather than discovery.","The vanishing of the mass formula at $M_\\psi = \\Lambda$ suggests an accidentally light ALP at that special point; a dedicated study of the NLO effective potential near this point could determine whether a large portion of parameter space actually contains a GeV ALP."],"forward_implications":["The ALP mass is radiatively generated and is not tied to $f_a$, so a TeV-scale $f_a$ naturally produces a GeV-scale ALP that is accessible to collider searches.","The ALP couplings to $W$, $Z$, and photons are one-loop generated and suppressed by $f_a$, with non-resonant LHC searches bounding $f_{aWW} \\geq 1.7$ GeV and $f_{aZZ} \\geq 1.3$ GeV.","The ALP-muon coupling $g_{a\\mu\\mu}$ can be continuously varied over many orders of magnitude, distinguishing this model from generic ultraviolet ALP constructions.","The muon $(g-2)_\\mu$ anomaly is resolved by electroweak contributions from the vector-like leptons, while the ALP contribution is negligible.","Neutrino masses arise from the linear seesaw mechanism, tying the heavy neutral lepton scale to $\\Lambda \\sim \\text{TeV}$."],"supporting_citations":[{"why":"Supplies the underlying low-scale seesaw model and the electroweak contribution that drives $(g-2)_\\mu$.","marker":"[1]"},{"why":"Companion paper containing the full analysis of all four model realisations; this proceeding reports Model B.","marker":"[2]"},{"why":"Gives the LHC non-resonant ALP search bounds used to set the $f_{aWW}$ and $f_{aZZ}$ limits.","marker":"[3]"},{"why":"Provides the axion/ALP exclusion plot used to compare $g_{a\\gamma\\gamma}$ with $m_a$.","marker":"[4]"}],"fun_headline_variants":["GeV axion from TeV leptons","TeV leptons yield GeV axion","Heavy leptons, light axion","Light axion from heavy leptons","TeV-scale leptons spawn GeV axion"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The prediction rests entirely on one-loop expressions for the ALP mass and couplings that are stated without derivation; if those calculations contain an error, or if the neglected higher-order terms become large where the two heavy masses are equal, the GeV ALP may not exist.","fun_headline_variants_meta":{"raw":{"variants":["GeV axion from TeV leptons","TeV leptons yield GeV axion","Heavy leptons, light axion","Light axion from heavy leptons","TeV-scale leptons spawn GeV axion"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000518,"raw_usage":{"total_tokens":2479,"prompt_tokens":883,"completion_tokens":1596,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":499,"completion_tokens_details":{"reasoning_tokens":1529}},"tokens_in":499,"tokens_out":1596,"duration_ms":13202,"temperature":1.0,"reasoning_tokens":1529,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:25:08.882573+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the ALP mass from the full two-loop effective potential in Model B and check whether $m_a$ stays in the GeV range when $M_\\psi \\approx \\Lambda$; if it does not, the predicted parameter space collapses. Independently, confirmation of the lattice value of the muon $g-2$ would remove the anomaly this model is built to explain, turning the claimed signature into a constraint.","supporting_citations":[{"cited_title":"The Low-Scale Seesaw Solution to the $M_W$ and $(g-2)_\\mu$ Anomalies","cited_arxiv_id":"2211.03797","evidence_quote":"Supplies the underlying low-scale seesaw model and the electroweak contribution that drives $(g-2)_\\mu$."},{"cited_title":"cajohare/axionlimits: Axionlimits","cited_arxiv_id":null,"evidence_quote":"Provides the axion/ALP exclusion plot used to compare $g_{a\\gamma\\gamma}$ with $m_a$."}],"review_version":1}