{"id":"0baf206a-34de-4d7b-990d-c8c199013c75","arxiv_id":"1908.03413","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"Under a thermally optimistic 20 MeV core model, nine years of Fermi data on 17 dark pulsars set an axion mass upper limit of 9.6e-3 eV, but realistic cooler cores suppress the signal to undetectability.","lead":"The paper searches for axions produced in pulsar cores by analyzing nine years of Fermi gamma-ray data toward 17 radio pulsars and finds no signal. It reports a stricter upper limit on the axion mass than previous work, but also shows that the limit relies on an unrealistically hot pulsar core and that realistic temperatures would make the predicted signal negligibly small.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline axion mass limit rests on a 20 MeV core temperature that the paper itself shows is inapplicable to its old pulsar sample; at realistic temperatures the claimed factor-of-8 improvement evaporates.","rationale":"The reader's weakest-assumption analysis identifies exactly the load-bearing issue: the 9.6e-3 eV limit derives from a 20 MeV core temperature that the paper itself shows is inapplicable to its sample of old pulsars. This is not a peripheral concern but a direct threat to the central claim, because the flux model's normalization, S_sigma, is exponentially sensitive to Tc, and the sample ages preclude such high temperatures. The paper contains independent confirmatory value: the Fermi-LAT analysis appears carefully done, the reproduction of the [12] emissivity plot lends credibility to the Monte Carlo method, and the explicit temperature scaling in Fig. 4 provides the evidence needed to demonstrate the fragility of the headline result. However, the Abstract presents the 9.6e-3 eV limit without the crucial caveat, and the Conclusions similarly state it as a result before discussing its invalidity at realistic temperatures. The reader's CONDITIONAL verdict is appropriate: the central claim should be reframed to separate the conditional limit under the 20 MeV assumption from the realistic conclusion that the method is temperature-limited. Our proposed check would quantitatively confirm the impact of the temperature choice by recalculating Eqn. 8 with the reduced S_sigma, making the concern concrete and testable. We therefore see no need to change the reader's verdict; the concern, while real, is already captured by the CONDITIONAL classification.","tokens_in":18919,"tokens_out":4236,"duration_ms":44081,"concrete_test":"Re-evaluate Eqn. 8 for pulsar J0108-1431 using its UL photon flux from Table V (1.75e-9 cm^-2 s^-1) with the same 20 MeV inputs, but replace S_sigma(100 MeV) by its value at Tc = 4 MeV using the factor 10^8 reduction shown in Fig. 4. If the resulting UL ma increases from the tabulated ~6.9e-3 eV to ~3 eV, the abstract's 9.6e-3 eV limit is an artifact of the 20 MeV assumption and does not constrain axions for realistic pulsar cores.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The Abstract's central result, ma <= 9.6e-3 eV at 95% CL, is derived from Eqn. 8 using the flux model of [12], which assumes Tc = 20 MeV and mu/T = 10. Section VI.B of the same paper demonstrates that this assumption is not valid for the sample: all 17 pulsars have characteristic ages > 10^5 yr (Table I), and cooling models (Nomoto & Tsuruta; Yakovlev & Pethick) give Tc <= 17 keV at 10^5 yr, with inferred internal temperatures near 0.1 keV for the oldest pulsars such as J0953+0755. The paper's own Monte Carlo calculation (Fig. 4) shows that lowering Tc from 20 MeV to 4 MeV reduces axion emissivity - and therefore the predicted gamma-ray flux in Eqn. 6, which scales with S_sigma(2E) - by a factor of 10^8 at omega = 100 MeV. Since Eqn. 8 scales as [flux / S_sigma]^(1/3), the resulting UL ma would grow by roughly (10^8)^(1/3) ~ 460, pushing the limit to ~1 eV or above, far from the claimed 9.6e-3 eV and outside the classic axion window. This is an internal inconsistency between the Abstract/Conclusions and Section VI.B, not merely a disagreement with external cooling rates: the paper's own alternative model (Eqn. 11) already gives UL ma ~ 0.7 eV at 20 MeV for radiative decay (point C, Fig. 5), a factor ~70 above the headline limit. The central numerical claim is therefore not robust; it is an artifact of a temperature assumption the authors themselves argue is implausible for these old pulsars.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper analyzes 9 years of Fermi-LAT Pass 8 data (60–500 MeV) for 17 radio pulsars that are not detected in gamma rays, determines 95% confidence flux upper limits, and converts these into upper limits on the QCD axion mass using a published model [12] in which axions are produced by nucleon-nucleon bremsstrahlung in a pulsar core at a fixed temperature Tc = 20 MeV. The authors obtain an average upper limit ma < 9.6 × 10^-3 eV at an axion energy of 100 MeV, which they describe as a factor-of-8 improvement over the previous limit. They also study the temperature dependence of the axion emissivity with a Monte Carlo evaluation of the spin structure function, showing that at Tc = 4 MeV the emissivity is suppressed by about 10^8 at ω = 100 MeV, and they propose an alternative energy-loss-rate model that gives limits in the eV range at realistic core temperatures. The paper concludes that the 20 MeV model is not applicable to the old pulsars in the sample and that future MeV missions would be needed to improve constraints.","tokens_in":19303,"tokens_out":3551,"duration_ms":38064,"significance":"The Fermi-LAT analysis itself is careful and useful: the flux upper limits are derived with standard tools, the stacking procedure is clearly described, and the comparison with [12] for the four overlapping pulsars provides a sanity check. The Monte Carlo recomputation of ω^4 S_σ(ω) as a function of Tc is a valuable contribution, since it quantifies how strongly the axion flux depends on the assumed core temperature. If the headline mass limit were robust, it would be a meaningful step in axion searches. However, as the authors themselves argue in Section VI.B, the Tc = 20 MeV assumption is not appropriate for their pulsar sample, and the central numerical claim therefore rests on an internal inconsistency rather than on a defensible astrophysical model. The alternative model (Eq. 11) contains a free conversion probability and an ad hoc 0.25 correction factor, so it does not provide a precise limit either. The paper is best viewed as a negative result: current Fermi-LAT observations do not robustly constrain axion masses for realistic pulsar core temperatures, and the paper's real value is in demonstrating the strong temperature sensitivity of the expected signal.","major_comments":[{"comment":"The headline limit ma = 9.6 × 10^-3 eV is obtained from Eq. (8) using values of S_σ(2E) that are valid only for Tc = 20 MeV (and μ/T = 10). In Section VI.B the paper itself shows that all pulsars in Table I have characteristic ages exceeding 10^5 years, and that cooling models place their core temperatures at tens of keV at most, with even the youngest plausible temperature being orders of magnitude below 20 MeV. Figure 4 then shows that lowering Tc from 20 MeV to 4 MeV reduces ω^4 S_σ(ω) by a factor of 10^8 at ω = 100 MeV. Since Eq. (8) scales as [flux / S_σ]^(1/3), the corresponding mass limit would grow by roughly (10^8)^(1/3) ≈ 460, pushing the limit to ~1 eV or above. This is an internal inconsistency: the abstract and conclusions present an improved limit, while the paper's own temperature analysis demonstrates that the underlying model is not applicable to the same pulsars. The central claim therefore needs to be reframed or dropped.","section":"Abstract and Section VI.B, Eq. (8)"},{"comment":"The alternative model for UL ma relies on Eq. (9), which includes an unexplained multiplicative factor of 0.25 that is labeled as a soft-neutrino approximation correction. This factor is not derived from any calculation in the paper, and it directly changes the numerical limits by a factor of 2 in mass (since ma scales as the square root of the emissivity). Furthermore, the axion-to-photon conversion probability Pa→γ is treated as a free parameter varied from 0.001 to 1, and the paper explicitly declines to provide a preferred value. Consequently, the alternative model yields only a range of indicative limits (0.1–70 eV depending on Tc and Pa→γ), not a constraint. The paper acknowledges this, but the abstract's statement that this model yields a 'plausible UL ma of 10^-6 eV' requires assumptions about both Tc and Pa→γ that are not established; as the text itself notes, at Tc = 0.1 MeV with radiative decay the limit is 67.5 eV, and even total conversion gives only 3 eV at Tc = 1 keV.","section":"Section VI.B, Eq. (11) and Figure 5"},{"comment":"The stacking result of ma < 4.8 × 10^-3 eV is presented as a two-fold improvement over the average limit, but the stacking procedure sums individual likelihood profiles without examining whether the 17 pulsars have independent systematic uncertainties or whether the five pulsars with >3σ residuals (Section V.C) bias the stacked flux. The five pulsars have higher UL fluxes; omitting them changes the average from 9.6 × 10^-3 to 8.9 × 10^-3 eV, which is small. The methodological concern is that the stacked limit is quoted as if it were a single-source limit, while the underlying pulsars have different distances, spectral assumptions, and background models; a more careful treatment would propagate these differences or explicitly state that the stack is only a shorthand. This does not change the qualitative conclusion, but it affects the precision of the central number.","section":"Section V.B and Table II/III"}],"minor_comments":[{"comment":"The first sentence of the Conclusions gives '0.96 and 3.21 × 10^-2 eV' for the two axion energies, but Table II and Section V.B give the average upper limits as 9.6 × 10^-3 eV and 3.21 × 10^-2 eV. The missing exponent on the first value is misleading and should be corrected.","section":"Section VII (Conclusions)"},{"comment":"The expression for p2 · p3 appears to have typographical errors: it reads 'p2p3cosαcosθ + sinα + sinθ + cosβ', but the correct form should contain products such as sinα sinθ cosβ. Please check and correct the equation.","section":"Appendix, Eq. (A.4)"},{"comment":"The numerical values of S_σ(2E) = 2.4 × 10^7 MeV^2 and 6.25 × 10^4 MeV^2 are stated as being read from a plot in [12]. These values should be reported with uncertainties or at least with a clear statement that they are extracted from a figure; a table with the Monte Carlo results would allow readers to reproduce Eq. (8) without re-digitizing the plot.","section":"Section II, Eq. (6) and (8)"},{"comment":"The stacked likelihood procedure sums the individual ΔLog(L) profiles to obtain a combined profile, assuming independence among the pulsars. The paper does not discuss whether the ROIs overlap (they may for nearby sources) or whether correlated systematic uncertainties affect the combined limit; a brief justification of the independence assumption would be helpful.","section":"Section IV.C"},{"comment":"The column headers 'B Surface' and 'B Light Cylinder' are ambiguous; it would be clearer to use 'Surface magnetic field (G)' and 'Light-cylinder magnetic field (G)'. Also the spin-down ages are listed as multiples of 10^5 yr, but the units are not explicitly stated in the header.","section":"Table I"},{"comment":"The discussion of pulsar cooling cites several models, but the conversion from surface temperature to core temperature uses a relation Tc ≈ 12 × (ST/10^6 K)^1.82 keV without stating the range of validity or the uncertainty on the exponent; a reference to the original derivation would be useful.","section":"Section VI.B"}],"recommendation":"major_revision","confidential_remarks":"The paper contains an honest and detailed discussion of the temperature problem in Section VI.B, but the abstract and conclusions still lead with the 9.6 × 10^-3 eV limit without sufficiently flagging that this limit is conditional on a 20 MeV core temperature that the authors themselves argue is unrealistic for the sample. The referee's view is that the manuscript would be acceptable if the authors reframed the paper as a negative result: namely, that current Fermi-LAT data do not constrain axion masses for realistic old pulsar temperatures, and that the 20 MeV model is disfavored by cooling considerations. The data analysis and the Monte Carlo temperature study are valuable and should be retained. The alternative model (Eq. 11) needs either a derivation of the 0.25 factor and a concrete treatment of Pa→γ, or it should be presented purely as an illustration of the sensitivities required. The paper's scope is appropriate for the journal; the issue is the overstatement of the central claim, not the quality of the analysis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I'll keep it short. The useful thing in this paper is not the headline mass limit—it's the demonstration that axion-decay gamma-ray searches from old pulsars are temperature-limited. The Fermi-LAT analysis is solid and the 17-pulsar upper limits look carefully derived. But the 9.6×10^-3 eV limit is a conditional number: it follows from Eqn 8 with the Berenji et al. model that assumes Tc=20 MeV, and Section VI.B shows that these pulsars, with ages >10^5 yr, have core temperatures more like 10 keV or below. At 4 MeV the emissivity is down by 10^8, which pushes the implied limit up by roughly two orders of magnitude. The paper says this clearly, so it's not a hidden flaw; it's an abstract that leads with a number the paper itself undermines. That should be reframed.\n\nWhat's genuinely new: the Monte Carlo calculation of the axion emissivity's temperature dependence (the 10^8 drop, Fig 4), and the alternative energy-loss model. The latter is only sketched, with an ad hoc 0.25 SNA factor and an unknown axion-to-photon conversion probability, so it doesn't yield a real bound. Also, part of the \"factor of 8 improvement\" over Berenji et al. comes from using their flux upper limits with a different mass formula, not from the new data alone—Table V shows similar gains. That's worth being candid about.\n\nThe paper is worth engaging with. It's a competent reanalysis with a useful negative result and a cautionary tale about model-dependent limits. But a referee should push for the abstract and conclusions to separate the conditional 20 MeV limit from the realistic-temperature conclusion, and to propagate systematic uncertainties into the mass limit. I'd send it to review with that expectation.","headline":"Competent Fermi-LAT reanalysis whose headline axion mass limit is conditional on a 20 MeV core temperature the paper itself shows is unrealistic; the real value is the negative temperature-sensitivity result.","tokens_in":19875,"tokens_out":2490,"would_cite":true,"duration_ms":26765,"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":"This paper uses nine years of Fermi-LAT data on 17 quiet pulsars to push the axion mass upper limit to $9.6\\times10^{-3}$ eV and then shows the temperature assumption behind that limit is likely unrealistic.","keywords":["axion","axion mass","pulsars","Fermi-LAT","gamma-ray upper limits","nucleon-nucleon bremsstrahlung","neutron star core temperature","axion-to-photon conversion"],"falsifier":"Measure or observationally bound the core temperature of one sample pulsar, say J0108-1431, via surface temperature observations and a temperature-to-core mapping. If $T_c \\lesssim 4$ MeV, the predicted axion-decay gamma-ray flux at 100 MeV drops by about $10^8$ relative to the 20 MeV model, so the non-detection can no longer support the $9.6\\times10^{-3}$ eV limit.","tokens_in":18690,"feed_emoji":"🛰️","tokens_out":7290,"duration_ms":69160,"temperature":0.7,"pith_summary":"This paper tries to use the absence of gamma rays from 17 nearby, radio-loud pulsars to weigh the axion, a proposed dark-matter particle. Analyzing nine years of Fermi-LAT data between 60 and 500 MeV, the authors see no pulsed or unpulsed emission and convert that silence into an upper limit on the axion mass of $9.6 \\times 10^{-3}$ eV at 95% confidence, eight times tighter than the previous limit. The limit, however, depends on assuming the pulsar cores sit at a high 20 MeV temperature; the paper itself computes that at the more realistic few-MeV temperatures, axion emission drops by eight orders of magnitude and the signal becomes undetectable. It therefore proposes an alternative energy-loss-rate model that could constrain axions down to $10^{-6}$ eV if the core temperature and axion-to-photon conversion in the pulsar's magnetic field were known.","feed_headline":"Gamma-ray silence tightens axion mass bound eightfold","feed_subtitle":"Nine years of Fermi data on 17 quiet pulsars push the axion mass bound to about 0.01 eV — but only if their cores are hot.","key_machinery":"The load-bearing object is the spin structure function $S_\\sigma(\\omega)$: a phase-space integral over the four nucleons participating in one-pion-exchange bremsstrahlung that fixes how many axions of energy $\\omega$ are produced. Its temperature dependence enters through the Fermi-Dirac occupation factors, and the axion emissivity scales as $\\int \\omega^4 S_\\sigma(\\omega)\\,d\\omega$. Combining $S_\\sigma$ with the axion decay rate gives the gamma-ray flux relation (the paper's Eq. 6) and hence the mass upper limit; a Monte Carlo evaluation of $S_\\sigma(\\omega)$ at lower temperatures is what exposes the $10^8$ suppression of the signal at 4 MeV.","core_discovery":"The central claim is that the non-detection of 60–500 MeV gamma rays from 17 gamma-ray-dark pulsars, stacked in likelihood, gives an upper limit on the axion mass of $m_a \\lesssim 9.6\\times10^{-3}$ eV (95% CL; $9.8\\times10^{-3}$ eV for the four pulsars studied previously), a factor-of-eight improvement over the earlier $7.9\\times10^{-2}$ eV. The argument runs through the axion-decay photon flux relation, in which the flux scales as $m_a^5$ and the emission timescale as $m_a^{-2}$, leaving $m_a \\propto \\Phi^{1/3}$. The authors also show that the 20 MeV core temperature on which this model rests is unrealistically high for pulsars older than $10^5$ yr: reducing the core temperature from 20 MeV to 4 MeV lowers the axion emissivity by a factor of $10^8$, making the predicted gamma-ray signal negligible. They conclude that the 20 MeV-based flux method cannot robustly constrain axions for realistic pulsars, and that a mass-based energy-loss model can reach $m_a \\sim 10^{-6}$ eV only with known core temperatures below 0.1 MeV and known axion-to-photon conversion.","pith_inferences":["If the 20 MeV assumption fails for old pulsars, the logical next target is young, hot neutron stars (ages $\\lesssim 10^3$ yr) such as Cas A, where the alternative model's $m_a\\sim10^{-6}$ eV reach could actually be tested with MeV-band observations.","The paper's own Monte Carlo integration of $S_\\sigma(\\omega)$ could be extended to compute predicted gamma-ray spectra for measured surface temperatures of the sample; that would turn a mass limit into a temperature-dependent exclusion plot.","The same silence-based method could be applied to magnetars, where high $B$-field conversion probabilities make axion-to-photon conversion a plausible signal channel, rather than relying on radiative decay alone.","A stacked likelihood analysis in the 0.2–10 MeV band could detect the axion-decay bump directly; a null detection there would push the constraint below the $10^{-2}$ eV scale without needing the 20 MeV assumption."],"forward_implications":["The 95% upper limit on the axion mass from stacking all 17 pulsars is $4.8\\times10^{-3}$ eV (at $\\omega=100$ MeV), a further factor-of-two improvement over the averaged value.","Because the axion spectrum peaks near photon energies $\\sim T_c$, a core temperature of order 1 MeV means any axion-decay signal appears below about 1 MeV, outside Fermi-LAT's band; this motivates medium-energy gamma-ray missions.","The alternative energy-loss model yields $m_a \\sim 10^{-6}$ eV for $T_c < 0.1$ MeV, but only if the axion-to-photon conversion probability in the pulsar magnetic field is known.","For magnetar-strength fields, published conversion probabilities (e.g. $P_{a\\to\\gamma}=0.225$ at $\\omega=3$ keV) would put constraints in the classic axion search range using this model.","No pulsar in the sample is detected as a point source; five apparent $>3\\sigma$ sources coincide with extended diffuse emission and are not claimed as detections."],"supporting_citations":[{"why":"Supplies the axion-decay gamma-ray flux model (Eq. 6) and the previous $m_a<7.9\\times10^{-2}$ eV limit that this work improves by a factor of 8.","marker":"[12]"},{"why":"Provides the axion emissivity expression and the soft-neutron-approximation reduction factor used in Eq. 5.","marker":"[15]"},{"why":"Gives the analytic simplification of the spin structure function $S_\\sigma(\\omega)$ that the Monte Carlo integration for low temperatures relies on.","marker":"[16]"},{"why":"Establishes the $T^6$ temperature dependence of axion emission rates that underlies the $10^8$ suppression at 4 MeV.","marker":"[17]"},{"why":"Provides the energy-loss-rate-per-mass formula and the spectrum peaking at $\\omega/T_c=2$ used for the alternative mass limit.","marker":"[19]"},{"why":"Gives the axion radiative decay rate used to convert energy loss into gamma-ray luminosity.","marker":"[20]"},{"why":"The pulsar catalogue from which the 17 pulsars and their distances, ages and spin-down properties are selected.","marker":"[21]"},{"why":"The Second Fermi-LAT pulsar catalogue used to exclude known gamma-ray pulsars from the sample.","marker":"[24]"},{"why":"Provides the Cas A cooling-based axion mass limit $(1.7-4.8)\\times10^{-2}$ eV used for comparison.","marker":"[48]"},{"why":"Supplies magnetar axion-to-photon conversion probabilities that indicate how the alternative model could reach the classic axion range.","marker":"[65]"}],"fun_headline_variants":["Axion mass bound tightened eightfold by pulsar silence","Quiet pulsars push axion mass limit to 0.01 eV","Gamma-ray gaps in pulsars refine axion mass constraint","Axion mass probe from dark pulsars: eightfold improvement","Hot pulsar cores essential for new axion mass limit"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole 20 MeV flux-based limit assumes the sample pulsars actually have core temperatures near 20 MeV; if their cores are as cool as the paper argues (a few MeV), axion emission is roughly $10^8$ times weaker and the derived mass upper limit does not constrain axions.","fun_headline_variants_meta":{"raw":{"variants":["Axion mass bound tightened eightfold by pulsar silence","Quiet pulsars push axion mass limit to 0.01 eV","Gamma-ray gaps in pulsars refine axion mass constraint","Axion mass probe from dark pulsars: eightfold improvement","Hot pulsar cores essential for new axion mass limit"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000274,"raw_usage":{"total_tokens":1739,"prompt_tokens":1143,"completion_tokens":596,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":759,"completion_tokens_details":{"reasoning_tokens":510}},"tokens_in":759,"tokens_out":596,"duration_ms":6187,"temperature":1.0,"reasoning_tokens":510,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:13:19.730062+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure or observationally bound the core temperature of one sample pulsar, say J0108-1431, via surface temperature observations and a temperature-to-core mapping. If $T_c \\lesssim 4$ MeV, the predicted axion-decay gamma-ray flux at 100 MeV drops by about $10^8$ relative to the 20 MeV model, so the non-detection can no longer support the $9.6\\times10^{-3}$ eV limit.","supporting_citations":[{"cited_title":"Sedrakian ,\\ title title Axion cooling of neutron stars , \\ https://doi.org/10.1103/PhysRevD.93.065044 journal journal Phys","cited_arxiv_id":null,"evidence_quote":"Supplies the axion-decay gamma-ray flux model (Eq. 6) and the previous $m_a<7.9\\times10^{-2}$ eV limit that this work improves by a factor of 8."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the axion emissivity expression and the soft-neutron-approximation reduction factor used in Eq. 5."},{"cited_title":"Hanhart , author D","cited_arxiv_id":null,"evidence_quote":"Gives the analytic simplification of the spin structure function $S_\\sigma(\\omega)$ that the Monte Carlo integration for low temperatures relies on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the axion radiative decay rate used to convert energy loss into gamma-ray luminosity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The pulsar catalogue from which the 17 pulsars and their distances, ages and spin-down properties are selected."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The Second Fermi-LAT pulsar catalogue used to exclude known gamma-ray pulsars from the sample."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Cas A cooling-based axion mass limit $(1.7-4.8)\\times10^{-2}$ eV used for comparison."},{"cited_title":"Perna , author W","cited_arxiv_id":null,"evidence_quote":"Supplies magnetar axion-to-photon conversion probabilities that indicate how the alternative model could reach the classic axion range."}],"review_version":1}