{"id":"75c1130f-10fe-4754-be9b-939df4796773","arxiv_id":"2507.08678","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A simulation study claims a future ILC run could discover the Einstein-Cartan dark gauge boson A' in the muon-pair plus missing-energy channel for most tested mass points.","lead":"This paper uses computer simulations and machine learning to estimate whether a proposed future electron-positron collider could discover a dark gauge boson predicted by a modified gravity theory. It reports that most of the model's benchmark points would be visible at 5-sigma significance within 500 inverse femtobarns of data.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The A'→μμ branching ratio is never defined: Section II gives A' a coupling only to dark fermions, so the σ×BR values and all discovery significances rest on an unspecified kinetic-mixing coupling.","rationale":"I read the paper in good faith. The simulation pipeline is coherent: WHIZARD + PYTHIA + Delphes is a standard setup, k-fold cross-validation is used, and the Kolmogorov-Smirnov tests in Figure 7 suggest the BDT is not grossly overtrained. The MVA machinery and the reported kinematic distributions are plausible. The decisive problem is upstream of the MVA: the Lagrangian in Section II does not contain an A'–μ+μ− coupling, so the muonic final state is justified only by an unquantified kinetic-mixing assumption. Since Table II's σ×BR values are the input to every significance calculation, the entire discovery claim inherits this missing ingredient. This is not a matter of disagreeing with the ECT framework or of demanding a different background model; it is an internal consistency and reproducibility issue. The reader identified this same weakest assumption, and I agree with that diagnosis. The concrete test of releasing the UFO files and recomputing BR(A'→μ+μ−) would settle whether the quoted cross-sections are meaningful. For now, the result should remain conditional rather than being accepted as a demonstrative discovery claim.","tokens_in":12637,"tokens_out":5113,"duration_ms":65429,"concrete_test":"Release the UFO implementation, or independently reconstruct it from an explicit Lagrangian that includes a defined kinetic-mixing term, and recompute the e+e−→ST→χχA'→χχμ+μ− cross-section for all ten benchmark points with gη=0.125, gD=1.2, Mχ=90 GeV, MST=1500/2000 GeV, and MA'=50–90 GeV. In particular, report BR(A'→μ+μ−) and verify that each σ×BR entry in Table II is reproduced. If the entries cannot be reproduced for any allowed mixing parameter, or if they shift by more than the quoted uncertainty, the claimed discovery significances in Table VI are not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that the ILC can discover the Einstein-Cartan dark gauge boson A' in the μ+μ− + EmissT final state. For that final state to exist, A' must decay to muons. Section II, however, defines no such coupling: Eq. (1) couples the torsion field Sμ to SM fermions ψ with strength gη, while Eq. (2) couples the dark fermion χ to Sμ and A' via gD. There is no term coupling A' to muons, and the kinetic mixing mentioned in the Introduction is never assigned a parameter or a value. Table II reports σ×BR for each benchmark, and Table VI derives all significances from those numbers, yet no branching ratio is computed, stated, or constrained. The UFO implementation was 'requested from the author of [13]' and is not included in the paper; the Data Availability Statement says the manuscript has no associated data. Consequently, every benchmark cross-section and every quoted significance depends on an unstated and unverified A'→μ+μ− assumption. If that branching ratio is small or the mixing is absent, the signal effectively disappears; if it is large, the model may conflict with existing limits. The central discovery claim is therefore not independently checkable from the paper as written.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a Monte Carlo study of the process e+e− → χχA′, A′ → μ+μ− at the ILC (√s = 500 GeV, L = 500 fb−1) within an Einstein-Cartan theory model with a torsion mediator. The authors generate SM backgrounds (Drell-Yan, WW, ZZ, t-tbar) and ten signal benchmark points with M_ST = 1500/2000 GeV and M_A′ = 50–90 GeV, apply Fisher, DNN, and BDT classifiers using nine kinematic variables, and report statistical significances between 1.22σ and 19.33σ after an optimized BDT cut. They conclude that most benchmark points are discoverable within 500 fb−1 and provide required luminosities for 5σ discovery.","tokens_in":12981,"tokens_out":5866,"duration_ms":75082,"significance":"If the model input and significance calculation were self-contained, this would be a useful projection for a low-mass dark gauge boson at a lepton collider. The MVA pipeline is conventional and reasonably documented: the paper gives a hyperparameter table, k-fold cross-validation, KS overtraining checks, ROC curves, and variable-ranking information. However, the central numerical claim currently rests on an unspecified A′→μμ branching ratio, on a statistical-only significance with an in-sample or unspecified cut-optimization procedure, and on an incomplete SM background list. These issues must be resolved before the quoted significances can be considered reliable; with the present text the discovery claim is not independently checkable.","major_comments":[{"comment":"No coupling of A′ to muons is defined. Equation (2) couples A′ only to the dark fermion χ through g_D, and Eq. (1) couples the torsion field to SM fermions; the kinetic mixing mentioned in the Introduction is never given a parameter, mass-mixing term, or numerical value. Table II nonetheless quotes σ×BR for A′→μ+μ−, and Table VI converts these numbers into discovery significances. Unless a kinetic-mixing coupling and the resulting BR(A′→μ+μ−) are specified, computed, and constrained, the signal rates and every significance in Table VI are not determined by the model as presented.","section":"Section II, Eqs. (1)–(3) and Table II"},{"comment":"The significance is computed as S = N_S / sqrt(N_S + N_B) using numbers of events after a BDT 'optimized cut,' but the paper does not describe how BDT_opt is selected or whether it is evaluated on an independent sample. If the cut is chosen to maximize the same quantity on the events that are then used for counting, the quoted significances are in-sample estimates and are biased upward. In addition, no systematic uncertainties are propagated into Eq. (6), despite the statement in Section III that systematic uncertainties were considered; the background counts after the BDT cut are as low as 70 events, so a modest systematic uncertainty or a background fluctuation would change several points by more than 1σ. The authors should use a likelihood-based or profile-likelihood significance, quantify all relevant systematic uncertainties, and validate the cut choice on a held-out sample.","section":"Section V, Eq. (6), and Table VI"},{"comment":"The SM background list omits e+e− → τ+τ− with both taus decaying leptonically to muons (τ → μνν). This process has the same μ+μ− + missing transverse energy signature as the signal and is not included in the total background. At √s = 500 GeV its contribution after the muonic branching fractions is expected to be comparable to or larger than the listed ZZ background and non-negligible relative to the signal rates in Table II. The authors should add this process to the background samples or provide a quantitative argument for its negligibility.","section":"Section III, Table I"},{"comment":"The ECT signal is generated with UFO files 'requested from the author of [13]' that are not included in the paper, and the Data Availability Statement says the manuscript has no associated data. Consequently the σ×BR values in Table II cannot be reproduced or cross-checked by a reader. The authors should provide the model files or, at minimum, a complete Lagrangian with all parameters, the derived BR(A′→μ+μ−), and a validation of the generator output against an independent calculation of the production cross-section.","section":"Section III and Data Availability Statement"}],"minor_comments":[{"comment":"The text calls S_μ the 'scalar torsion field (ST)' while Eq. (1) treats it as an axial-vector coupling (γ^μ γ^5 S_μ); the terminology is inconsistent and should be corrected.","section":"Section II"},{"comment":"There are several typos and spacing issues, e.g. 'MV A' for MVA, 'psuedo-rapidity', 'proved discoverable' (should be 'shown to be discoverable'), and 'Finally' in the Table VI caption.","section":"Throughout"},{"comment":"The y-axis labels such as '6.22 GeV / (1/N) dN' appear to be misplaced bin-width annotations; the axes should be labeled as normalized event counts per bin.","section":"Figure 3"},{"comment":"The legend entries 'S+B' and 'S/0' are not defined in the caption or text; presumably one is S/√(S+B), but this should be stated explicitly.","section":"Figure 9"},{"comment":"The statement that BMPs 5 and 9 may be reachable at √s = 1000 GeV and L = 1000 fb−1 is an extrapolation, since no simulation at that energy is presented; this should be phrased as a conjecture or supported by a dedicated study.","section":"Section V"}],"recommendation":"major_revision","confidential_remarks":"The paper is a phenomenological projection rather than a complete collider analysis, but it fits the journal's scope if the technical gaps are closed. The main concern is not circularity—the benchmark rates come from an external model, and the significance numbers are not derived from the target conclusion—but rather that the A′→μμ branching ratio is never defined. This is fixable in revision, as are the missing τ+τ− background and the absence of a systematic-uncertainty treatment, but all three affect the central claim. If the revised version does not quantify the branching ratio and systematics, or does not provide the model implementation for reproducibility, I would not be able to support publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a concrete and mostly readable sensitivity projection for a dark gauge boson A' from Einstein-Cartan theory at the ILC, using standard MVA tools. The genuinely new piece is a scan over A' masses from 50 to 90 GeV (with ST masses 1.5 and 2 TeV) in the muonic decay channel, which the authors' previous work did not cover. The simulation pipeline is coherent: WHIZARD, PYTHIA, DELPHES, TMVA. They document their observables, separating power, correlation matrices, and overtraining checks—more than many phenomenological studies do.\n\nThe main flaw is exactly the one a referee should press on: the paper never defines the A' -> mu+mu- coupling. Section II gives A' a coupling to dark fermions via g_D, and the torsion field couples to SM fermions via g_eta, but there is no term that lets A' decay to muons. The introduction mentions kinetic mixing, but no parameter is introduced, and no branching ratio is computed or stated. The signal cross-sections in Table II are labeled sigma x BR, yet the BR is not derived anywhere. The model implementation was requested from the author of [13] and is not included; the Data Availability statement says there is no associated data. So the central discovery numbers are not checkable from the paper alone. If the mixing is absent or small, the signal disappears; if it is large, the model could conflict with existing dilepton resonance limits. This is not a stylistic quibble—it is the load-bearing piece.\n\nThere are also smaller issues. The SM background list omits tau+tau- production, which gives the same mu+mu- plus missing transverse energy final state via leptonic tau decays; it is not huge, but it should be included. The BDT cut appears to be optimized on the same sample used to evaluate the significance, which introduces optimism; with k-fold CV they may have mitigated it, but they do not say. Systematic uncertainties are mentioned but not quantified, and the significance S = N_S/sqrt(N_S+N_B) is purely statistical. For a projection study that is acceptable, but it should be stated honestly.\n\nThe result is not circular: the signal rates are generated from the model parameters, not fitted to a target. The citations are appropriate, including their own earlier fixed-mass study.\n\nThis paper deserves peer review. It is a legitimate sensitivity estimate for a specific model, and the ILC physics case can use such inputs. But I would send it back for a revision that includes (or at least specifies) the A' decay model and the resulting branching ratio, the tau+tau- background, and a note on how the BDT cut was chosen. Without that, the quoted significances remain conditional.\n\nRecommendation: engage with it as a referee, but treat the central numbers as provisional until the model implementation is visible.","headline":"A solid MVA sensitivity projection for an Einstein-Cartan dark gauge boson at the ILC, but the quoted significances rest on an undefined A'->mu+mu- coupling; worth refereeing with a required revision.","tokens_in":13491,"tokens_out":4466,"would_cite":false,"duration_ms":52539,"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":"Machine-learning analysis finds 8 of 10 dark-boson points discoverable","keywords":["dark gauge boson","Einstein-Cartan theory","dark matter","International Linear Collider","multivariate analysis","boosted decision tree","muonic decay channel","missing transverse energy"],"falsifier":"Search for a di-muon resonance plus missing transverse energy in 500 fb$^{-1}$ of 500 GeV electron-positron collisions; if no excess appears at invariant masses from 50 to 80 GeV, the paper's discovery claim for the benchmark points is contradicted.","tokens_in":12467,"feed_emoji":"⚛️","tokens_out":11612,"duration_ms":113232,"temperature":0.7,"pith_summary":"The paper argues that a dark gauge boson called $A'$, predicted by an Einstein-Cartan extension of the Standard Model, can be discovered at a 500 GeV electron-positron collider through its decay into a muon pair. After training a boosted decision tree on nine kinematic variables, eight of ten benchmark mass points reach statistical significances between 5.87 and 19.33 $\\sigma$ with 500 fb$^{-1}$ of data. The reachable region covers $A'$ masses from 50 to 80 GeV with the heavy torsion mediator at 1.5 or 2 TeV. For the most favorable point a 5-$\\sigma$ discovery would need only about 33 fb$^{-1}$, so the search could succeed early in a collider run.","feed_headline":"Machine-learning analysis finds 8 of 10 dark-boson points discoverable","feed_subtitle":"Muonic decays of the A' yield up to 19-sigma significance at 500 GeV with 500 fb$^{-1}$.","key_machinery":"The carrying object is the signal topology $e^+e^- \\to ST \\to \\chi\\bar{\\chi} \\to \\chi\\bar{\\chi} A' \\to \\chi\\bar{\\chi} \\mu^+\\mu^-$, in which a heavy scalar torsion field $ST$ produces two dark fermions $\\chi$, one of which radiates $A'$ that decays to a muon pair. The discriminating engine is a boosted decision tree trained on nine observables: missing transverse energy, di-muon invariant mass, di-muon angular separation, azimuthal angle between the di-muon system and missing momentum, pseudorapidities and transverse momenta of the two muons, and the cosine of the 3D angle between the di-muon vector and missing momentum. The di-muon invariant mass has the largest separating power of any single variable.","core_discovery":"Within the Einstein-Cartan model, the paper's central claim is that the dark gauge boson $A'$ is visible above Standard Model backgrounds in the muon-pair-plus-missing-energy final state. Using a boosted decision tree, the analysis quotes discovery significances at 500 fb$^{-1}$ of 19.33, 17.07, 14.42, 11.20, 8.72, 7.01, and 5.87 $\\sigma$ for the benchmark points with $A'$ masses of 50, 60, 70, 80 GeV at mediator mass 1.5 TeV and 50, 60, 70 GeV at mediator mass 2 TeV. The two points with $A'$ at 90 GeV, where the di-muon invariant mass sits close to the $Z$ pole, fall below 5 $\\sigma$, and the heaviest point (90 GeV $A'$, 2 TeV mediator) is effectively unreachable.","pith_inferences":["The paper leaves the $A'$-muon kinetic-mixing term unspecified and the model implementation files unavailable, so re-deriving the cross-sections from the stated Lagrangian would be a direct check of whether the quoted significances survive.","The same classifier pipeline could be exported to other proposed lepton colliders, and the accessible $A'$ mass window would likely shift with center-of-mass energy while the analysis logic stays unchanged.","If the dark fermion mass were lowered so that $A'$ could decay invisibly, the clean muon-pair tag would disappear and the search would have to rely on missing-energy-only signatures such as mono-photon events."],"forward_implications":["If the central claim is correct, a 500 GeV electron-positron collider can probe Einstein-Cartan dark matter in a mass range that hadron colliders struggle to reach.","The required luminosity for 5-sigma discovery ranges from about 33 to 363 fb$^{-1}$ across the eight discoverable points, so most of the parameter space opens up before the full 500 fb$^{-1}$ dataset is collected.","$A'$ masses near the $Z$ mass are the difficult corner of the model, needing several times more luminosity or new discriminating variables to reach 5 sigma.","Before the boosted decision tree cut the signal is entirely hidden; the multivariate step is what actually makes the search sensitive."],"supporting_citations":[{"why":"This reference supplies the Einstein-Cartan model, the torsion-mediated production topology, and the couplings $g_\\eta$ and $g_D$ on which the signal cross-sections depend.","marker":"[13]"},{"why":"This reference defines the collider scenario at 500 GeV with the beam polarizations used in the simulation.","marker":"[29]"},{"why":"This reference sets the 500 fb$^{-1}$ luminosity goal adopted for the discovery potential.","marker":"[30]"},{"why":"This reference excludes low-mass dilepton resonances between 11.5 and 45 GeV, motivating the 50-90 GeV $A'$ mass window.","marker":"[31]"},{"why":"This reference reports a prior study of the same model at a 10 GeV $A'$ mass that constrains the free parameters used here.","marker":"[32]"},{"why":"This reference provides the Monte Carlo event generator used to produce signal and background event samples.","marker":"[33]"},{"why":"This reference provides the multivariate classifiers and the significance formula used to quote the discovery significances.","marker":"[36]"}],"fun_headline_variants":["ILC multivariate search finds 8/10 dark-boson masses above 5 sigma","Boosted trees reveal dark A' at ILC, top significance 19 sigma","Einstein-Cartan dark boson probed: 8 points discoverable at ILC","MVA at ILC spots dark gauge boson in muon channel, up to 19 sigma","Dark boson hunt with BDT: 8/10 masses pass 5-sigma at ILC"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire signal rate rests on unpublished model implementation files and on the assumption that $A'$ decays to muon pairs with the implied branching fraction; if either is wrong, every quoted cross-section and significance changes.","fun_headline_variants_meta":{"raw":{"variants":["ILC multivariate search finds 8/10 dark-boson masses above 5 sigma","Boosted trees reveal dark A' at ILC, top significance 19 sigma","Einstein-Cartan dark boson probed: 8 points discoverable at ILC","MVA at ILC spots dark gauge boson in muon channel, up to 19 sigma","Dark boson hunt with BDT: 8/10 masses pass 5-sigma at ILC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000359,"raw_usage":{"total_tokens":1949,"prompt_tokens":956,"completion_tokens":993,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":572,"completion_tokens_details":{"reasoning_tokens":874}},"tokens_in":572,"tokens_out":993,"duration_ms":10998,"temperature":1.0,"reasoning_tokens":874,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T18:14:11.869808+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Search for a di-muon resonance plus missing transverse energy in 500 fb$^{-1}$ of 500 GeV electron-positron collisions; if no excess appears at invariant masses from 50 to 80 GeV, the paper's discovery claim for the benchmark points is contradicted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference supplies the Einstein-Cartan model, the torsion-mediated production topology, and the couplings $g_\\eta$ and $g_D$ on which the signal cross-sections depend."},{"cited_title":"High Energy Phys","cited_arxiv_id":null,"evidence_quote":"This reference defines the collider scenario at 500 GeV with the beam polarizations used in the simulation."},{"cited_title":"High Energy Phys","cited_arxiv_id":null,"evidence_quote":"This reference sets the 500 fb$^{-1}$ luminosity goal adopted for the discovery potential."},{"cited_title":"Cvetiˇ c and S","cited_arxiv_id":null,"evidence_quote":"This reference excludes low-mass dilepton resonances between 11.5 and 45 GeV, motivating the 50-90 GeV $A'$ mass window."},{"cited_title":"Leike, Phys","cited_arxiv_id":null,"evidence_quote":"This reference reports a prior study of the same model at a 10 GeV $A'$ mass that constrains the free parameters used here."},{"cited_title":"Cvetiˇ c, P","cited_arxiv_id":null,"evidence_quote":"This reference provides the Monte Carlo event generator used to produce signal and background event samples."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference provides the multivariate classifiers and the significance formula used to quote the discovery significances."}],"review_version":1}