{"id":"890333bc-b3c3-485d-974a-294f572bc347","arxiv_id":"2601.20406","paper_version":4,"verdict":"REJECT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Simulated HL-LHC dimuon angular distributions are used to set expected 95% CL mass limits on an Einstein-Cartan torsion portal dark matter model, but the signal is incorrectly treated as spin-2.","lead":"This paper uses private simulations of the planned HL-LHC to study the angular distribution of high-mass muon pairs from a dark matter model based on Einstein-Cartan gravity. It reports expected 95% confidence limits on the masses of a dark gauge boson and a torsion field, giving collider physicists a target for future searches.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed spin-2 cosθCS template is applied to a spin-1 vector A', so the shape discrimination and the exclusion ranges rest on an unsupported spin assignment.","rationale":"I read the paper as a Monte Carlo case study whose central deliverable is the expected 95% CL exclusion of torsion-field masses based on the cos θ_CS shape of the muon pairs. The reader's weakest-assumption identification matches my own: the signal template assumes a spin-2 angular distribution for a state that the model defines as a spin-1 vector field. The Lagrangian in Sec. II contains A'_μ as an ordinary gauge field, not a graviton-like spin-2 field. A vector boson decaying to a fermion pair has an angular distribution with at most cos^2 θ in its rest frame; the (1 - cos^4 θ) shape is a spin-2 signature. The paper applies that spin-2 template in Fig. 3 and uses it, through the CLs procedure, to obtain the quoted MTS exclusion intervals. If the real distribution is spin-1-like, those intervals are not valid. The abstract's own phrase 'spin-2 dark neutral gauge boson' confirms the mismatch is internal to the paper, not merely a disagreement with external conventions. I do not regard the absence of deposited data or the ad-hoc 10% systematic as the single most load-bearing issue; those affect robustness but not the core interpretation. The concrete test above would settle the spin question directly, but as written the central claim is not supported. Hence REJECT, with high confidence in the reader's verdict.","tokens_in":17006,"tokens_out":4218,"duration_ms":44295,"concrete_test":"Regenerate the signal at parton level with the UFO of Ref. [15] (or implement q qbar → A' χ χ, A' → μ+ μ− in MadGraph) for MA' = 500 GeV, MTS = 2000 GeV, Mχ = 500 GeV, apply the same 460–540 GeV mass window and pre-selection, and fit the resulting cos θ_CS histogram in the bins of Fig. 3 to both par[0](1 + cos^2 θ_CS) and par[0](1 - cos^4 θ_CS). Report the fit χ²/dof. If the spin-1 form is preferred or the spin-2 form is disfavored, the template and the derived exclusion ranges in Sec. VIII are unsupported.","verdict_should_be":"REJECT","load_bearing_attack":"The load-bearing step is Eq. (2), which fits the A' → μ+μ− signal with par[0](1 - cos^4 θ_CS), described as the characteristic of a spin-2 boson. In the model of Sec. II, A'_μ is a vector field entering through D_μ = ∂_μ + i gη γ5 S_μ + i gD A'_μ; it is spin-1, not spin-2. A spin-1 boson produced via q qbar annihilation and decaying to muons has, in the Collins-Soper frame, a tree-level angular distribution of the form c0(1 + cos^2 θ_CS) + c1 cos θ_CS, with no cos^4 term. The shape (1 - cos^4 θ_CS) is specific to a spin-2 Randall-Sundrum graviton, and Eq. (2) is taken from a graviton search note [50]. The MC distributions in Figs. 2 and 3 are fitted with this spin-2 template, and that template drives the CLs limits quoted in Sec. VIII. If the true A' distribution is spin-1-like, the shape discrimination against Drell-Yan changes and the quoted MTS exclusion ranges (e.g., 1396–5545 GeV for MA' = 200 GeV) are not determined. The internal inconsistency is visible in the abstract itself, which labels A' a 'spin-2 dark neutral gauge boson.' The rest of the analysis uses standard MC and CLs tools, but the central claim is conditioned on an incorrect spin hypothesis.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents a Monte Carlo study of high-mass dimuon angular distributions at the HL-LHC (14 TeV, 3000 fb^-1) in a simplified Einstein-Cartan model [15]. The process is pp -> S -> chi chi followed by chi -> A' chi and A' -> mu+ mu-, with a heavy torsion field S mediating the production. The author generates signal and Standard Model backgrounds with MadGraph/Pythia/Delphos, applies a preselection and a tighter MET-based selection, shows cos(theta_CS) distributions in several mass windows, estimates luminosities needed for 5-sigma discovery, and uses CLs in the asymptotic approximation to derive expected 95% CL upper limits on sigma x Br(A' -> mu+ mu-) as a function of the torsion mass M_TS. The paper concludes that the A' signal has a spin-2 angular distribution and quotes excluded M_TS intervals such as 1396-5545 GeV for M_A' = 200 GeV.","tokens_in":17477,"tokens_out":8543,"duration_ms":81085,"significance":"The question is timely: angular distributions in the Collins-Soper frame can in principle distinguish spin hypotheses for new dilepton resonances at the HL-LHC, and the paper uses standard public tools with an explicit cross-section table and expected CLs limits. These are useful ingredients for a projection study if the signal shape is modeled correctly. However, the central physics claim, that the A' signal has the spin-2 shape par[0](1 - cos^4 theta_CS), contradicts the model definition in Sec. II where A'_mu is a spin-1 vector gauge boson. Because that shape drives the shape-based discrimination and the quoted exclusion intervals, the main result as presented is not supported. The manuscript also has limited reproducibility: no generator cards, no fit-quality statistics, and no derivation of the systematic uncertainty. The strength of the paper is its clear layout and the explicit use of a published model, but the internal spin inconsistency is load-bearing.","major_comments":[{"comment":"The analysis's discriminating variable and the resulting exclusion intervals are built on an unsupported spin hypothesis. The model Lagrangian in Sec. II defines A'_mu as a spin-1 vector gauge boson through D_mu = partial_mu + i g_eta gamma_5 S_mu + i g_D A'_mu. Yet Eq. (2) fits the A' -> mu+ mu- Monte Carlo shape with par[0] (1 - cos^4 theta_CS), the form used for a spin-2 Randall-Sundrum graviton, and the abstract and Sec. VIII label A' a 'spin-2 dark neutral gauge boson.' A vector boson produced through fermion annihilation and decaying to muons has a tree-level Collins-Soper distribution with at most 1 + cos^2 theta_CS and cos theta_CS terms; it does not contain cos^4 theta_CS. Since cos theta_CS is described in Sec. VII.A as the key discriminator, and since the CLs limits in Figs. 9 are computed from these shapes, the quoted M_TS exclusions, for example 1396-5545 GeV for M_A' = 200 GeV, are conditioned on the wrong spin assignment. The MC histograms in Figs. 2 and 3 should be compared with the matrix-element prediction for spin-1 production and decay; as written, this is an internal inconsistency, not merely a matter of interpretation.","section":"Sec. II, Sec. VII, Eq. (2)"},{"comment":"The treatment of systematic uncertainties is not adequate for the central limits. The text states: 'An ad-hoc flat 10% uncertainty is applied to cover all possible systematic effects.' No source, correlation structure, or dependence on the fitted variable is given. With an integrated luminosity of 3000 fb^-1 and the tight final selection, the background yields in the cos theta_CS bins in Fig. 7 are at the level of tens to hundreds of events, so the CLs limits can be sensitive to the assumed systematic uncertainty. The author should either derive the systematic covariance from the detector simulation and background modeling or show explicitly that the 10% choice does not change the exclusion intervals beyond the quoted precision.","section":"Sec. VII.A"},{"comment":"The translation from the expected upper-limit curves to the mass exclusions is not described. In Fig. 9, the solid black curves are theory predictions and the vertical red dotted lines are said to indicate 'limit values,' but the text does not state the algorithm used to obtain the intervals quoted in Sec. VIII. For example, it is not specified whether each interval is the set of M_TS for which the theory sigma x Br exceeds the expected 95% CL upper limit, nor how interpolation between the discrete M_TS points of Table II is performed. This step is load-bearing for the final claim and should be specified precisely.","section":"Sec. VIII, Fig. 9"}],"minor_comments":[{"comment":"The sentence 'The model includes several free parameters: the masses of the torsion field, dark gauge boson, and dark matter' is misleading because g_eta and g_D are fixed and only M_TS and M_A' are scanned; clarify that M_chi is also fixed at 500 GeV.","section":"Sec. II"},{"comment":"The phrase 'for different tensor scalar masses (M_TS)' should read 'for different torsion-field masses (M_TS).'","section":"Fig. 8 caption"},{"comment":"The dash for (M_A' = 200 GeV, M_TS = 5000 GeV) is unexplained; the text in Sec. VIII quotes 'exceeding 2000 fb^-1,' so either enter the value or state explicitly that it exceeds the plotted range.","section":"Table IV"},{"comment":"Several axis labels and legends are garbled in the compiled version, for example 'Events (scaled to one)' and the pT axes, making it difficult to inspect the cut efficiencies; please regenerate the figures with clear labels.","section":"Figs. 5 and 6"},{"comment":"No goodness-of-fit statistic is reported for the fit of par[0](1 - cos^4 theta_CS) to the Monte Carlo distribution; a chi^2/ndf or similar quantity would help the reader assess the claimed spin-2 shape.","section":"Fig. 3 and Eq. (2)"},{"comment":"The manuscript does not provide the MadGraph run cards, Pythia settings, or Delphes configuration used for the private samples, so the generated signal shapes are not reproducible from the information given; a short reproducibility statement would strengthen the study.","section":"Sec. V"}],"recommendation":"reject","confidential_remarks":"The spin mismatch is a fundamental internal inconsistency, and the main quantitative result depends on it. Replacing the template with the correct spin-1 angular distribution and re-deriving the limits would not be a local revision; it would change the signal model and the exclusion ranges. I therefore recommend rejection, while noting that a thoroughly corrected resubmission could be reconsidered. I also note that the paper is a private-MC projection, not an analysis of real CMS HL-LHC data, and the data availability statement says no data will be deposited, which limits reproducibility."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nHere's my honest take on Elgammal's HL-LHC torsion study. What's genuinely new: a MadGraph/Pythia/Delphes simulation of the Einstein-Cartan simplified model from Nam (2022), with cross-section tables and a grid of expected 95% CL exclusions on the torsion mass MTS versus the dark gauge boson mass MA'. Those exclusion ranges don't exist elsewhere. The paper is clearly written and follows the standard LHC analysis recipe—preselection, N-1 efficiency curves, CLs limits. If you work on torsion portals, this is a useful template for how one would set such a search.\n\nThe soft spot is not minor. The central discriminator is the cos(theta_CS) shape, and the signal is fitted with the spin-2 graviton template par[0](1 - cos^4 theta_CS), borrowed from a Randall-Sundrum search. But the model in Section II defines A'_mu as a vector field, with covariant derivative D_mu = partial_mu + i g_eta gamma5 S_mu + i g_D A'_mu. A vector decaying to muon pairs has a spin-1 angular distribution, roughly c0(1 + cos^2 theta_CS) + c1 cos theta_CS, not (1 - cos^4 theta_CS). The abstract even calls A' a 'spin-2 dark neutral gauge boson', which directly contradicts the Lagrangian. This mislabeling is load-bearing: it is what makes the signal look distinct from Drell-Yan, and it determines the exclusion ranges. I can't see how the quoted limits survive if the correct spin-1 template is used.\n\nThere are smaller weaknesses too: the 10% flat systematic is ad hoc, no data are deposited, and the claim that W+jets events fail preselection is asserted without evidence. The significance formula uses the simple Ns/sqrt(Ns+Nb) rather than the profile likelihood used for the limits.\n\nThe MC workflow and cross-section tables are honest work, and the paper is not a waste of time. But as written, the central claim is not supported. My recommendation: desk reject, or at most send back for major revision with a required fix of the spin assignment and a rerun of the shape analysis. If the author resubmits with the correct spin-1 template, it becomes a reasonable niche phenomenological study worth refereeing.\n\nBest.","headline":"A clean MC study undone by a spin-2 template applied to a spin-1 vector, so the quoted exclusion ranges don't hold.","tokens_in":17857,"tokens_out":4443,"would_cite":false,"duration_ms":38033,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues that the Collins-Soper angular distribution of high-mass dimuons can expose the Einstein-Cartan torsion portal, with expected HL-LHC exclusions excluding torsion masses from roughly 1.4 to 7 TeV.","keywords":["Einstein-Cartan gravity","torsion portal","dark gauge boson","Collins-Soper frame","angular distribution","dimuon final state","HL-LHC","CLs limit"],"falsifier":"Generate the same $q\\bar q\\to S\\to A'\\to\\mu^+\\mu^-$ events without imposing any template, fit the resulting $\\cos\\theta_{CS}$ histogram against both $\\mathrm{par}[0](1-\\cos^4\\theta_{CS})$ and a spin-1 shape such as $1+\\cos^2\\theta_{CS}$, and check which template the Monte Carlo truth prefers; a preference for the spin-1 shape would overturn the mass exclusions.","tokens_in":1669,"feed_emoji":"⚛️","tokens_out":3483,"duration_ms":82401,"temperature":0.7,"pith_summary":"This paper argues that the angular distribution of muon pairs in the Collins-Soper frame can separate a simplified Einstein-Cartan gravity signal from Standard Model backgrounds at the High-Luminosity LHC. The signal is produced via quark-antiquark annihilation through a heavy torsion field into a dark neutral gauge boson $A'$ that decays to muons plus missing energy from dark matter. According to the simulation, the signal has a symmetric, spin-2-like $\\cos\\theta_{CS}$ distribution, in contrast to the forward-backward asymmetric Drell-Yan background. Using this shape difference, the analysis reports expected 95% CL upper limits that exclude torsion-field masses between roughly 1.4 and 7 TeV, depending on the $A'$ mass. The result matters because it gives the HL-LHC a concrete angular-distribution signature for a torsion portal that would otherwise hide in the dimuon-plus-missing-energy final state.","feed_headline":"Angular shape exposes a torsion field up to ~7 TeV","feed_subtitle":"A symmetric dimuon angle distribution would set 95% CL limits and mark the Einstein-Cartan portal.","key_machinery":"The machinery is the Collins-Soper variable $\\cos\\theta_{CS}$ combined with the spin-2 angular template $f(\\cos\\theta_{CS})=\\mathrm{par}[0](1-\\cos^4\\theta_{CS})$. The Collins-Soper frame is used to reconstruct the angle in a way that reduces distortions from the transverse momenta of the incoming partons, while the template supplies the expected signal shape. The analysis is built on the contrast between this symmetric distribution and the asymmetric Drell-Yan background, and it uses a set of five tight cuts on the azimuthal separation between the dimuon and missing transverse energy, the relative transverse-energy difference, the three-dimensional opening angle, the jet multiplicity, and the dimuon mass window. A profile-likelihood test using the $CL_s$ construction then converts the shape difference into the reported upper limits.","core_discovery":"The central claim is that, in the simplified Einstein-Cartan portal model, the angular distribution of the decay muons is symmetric around $\\cos\\theta_{CS}=0$ and follows the same template used for spin-2 graviton decays into dileptons, namely $\\mathrm{par}[0](1-\\cos^4\\theta_{CS})$. This symmetric shape provides a discriminating handle against the Standard Model Drell-Yan process, which has a sizable forward-backward asymmetry. The paper further claims that with 3000 fb$^{-1}$ at 14 TeV and optimized selection cuts on missing energy and dimuon kinematics, this shape-based analysis yields expected 95% CL exclusion intervals for the torsion field mass $M_{TS}$: 1396--5545 GeV for $M_{A'}=200$ GeV, 1402--6310 GeV for $M_{A'}=300$ GeV, 1537--7026 GeV for $M_{A'}=400$ GeV, and 1677--6927 GeV for $M_{A'}=500$ GeV, at the benchmark couplings $g_\\eta=0.125$, $g_D=1.0$, and dark matter mass $M_\\chi=500$ GeV.","pith_inferences":["An immediate test of the weakest assumption is to fit the generated $A'$ events with a spin-1 template such as $1+\\cos^2\\theta_{CS}$; if that fit is preferred, the exclusion intervals reported here would need to be recomputed.","The same shape-versus-shape logic could be applied to the $e^+e^-$ channel or to early HL-LHC data, where the forward-backward asymmetry of Drell-Yan is already measured, making the template comparison a model-independent spin test.","The reported limits come from private simulation with an ad-hoc flat 10% systematic uncertainty; a fuller experimental systematic treatment could shift the boundary masses by an amount the paper does not quantify."],"forward_implications":["A 5 sigma discovery of the $A'\\to\\mu^+\\mu^-$ plus missing-energy signal becomes reachable with 160 fb$^{-1}$ for $M_{A'}=400$ GeV and $M_{TS}=4000$ GeV, and with 500 fb$^{-1}$ for $M_{A'}=200$ GeV.","No signal in the excluded $M_{TS}$ windows would constrain the Einstein-Cartan portal at the benchmark couplings $g_\\eta=0.125$, $g_D=1.0$, and $M_\\chi=500$ GeV.","The symmetric signal shape, if confirmed, would distinguish the torsion portal from spin-1 alternatives such as $Z'$ models in the same dimuon plus missing-energy final state.","For $M_{A'}>500$ GeV the background after the final selection is too small for a meaningful statistical analysis, so the method's reach in $A'$ mass is limited at this benchmark."],"supporting_citations":[{"why":"Provides the simplified Einstein-Cartan model, the UFO implementation, and the benchmark couplings $g_\\eta=0.125$ and $g_D=1.0$.","marker":"[15]"},{"why":"Supplies the spin-2 angular template $\\mathrm{par}[0](1-\\cos^4\\theta_{CS})$ used to fit the signal shape.","marker":"[50]"},{"why":"Defines the Collins-Soper frame and the reconstruction of $\\cos\\theta_{CS}$ from lab-frame momenta.","marker":"[42]"},{"why":"Sets the recommended dark-sector coupling value $g_D=1.0$ adopted in the scan.","marker":"[41]"},{"why":"Provides the modified frequentist $CL_s$ construction used for the exclusion limits.","marker":"[53]"},{"why":"Supplies the asymptotic formulae used to compute the expected 95% CL limits.","marker":"[55]"}],"fun_headline_variants":["Dimuon angle shape constrains torsion field at HL-LHC","Torsion field exclusion to ~7 TeV from angular shape","Symmetric dimuon angles flag torsion field at HL-LHC","Einstein-Cartan portal probed by muon angle distribution","Angular shape tests torsion field up to 7 TeV"],"cache_read_input_tokens":19968,"weakest_assumption_plain":"The analysis assumes that the $A'$-signal angular distribution follows the spin-2 template $\\mathrm{par}[0](1-\\cos^4\\theta_{CS})$, even though the $A'_\\mu$ is a vector field with spin-1 coupling; if the true distribution has a different shape, the background discrimination and the resulting mass exclusions would be invalid.","fun_headline_variants_meta":{"raw":{"variants":["Dimuon angle shape constrains torsion field at HL-LHC","Torsion field exclusion to ~7 TeV from angular shape","Symmetric dimuon angles flag torsion field at HL-LHC","Einstein-Cartan portal probed by muon angle distribution","Angular shape tests torsion field up to 7 TeV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001272,"raw_usage":{"total_tokens":5225,"prompt_tokens":989,"completion_tokens":4236,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":605,"completion_tokens_details":{"reasoning_tokens":4147}},"tokens_in":605,"tokens_out":4236,"duration_ms":28323,"temperature":1.0,"reasoning_tokens":4147,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:39:12.190469+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate the same $q\\bar q\\to S\\to A'\\to\\mu^+\\mu^-$ events without imposing any template, fit the resulting $\\cos\\theta_{CS}$ histogram against both $\\mathrm{par}[0](1-\\cos^4\\theta_{CS})$ and a spin-1 shape such as $1+\\cos^2\\theta_{CS}$, and check which template the Monte Carlo truth prefers; a preference for the spin-1 shape would overturn the mass exclusions.","supporting_citations":[{"cited_title":"JHEP 07 (2021) 208","cited_arxiv_id":null,"evidence_quote":"Provides the simplified Einstein-Cartan model, the UFO implementation, and the benchmark couplings $g_\\eta=0.125$ and $g_D=1.0$."},{"cited_title":"Collins and D","cited_arxiv_id":null,"evidence_quote":"Supplies the spin-2 angular template $\\mathrm{par}[0](1-\\cos^4\\theta_{CS})$ used to fit the signal shape."},{"cited_title":"Search for new physics in the monophoton final state in proton-proton collisions at sqrt(s) = 13 TeV","cited_arxiv_id":"1706.03794","evidence_quote":"Defines the Collins-Soper frame and the reconstruction of $\\cos\\theta_{CS}$ from lab-frame momenta."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Sets the recommended dark-sector coupling value $g_D=1.0$ adopted in the scan."},{"cited_title":"MadGraph 5 : Going Be- yond","cited_arxiv_id":null,"evidence_quote":"Provides the modified frequentist $CL_s$ construction used for the exclusion limits."}],"review_version":2}