{"id":"74211a39-33c9-4a61-8b53-8302545672fb","arxiv_id":"2412.14235","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"At a 10 TeV muon collider, fermion-portal dark matter mediators could be discovered up to about 4.7 TeV, and including the muon parton distribution in simulations lowers the predicted reach and changes signal shapes.","lead":"This paper calculates how far a future 10 TeV muon collider could see four different dark matter models where dark matter connects to ordinary matter through a heavier mediator particle. It finds the collider could discover the mediators up to roughly 3,300 to 4,700 GeV in mass, and it builds a new way to include the internal structure of the muon beam in simulations, which changes the predicted discovery reach.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Prompt discovery reach assumes only SM backgrounds; unmodeled beam-induced backgrounds could contaminate signal regions and degrade the 3.3–4.7 TeV claim.","rationale":"The paper's central claim is a pair of numbers: a 3.3–4.7 TeV prompt discovery reach and roughly 10^3 long-lived-particle signal events. The LLP count is explicitly a signal-only statement, so the prompt reach is the only place where a genuine discovery is claimed. The reader's weakest-assumption points at beam-induced backgrounds, and that is the most load-bearing unvalidated premise. The significance calculation in Figs. 16, 18, 20, and 23 is cut-and-count on generator-level events with no detector response, no BIB, and no pile-up. The robustness statement in the text is about normalization systematics (shown in the right panels), not about additional background sources. BIB at a 10 TeV muon collider is known to be large, and although high-pT central dilepton/dijet plus missing-energy selections may survive, that survival needs to be demonstrated. Other potential concerns, such as the muon-PDF splitting pipeline or the relic-abundance input, are cross-checked in the paper (epsilon sensitivity, mass-splitting formula) or are standard in the field. The appropriate condition for acceptance is therefore a BIB-overlaid validation of at least one benchmark signal region. This agrees with the reader's conditional verdict, so no change of verdict is required.","tokens_in":33517,"tokens_out":5633,"duration_ms":56270,"concrete_test":"Using the official IMCC/MuCol 10 TeV BIB samples (e.g., from Ref. 2203.07964) overlaid on MadGraph-generated e-model events with m_phi = 3.3 TeV and m_chi small, apply the signal-region cuts of Eq. (11) with the Table 2 geometry; count events passing the cuts with and without BIB overlay. If the BIB-overlaid background exceeds the SM background by more than roughly 20% in either signal region, the quoted reach and tolerable-systematics plots are optimistic and the prompt-region claim needs revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central prompt-region claim (discovery for m_phi up to 3.3–4.7 TeV, Sec. 4 and Figs. 16, 18, 20, 23) rests on the assumption that the only backgrounds are the SM processes in Fig. 14 (Z/W pair production, ISR/FSR, VBF). Muon colliders have a known, copious beam-induced background (BIB) from muon decays in the beam pipe, and the paper neither simulates it nor argues quantitatively that the proposed kinematic cuts remove it. The 'tolerable systematic' analysis does not cover BIB because BIB is an additional source of events, not a normalization uncertainty on a known background. If BIB produces even a small number of events in the tight signal regions, the 5-sigma reach numbers in the abstract and conclusions are optimistic. The paper is honest about neglecting full detector simulation in the LLP section, but the prompt section presents reach as a physics result, so this missing ingredient is load-bearing.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies four renormalizable fermion-portal dark matter models in the freeze-in/superWIMP regime at a 10 TeV muon collider. For each model it determines the coupling that reproduces the observed relic abundance, computes the resulting mediator lifetimes, and uses these inputs to propose cut-based searches in the prompt regime and event-count estimates in the long-lived-particle regime. The paper also develops a pipeline for including a helicity-dependent muon component of the muon PDF in MadGraph/LHAPDF and shows that this component has a significant effect on kinematic distributions and, consequently, on reach. The headline results are a 5-sigma mediator mass reach of 3.3-4.7 TeV in the prompt regime and roughly 10^3 signal events in at least one detector component across the entire LLP region of each model's parameter space.","tokens_in":33579,"tokens_out":6433,"duration_ms":65002,"significance":"If the quoted reach is robust, the paper provides a useful and broad study of a well-motivated class of dark matter models at a future muon collider, and it makes a concrete methodological contribution through the muon-PDF implementation pipeline. The authors are candid about the rudimentary nature of their searches and about the absence of detector-level simulation in the LLP estimates. The main quantitative claims, however, are the prompt-region discovery reaches, and those rest on an assumption about backgrounds that is not demonstrated. The value of the paper depends on whether that load-bearing assumption can be supported; if it can, the results would be a valuable input to muon-collider detector design and to future phenomenological work on fermion-portal dark matter.","major_comments":[{"comment":"The prompt discovery reach is computed against only the Standard Model backgrounds of Fig. 14 (Z/W pair production, ISR/FSR, and VBF). A high-energy muon collider has a known, copious beam-induced background from muon decays in the beam pipe, and this is neither simulated nor shown to be rejected by the cuts of Eqs. (11)-(12). The 'tolerable systematics' panels in Figs. 16, 18, 20, and 23 treat a normalization uncertainty on the simulated backgrounds, not an additional source of events, so they do not cover beam-induced background. Since the central 3.3-4.7 TeV discovery claims depend on the signal regions being essentially background-free, this omission is load-bearing. Please either add a beam-induced background estimate (or a quantitative argument that the proposed cuts remove it) or soften the prompt-region discovery claims accordingly.","section":"Sec. 4.1.1; Figs. 14, 16, 18, 20, 23"},{"comment":"The relic-abundance calculation that fixes the coupling lambda, and through it all mediator lifetimes and collider event counts, is not shown for the three new models. The text states that the Boltzmann equations are solved and refers to Ref. [39] for the e model, but for the L, u, and Q models the reader is given no Boltzmann system, no list of included processes beyond Table 1, and no numerical method. The lambda contours in Figs. 2, 5, and 6, and the upper bounds in Eqs. (2), (4), (6), and (8), are central inputs to every subsequent prediction. The manuscript should present at least the differential equations, the relevant thermally averaged rates, and the numerical procedure, or release the code used to produce the contours, so that these results can be independently checked.","section":"Secs. 2.2-2.4; Eqs. (2), (4), (6), (8)"},{"comment":"The invariant-mass cuts in Eq. (12) appear inverted relative to the quoted mediator masses. Signal region SRq1 is assigned to m_phi = 1.6 TeV with m_jj >= 3600 GeV, while SRq2 is assigned to m_phi = 4.2 TeV with m_jj >= 1500 GeV. As written, the higher-mass signal region keeps substantially more Z-pair background, and the lower-mass region may be highly inefficient. Please confirm that these values are not accidentally swapped, and if they are correct, explain the kinematic reasoning and show the sensitivity of Figs. 20 and 23 to this choice.","section":"Eq. (12); Figs. 20 and 23"}],"minor_comments":[{"comment":"The abstract states an 'upper bound on the mediator's mass' from the relic abundance calculation, but the bounds derived in Sec. 2, Eqs. (2), (4), (6), and (8), are upper bounds on the dark matter mass m_chi. Please correct the wording in the abstract.","section":"Abstract and Sec. 2"},{"comment":"The significance variable sigma is used throughout but never defined. Please state explicitly whether sigma = S/sqrt(B) or includes a systematic term, and how the 'tolerable systematics as a fraction of statistical uncertainties' is computed.","section":"Sec. 4.1.1"},{"comment":"There is a typo in the text: 'the the gap' should read 'the gap'.","section":"Sec. 4.1.2"},{"comment":"The sentence 'alone could discover this model in most of the LLP region' is stronger than the analysis supports, given the paper's own statement that LLP backgrounds from detector response require Geant4-level simulation and are not modeled. Suggest replacing 'could discover' with 'could provide a sensitive signal region' or similar.","section":"Sec. 4.2.2"},{"comment":"The factorization scale Q_f is used in the decomposition of the parton luminosity, but it is not stated whether all terms on the right-hand side of Eq. (10) are evaluated at the same Q_f and how Q_f is chosen in the event generation. A sentence clarifying this would remove ambiguity.","section":"Sec. 3.1, Eq. (10)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the central use of lambda--fixed by the relic density and then used to predict collider rates--is physically legitimate rather than circular. The main concern is that the prompt-region reach claims are not yet supported because beam-induced backgrounds are unmodeled, and the relic-abundance calculation for the new models is not documented in sufficient detail. Both points are fixable within the scope of a revision. I would also encourage the authors to provide the Boltzmann-equation code or detailed inputs as ancillary material, since the numerical results form the backbone of the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things before reading: this is the first serious look at the L, u, and Q fermion portals at a 10 TeV muon collider, and the muon-PDF pipeline in Section 3 is the most citable bit. The paper does three things well. It extends Ref. [39] to three new models, showing that each has a viable parameter space bounded by relic density (mχ upper limits 2.0–6.7 TeV) and that a muon collider can probe mediators up to 3.3–4.7 TeV. It builds a method to splice the muon PDF into a continuum plus a delta-function piece, then implements it in MadGraph, with sensible cross-checks on the width parameter. And it shows that including that PDF changes kinematic distributions enough to reduce the e-model reach claimed in Ref. [39]—a useful, honest correction to an earlier paper by two of the same authors.\n\nThe soft spots are real but not load-bearing. The prompt reach assumes the only backgrounds are the SM processes in Fig. 14, with no modeling of beam-induced backgrounds from muon decays in the pipe. The paper just doesn't address this. I'd call that a caveat, not an error; the simple kinematic cuts likely kill most BIB, but “likely” should be quantified—a back-of-envelope estimate or a sentence explaining why the cuts are sufficient would have kept a referee from worrying. Second, the LLP section reports event counts only, with no background estimate, and says so explicitly. That's honest and appropriate for a first pass. Third, the relic-abundance calculation for the new models is presented through figures and references rather than an independent derivation; it makes the mass limits hard to audit. The lack of code or grid release for the PDF pipeline also limits reproducibility, though the method is described in enough detail that it could be reconstructed.\n\nThe circularity concern raised by the reader is unfounded: fixing λ from Ωh² is the physically right way to map the model's parameter space; the collider predictions are then genuine. I checked the branching-ratio discussion for the L and Q models—the two-mediator decay chains, the small mass splittings, the soft-lepton signatures—and it holds together.\n\nBottom line: this is a competent, clearly written phenomenology paper for the muon collider community, not a precision study. It would get a fair hearing at PRD, JHEP, or similar. The referee should ask for a BIB estimate, more Boltzmann-equation detail, and a statement about code availability. I'd cite it if I work on muon colliders or fermion-portal DM.","headline":"Solid, useful phenomenology that deserves refereeing; the missing beam-induced background discussion is a real caveat but not a fatal flaw.","tokens_in":34259,"tokens_out":2081,"would_cite":true,"duration_ms":22281,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A 10 TeV muon collider could discover fermion-portal dark-matter mediators up to 3.3–4.7 TeV and would see about 1,000 long-lived events across the full viable parameter space.","keywords":["fermion-portal dark matter","freeze-in","muon collider","long-lived particles","R-hadrons","disappearing tracks","muon PDF","M_T2"],"falsifier":"Simulate the proposed signal regions with a full detector response that includes beam-induced background from muon decays in the beam pipe; if the significance at the quoted boundary (mediator mass of 3.3–4.7 TeV) drops below 5 sigma, the paper's reach claim fails.","tokens_in":33205,"feed_emoji":"🌌","tokens_out":7140,"duration_ms":60146,"temperature":0.7,"pith_summary":"This paper argues that a future 10 TeV muon collider with 10 $ab^{-1}$ of data could discover the mediators of four freeze-in fermion-portal dark matter models—right- and left-handed lepton portals and right- and left-handed quark portals—through simple cut-and-count searches. In the prompt-decay regime, the claimed discovery reach spans mediator masses from about 3.3 TeV to 4.7 TeV, and in the long-lived-particle regime roughly 1,000 signal events land in at least one detector component across the entire viable parameter space. A byproduct of the work is a pipeline for including the muon's own parton distribution inside a muon beam, which changes event kinematics enough to lower the reach that a naive no-PDF estimate would suggest. The paper also computes upper bounds on the dark matter mass from the freeze-in plus superWIMP relic-abundance mechanism, ranging from 2.0 TeV to 6.7 TeV depending on the portal.","feed_headline":"Muon collider could spot dark-matter mediators up to 4.7 TeV","feed_subtitle":"Freeze-in fermion-portal dark matter yields about 1,000 long-lived signals across the viable parameter space.","key_machinery":"The machinery is a set of four renormalizable fermion-portal models in which a scalar mediator carries the same Standard Model quantum numbers as an SM fermion, plus the freeze-in/superWIMP duet that fixes the tiny Yukawa coupling lambda for each point on the (m_phi, m_chi) plane. The coupling then determines the mediator lifetime and, through it, whether the mediator decays promptly or is long-lived. For collider predictions, the paper adds a muon-component PDF pipeline: the muon PDF is split into a smooth part and a delta-function piece at x=1, with coefficients fixed by muon number and polarization sum rules, and the four pieces are generated separately and recombined. The prompt search uses the transverse-mass variable M_T2, which is bounded by the W mass for W-pair backgrounds, along with invariant-mass cuts to remove Z production and opening-angle, energy, and pseudorapidity cuts to kill ISR/FSR and VBF backgrounds. For LLP signals, the detector geometry (barrel dimensions per subsystem) is used to count displaced vertices, disappearing tracks, and detector-stable charged tracks.","core_discovery":"The central claim is that cosmologically motivated fermion-portal dark matter, with dark matter produced by freeze-in and the mediator abundance set by freeze-out followed by decay into dark matter, sits in a parameter region that a 10 TeV muon collider is well placed to explore. For each of the four portals, the paper finds an upper bound on the dark matter mass (3.6, 2.0, 6.7, and 5.4 TeV for the e, L, u, and Q models respectively) beyond which the universe would be overclosed. It then shows that mediator pair production, followed by decay to missing energy plus leptons or jets, can be separated from Standard Model backgrounds with cuts on invariant mass, M_T2, opening angle, energy, and pseudorapidity, giving a 5-$\\sigma$ discovery reach of roughly 3.3, 3.4, 4.2, and 4.7 TeV in mediator mass at 10 TeV and 10 $ab^{-1}$. In the long-lived regime, every point of every model's viable parameter space yields about 1,000 events (displaced leptons, disappearing tracks, or R-hadron displaced jets) in at least one detector barrel region. Including the muon parton distribution suppresses the earlier reach estimates, and the paper presents this as the more accurate picture.","pith_inferences":["A detector-level simulation that includes beam-induced backgrounds from muon decays in the beam pipe would be the decisive test; if those backgrounds enter the simple signal regions, the quoted reach could shrink, so the headline numbers should be read as signal-level projections.","The same muon-PDF splitting pipeline should apply to other BSM production processes at muon colliders, not just mediator pairs, since its impact on differential distributions is a general lesson rather than a model-specific artifact.","The upper bounds on the dark matter mass (2.0–6.7 TeV) suggest a complementary target for direct and indirect detection searches, as a substantial fraction of the cosmologically allowed parameter space lies beyond current probes."],"forward_implications":["A 10 TeV muon collider could discover all four freeze-in fermion portals at 5 sigma for mediator masses well above current LHC exclusions, up to 3.3–4.7 TeV.","If the mediators are long-lived, the models are testable everywhere: at least about 1,000 events appear in some detector component, so null results would exclude or strongly constrain the entire relic-abundance-viable region.","The muon PDF effect is large enough that previous no-PDF reach estimates are misleading; future BSM studies at muon colliders should include it or an equivalent treatment for accurate significances.","Distinct signatures such as displaced leptons, disappearing tracks, R-hadron displaced jets, and heavy stable charged tracks motivate dedicated trigger and dE/dx improvements in the tracker and muon system.","For lepton-portal models the neutral partner decays invisibly, so a complete search should combine charged-mediator tracks with mono-photon or forward-detector channels."],"supporting_citations":[{"why":"Defines the e-model signals and the no-PDF analysis that this paper extends with muon PDFs; the new cuts are designed against its signal regions.","marker":"[39]"},{"why":"Supplies the muon-component PDF grids that the paper splits and recombines to include the beam's muon parton distribution.","marker":"[48]"},{"why":"Provides the effective vector boson approximation used for the vector-boson-fusion production channel in the simulations.","marker":"[51]"},{"why":"Establishes the combined superWIMP and freeze-in production that fixes lambda from the relic abundance and sets mediator lifetimes.","marker":"[19]"},{"why":"Gives the one-loop electroweak mass splitting between the two mediators in the L and Q models, which controls their decay chains and LLP signals.","marker":"[81]"},{"why":"Defines the M_T2 variable whose kinematic endpoint is used to remove W-pair background in the prompt searches.","marker":"[94]"},{"why":"Provides the detector subsystem dimensions used to compute long-lived-particle event counts in each barrel region.","marker":"[33]"}],"fun_headline_variants":["Muon collider can probe dark matter mediators up to 4.7 TeV","Freeze-in dark matter leaves ~1000 long-lived tracks at muon collider","Fermion-portal dark matter within reach of 10 TeV muon collider","Muon collider's self-partons shrink dark matter discovery potential","4.7 TeV mediators: muon collider's dark matter hunt"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The quoted prompt-region reach assumes that the only relevant backgrounds are the Standard Model processes shown in the paper (Z/W pair production, ISR/FSR, and VBF), and that detector-level effects and beam-induced backgrounds from muon decays are negligible or removed by the proposed cuts; if those backgrounds contaminate the signal regions, the 5-sigma reach would be lower.","fun_headline_variants_meta":{"raw":{"variants":["Muon collider can probe dark matter mediators up to 4.7 TeV","Freeze-in dark matter leaves ~1000 long-lived tracks at muon collider","Fermion-portal dark matter within reach of 10 TeV muon collider","Muon collider's self-partons shrink dark matter discovery potential","4.7 TeV mediators: muon collider's dark matter hunt"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000391,"raw_usage":{"total_tokens":2166,"prompt_tokens":1160,"completion_tokens":1006,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":776,"completion_tokens_details":{"reasoning_tokens":900}},"tokens_in":776,"tokens_out":1006,"duration_ms":8117,"temperature":1.0,"reasoning_tokens":900,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:24:39.653622+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the proposed signal regions with a full detector response that includes beam-induced background from muon decays in the beam pipe; if the significance at the quoted boundary (mediator mass of 3.3–4.7 TeV) drops below 5 sigma, the paper's reach claim fails.","supporting_citations":[],"review_version":1}