{"id":"66920c1a-2129-4d3c-bc59-2b326080fb65","arxiv_id":"2607.18843","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A future muon–proton collider could discover or exclude a vector-like X quark decaying to tW up to about 8.3 TeV at weak coupling, with the fully hadronic channel giving the strongest reach.","lead":"This paper calculates how well a proposed muon–proton collider could detect a hypothetical heavy 'X quark' that decays into a top quark and a W boson. If such a particle exists, the collider could see or exclude it at masses up to roughly 8–9 TeV, well beyond current LHC limits.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Headline reach is not reproducible because the integrated luminosity and reference coupling for the cut-flow tables are never stated.","rationale":"The reader's weakest_assumption (APV relaxation) is a valid secondary concern: the 'broad region' wording is indeed overstated if the APV bound is not overlaid on the reach plots. However, the single most load-bearing issue is the missing integrated luminosity and reference coupling. Without these, the Asimov significance cannot be computed, so the headline reach numbers are not reproducible. This is not an attack on the authors' competence; the model setup and simulation workflow are clearly described, and the qualitative conclusion (a muon–proton collider has good sensitivity to this simplified model) is likely robust. But the quantitative claim of 8.3 TeV at g* = 0.009 is presented without the necessary context. The reader's conditional verdict already requires additional information; our concern confirms that condition. We therefore recommend keeping the verdict unchanged (CONDITIONAL) until the luminosity and reference coupling are stated and the reach is recomputed.","tokens_in":23799,"tokens_out":15115,"duration_ms":131684,"concrete_test":"Contact the authors (or check the published source) for the integrated luminosity L and the reference g* used for the cut-flow cross sections. Then recompute Z_exc for the FH benchmark using Eqs. (8)–(9) with L = 10 and 100 fb−1 and the Table XIV final-state signal and background cross sections, scaling signal by (0.009/g*_ref)^2 and by the m_X=8300/2500 production ratio. If Z_exc < 2 at the stated L (or if no L is stated), the headline 8.3 TeV claim is unsupported. Also verify whether the m_X = 8300 point was generated explicitly or obtained by extrapolation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim — 2σ exclusion of m_X ≃ 8.3 TeV at g* = 0.009, R_L = 0.1, √s = 9.16 TeV (abstract; Sec. V) — depends on the Asimov significance Eqs. (8)–(9), which require signal and background event yields s and b. These yields are obtained by multiplying the cross sections in Tables II–V and XI–XVIII by an integrated luminosity L. However, the paper never states the value of L used for the reach curves and Tables VI–IX; the text only mentions 'target integrated luminosities ranging from 10 to 100 fb−1' (Sec. I). Moreover, the cut-flow tables report 'Signal(fb)' without specifying the reference g* value that enters the signal cross sections. For example, Table XIV at √s = 9.16 TeV lists a signal of 23.99 fb after all cuts for X2500, but one cannot map this to the g* axis of the reach plots without knowing the reference coupling. Consequently, the g* lower bounds in Tables VI–IX (e.g., 0.009 for FH at 9.16 TeV) cannot be verified from the provided information. If L were 10 fb−1 rather than 100 fb−1, the m_X reach at g* = 0.009 would be substantially smaller; if a larger L is implicitly assumed, the abstract's 'broad region' claim is overstated. This missing input is more fundamental than the APV relaxation: it affects every numerical result in the paper.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies single production of a vector-like X quark (charge +5/3) in a simplified triplet model at future muon-proton colliders, via the process μ+p → ν̄_μ X, X → tW+. The model parameters are the coupling g*, the generation-mixing parameter R_L, and the mass m_X. The analysis simulates four final-state channels (FL, FH, SL1, SL2) with MadGraph5_aMC@NLO, Pythia 8, and Delphes, uses fat-jet reconstruction and 80% muon beam polarization, and computes Asimov exclusion/discovery significances at √s = 5.29, 6.48, and 9.16 TeV. The central claim is that the FH channel is the most sensitive, reaching a 2σ exclusion of m_X ≃ 8.3 TeV at g* = 0.009, R_L = 0.1, and √s = 9.16 TeV. The paper explicitly relaxes the APV constraint and scans g* up to 0.5.","tokens_in":24171,"tokens_out":5416,"duration_ms":51914,"significance":"Future μp collider projections for a vector-like X quark are timely, and the paper offers a genuine phenomenological study with a full simulation chain, external LHC/EWPO comparisons, and a four-channel analysis. If the quantitative claims are correct, the proposed search would substantially extend the current and HL-LHC reach. However, the numerical results are not currently reproducible or fully verifiable because the integrated luminosity and reference g* used in the reach calculation are not stated, and at least one quoted mass point lies at the kinematic boundary. The APV relaxation is disclosed, but the abstract's 'broad region' wording overstates what remains allowed under existing constraints.","major_comments":[{"comment":"The Asimov significances require event yields s and b, which depend on the integrated luminosity L. The paper never states the L used for the reach curves; Sec. I only mentions 'target integrated luminosities ranging from 10 to 100 fb−1'. In addition, the cut-flow tables quote only 'Signal(fb)' without the reference g* value. For example, the 23.99 fb after all cuts for X2500 at √s = 9.16 TeV in Table XIV cannot be mapped to the g* axis of Tables VI-IX without knowing the reference coupling. Without specifying L and g*_ref, the g* lower bounds in Tables VI-IX cannot be verified. Please provide these inputs explicitly, or report absolute event yields.","section":"Section V, Eqs. (8)-(9); Tables VI-IX and II-V"},{"comment":"For R_L = 0.3 and 0.5, the 2σ exclusion upper limit is quoted as m_X = 9160 GeV, equal to the nominal √s. At m_X = √s, the subprocess requires the proton parton momentum fraction x ≈ 1, where the PDF vanishes; the production cross section is zero. Thus the reach cannot extend to 9160 GeV. The threshold and PDF suppression should be handled explicitly, and the kinematic edge must be reflected in the reported mass limits.","section":"Table VII, FH row at √s = 9.16 TeV"},{"comment":"The APV constraint g* sqrt(R_L/(1+R_L)) < 6.5×10^-2 is relaxed, as stated in Sec. II. For R_L = 0.5 this bound gives g* ≲ 0.11, and for R_L = 0.1 it gives g* ≲ 0.22. Consequently, large parts of the displayed parameter space with g* up to 0.5 are excluded under that bound, and the abstract's 'broad region' claim depends on the relaxation. Please overlay the APV-excluded region in the reach plots or explicitly qualify that the displayed regions above the bound are only valid once the APV constraint is dropped.","section":"Sec. II, Fig. 1 and Figs. 11-14; Tables VI-IX"},{"comment":"The text states that 'the same event selection is adopted' for the higher center-of-mass energies, but the appendix cut-flow tables use different selection criteria. For example, the FH selection at 9.16 TeV (Table XIV) uses HT > 800 GeV and p_bT > 500 GeV, whereas at 5.29 TeV (Table III) it uses HT > 900 GeV and p_bT > 400 GeV. Similar differences appear in the FL pseudorapidity windows and the SL1 η_b window. Please correct the text or document the exact selection used at each energy.","section":"Sec. IV.B and Appendix Tables XI-XVIII"}],"minor_comments":[{"comment":"The Asimov significances include only statistical uncertainties. No background systematic uncertainty is incorporated. Please state explicitly that the contours are statistical-only, or include a nuisance-parameter treatment if systematics are intended.","section":"Section V, Eqs. (8)-(9)"},{"comment":"'Branch ratio' should be 'branching ratio' in several places (e.g., Sec. I and Table captions).","section":"Throughout"},{"comment":"In the 5.29 TeV, R_L = 0.5 row, the 2σ upper edge of g* is 0.29, which is lower than the R_L = 0.3 value. Please check whether this is a scan-range clipping or a physical NWA/width cut.","section":"Table VII"},{"comment":"A summary of the Delphes detector parameters (b-tagging efficiency, jet radius, jet energy scale) would improve reproducibility.","section":"Sec. III"},{"comment":"The Γ_X/m_X contours are used to justify the NWA, but the actual contour values are not stated in the text. Please provide the relevant Γ_X/m_X values for the benchmark points.","section":"Figs. 11-15"}],"recommendation":"major_revision","confidential_remarks":"The paper is worth publishing after a major revision. The most important issue is not the APV relaxation itself, which is disclosed, but the missing luminosity and reference coupling, which makes every numerical reach result uncheckable. The phase-space endpoint in Table VII and the inconsistent cut definitions in the appendix must also be corrected."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is a competently done simplified-model study of single vector-like X production at future muon-proton colliders, with new quantitative reach tables and a channel ranking. The FH mode is genuinely the strongest, and the headline 2-sigma exclusion of mX ~ 8.3 TeV at g* = 0.009 for R_L = 0.1 is a concrete search target well beyond current LHC coverage. If that benchmark holds up, it is useful input for future collider discussions.\n\nWhat it does well: the cut flows are internally consistent, the background list is reasonable for the final states, and the mode comparison (FH > SL1, SL2 > FL) is credible. It also checks LHC pair-production constraints at fixed R_L, which is a good sanity anchor. Nothing here is formally verified or reproducible from the text alone, but the workflow is standard and the numbers do not look cooked.\n\nNow the soft spots, in roughly increasing severity.\n\nFirst, several reach tables extend m_X up to 9160 GeV at sqrt(s) = 9.16 TeV. That is the kinematic edge where the production phase space closes, so those entries are limits of the scan grid, not genuine bounds, and they should not be quoted as reach without qualification.\n\nSecond, the paper explicitly relaxes the APV bound cited in its own Section II and scans g* up to 0.5. Enforcing that bound would cut away a large fraction of the plotted parameter space. The headline benchmark survives, but the advertised 'broad region' claim does not.\n\nThird, and most important: the integrated luminosity used to convert cross sections into the Asimov significances is never stated. The paper only mentions a 10-100 fb-1 target range. Without L, none of the g* lower bounds in Tables VI-IX can be checked. This is a missing input that affects every numerical result, and the stress-test note is right to flag it. If the authors intended L = 100 fb-1, they need to say so; if some points use something else, the tables need that stated per point.\n\nThere are also no systematic uncertainties in the significances. For a projection paper that is a known weakness but a common one; mentioning it and quoting a band would be enough.\n\nWho is this for? Collider phenomenologists working on VLQ benchmarks and future muon-proton collider studies. It deserves a serious referee, but the referee should demand the luminosity input, the APV overlay on the reach plots, and removal or clarification of the kinematic-edge entries. I would not cite it as is; after those fixes I would.\n\nRecommendation: send to peer review, with the missing luminosity as the main required revision.","headline":"Solid, standard simplified-model projection for VLX at muon-proton colliders; headline reach plausible but the paper omits the luminosity used for its central numbers, and much of the scanned parameter space is already excluded by the APV bound it relaxes.","tokens_in":24657,"tokens_out":1371,"would_cite":false,"duration_ms":13605,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A future muon–proton collider could exclude the vector-like X quark — a hypothetical +5/3-charge partner of the top quark — for masses up to about 8.3 TeV through its tW decay channel, at couplings far below today's LHC reach.","keywords":["vector-like quark","X quark","muon-proton collider","tW channel","single VLQ production","boosted fat jets","beyond Standard Model","Asimov significance"],"falsifier":"Two checks would settle the matter: re-drawing the exclusion contours with the APV constraint g* √(R_L/(1+R_L)) < 6.5×10⁻² enforced — if the g* > 0.1 regions vanish, the broad-reach claim is falsified; and a 9.16 TeV muon–proton run in the fully hadronic channel with about 100 fb⁻¹, which would either confirm the predicted m_X ≈ 7.3 TeV 5σ discovery or rule out the projection with a null result.","tokens_in":23638,"feed_emoji":"⚛️","tokens_out":13753,"duration_ms":104800,"temperature":0.7,"pith_summary":"This paper argues that a future muon–proton collider could find or rule out the vector-like X quark, a hypothetical new fermion of electric charge +5/3, produced singly through μ+p → ν̄μ X with X → tW+. Working in a simplified model with three free parameters — the coupling strength g*, the generation-mixing ratio R_L, and the mass m_X — the authors simulate all four decay topologies of the tW final state at collision energies of 5.29, 6.48, and 9.16 TeV, finding the fully hadronic channel the most sensitive: a 2σ exclusion at m_X ≃ 8.3 TeV with g* = 0.009 for R_L = 0.1 at 9.16 TeV. If correct, this means a muon–proton collider could probe a high-mass, weak-coupling regime where current LHC searches lose sensitivity, at masses several TeV beyond present limits. The reach narrows, however, if the atomic parity violation bound — which the paper deliberately sets aside when scanning g* up to 0.5 — is enforced.","feed_headline":"8.3 TeV: the reach for an exotic X quark at a muon–proton collider","feed_subtitle":"The fully hadronic channel is the strongest, probing couplings far below current LHC limits.","key_machinery":"The central object is the effective Lagrangian for the X–W–quark vertex: LX = g* [ √(R_L/(1+R_L)) (g/√2) X̄_L W+_μ γ^μ u_L + √(1/(1+R_L)) (g/√2) X̄_L W+_μ γ^μ t_L ] + h.c., which concentrates all model dependence into the coupling strength g* and the generation-mixing ratio R_L. Detection rides on the charged-current single-production process μ+p → ν̄μ X and the subsequent decay X → tW+, whose final state is partitioned into four channels — fully leptonic, fully hadronic, and two semi-leptonic modes — according to how the two W bosons decay. The fully hadronic channel is reconstructed with large-radius (fat) jets plus a W-mass window, which is what lets it exploit the highly boosted topology","core_discovery":"The paper's central claim is that single production of the vector-like X quark at a muon–proton collider, followed by X → tW+ decay, is observable over a broad parameter region, with the fully hadronic final state the most powerful of the four channels studied. With an 80% polarized muon beam and fat-jet reconstruction of the boosted hadronic W bosons, the projected 2σ exclusion reaches m_X ≃ 8.3 TeV at √s = 9.16 TeV for g* = 0.009 and R_L = 0.1, and the corresponding 5σ discovery reaches m_X ≃ 7.3 TeV at g* = 0.016. Sensitivity improves monotonically with centre-of-mass energy and with R_L, and the two semi-leptonic modes sit between the hadronic and leptonic extremes. The paper states in S","pith_inferences":["Enforcing the atomic parity violation bound instead of relaxing it would not destroy the headline benchmark — g* = 0.009, R_L = 0.1 sits safely below the limit — but it would erase most of the g* ≳ 0.1 exclusion contours, so the 'broad region' claim should be read as conditional on that relaxation.","The analysis uses sequential cuts; replacing them with a multivariate discriminator over the same boosted-jet observables would likely push the reach beyond what any single cut optimization achieves here.","The same effective-Lagrangian structure and four-channel final-state decomposition transfers to the vector-like T and B quarks and to the (X,T) doublet representation, making this a template for a broader vector-like quark programme at a muon–proton collider.","Since production is mediated by a W boson from the muon, the attainable mass limit inherits the proton PDF behaviour; a higher-energy proton beam, or a larger R_L, would push the exclusion boundary toward 10 TeV, as Tables VI–IX already hint."],"forward_implications":["At the highest energy considered (√s = 9.16 TeV), a null result in the fully hadronic channel would exclude X-quark masses up to about 8.3 TeV at 2σ for R_L = 0.1, several TeV beyond present LHC bounds.","A 5σ discovery in the same channel would be possible up to m_X ≃ 7.3 TeV, opening a multi-TeV window that pair-production searches cannot reach for weakly coupled states.","Because the reach extends down to g* ≈ 0.006–0.016, the analysis covers couplings far below the κ > 0.16–0.2 range probed by current LHC single-production searches.","Sensitivity scales strongly with centre-of-mass energy and with R_L, so the same analysis design transfers directly to any future upgrade of the muon beam energy.","The fully leptonic mode, despite its clean signature, has the weakest mass reach, so a complete programme would need all four channels to cover the parameter space."],"fun_headline_variants":["Exotic X quark: muon-proton collider reaches 8.3 TeV exclusion","Hadronic channel gives best shot at X quark: 8.3 TeV at μp collider","Muon-proton collider could exclude vector-like X up to 8.3 TeV","Future μp collider probes X quark with 8.3 TeV sensitivity","X quark hunt: fully hadronic decay is key at muon-proton collider"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The claim of a 'broad region' of reachable parameter space rests on relaxing the atomic parity violation bound that constrains the X–u–W coupling; if that low-energy bound is enforced, most of the scanned coupling range g* ≳ 0.1–0.2 is already excluded, and only the low-coupling benchmarks near g* = 0.009 survive.","fun_headline_variants_meta":{"raw":{"variants":["Exotic X quark: muon-proton collider reaches 8.3 TeV exclusion","Hadronic channel gives best shot at X quark: 8.3 TeV at μp collider","Muon-proton collider could exclude vector-like X up to 8.3 TeV","Future μp collider probes X quark with 8.3 TeV sensitivity","X quark hunt: fully hadronic decay is key at muon-proton collider"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000788,"raw_usage":{"total_tokens":3400,"prompt_tokens":918,"completion_tokens":2482,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":662,"completion_tokens_details":{"reasoning_tokens":2374}},"tokens_in":662,"tokens_out":2482,"duration_ms":16841,"temperature":1.0,"reasoning_tokens":2374,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T14:09:29.850955+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Two checks would settle the matter: re-drawing the exclusion contours with the APV constraint g* √(R_L/(1+R_L)) < 6.5×10⁻² enforced — if the g* > 0.1 regions vanish, the broad-reach claim is falsified; and a 9.16 TeV muon–proton run in the fully hadronic channel with about 100 fb⁻¹, which would either confirm the predicted m_X ≈ 7.3 TeV 5σ discovery or rule out the projection with a null result.","supporting_citations":[],"review_version":1}