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A future muon–proton collider at 9.16 TeV could find vector-like singlet top quarks with masses up to 4–5 TeV, a range far beyond the reach of current LHC searches, using machine-learning classifiers on hadronic and leptonic final states.

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2026-08-03 05:48 UTC pith:6LXGGFLL

load-bearing objection The 500 and 3000 fb^-1 significance tables are identical, so the paper's headline luminosity reach is not supported by its own numbers. the 4 major comments →

arxiv 2602.01010 v2 pith:6LXGGFLL submitted 2026-02-01 hep-ph

Search for Vector-Like Singlet Top (T) Quark in a Future Muon-Proton (μ p) Collider at sqrt{s} = 5.29, 6.48, and 9.16 TeV using Advanced Machine Learning Architectures

Haroon Sagheer , M. Tayyab Javaid , Mudassar Hussain , M. Danial Farooq , Ijaz Ahmed , Jamil Muhammad This is my paper
classification hep-ph PACS 12.60.Fr14.65.Jk12.60.-i14.80.Fd
keywords vector-like top quarkmuon-proton collidersingle productionT->Wb decaymachine learning classifierssignal significanceAsimov significancebeyond Standard Model
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper sets out to show that a future muon–proton collider can discover a vector-like singlet top quark (T) through single electroweak production, using the T→Wb decay in both fully hadronic (bjj) and leptonic (blν) final states. It claims that at a center-of-mass energy of 9.16 TeV, even 100 fb–1 of data gives a statistical significance above 5σ for T masses up to 4 TeV, and that with 3000 fb–1 the leptonic channel with a boosted decision tree extends the 5σ reach to about 5 TeV for couplings g* down to 0.10. The study maps this reach onto the (m_T, g*) parameter plane, identifies a mass-dependent crossover between hadronic and leptonic sensitivity, and folds in a 20% systematic uncertainty through an Asimov significance. The result matters because it would probe mass scales beyond current collider limits and test composite-Higgs and extra-dimensional models.

Core claim

The central claim is that single production of a vector-like singlet T quark at a future muon–proton collider is discoverable with high statistical significance over Standard Model backgrounds. Concretely, the paper reports that at √s = 9.16 TeV the hadronic channel yields Z > 5σ at 100 fb–1 for m_T up to 4 TeV, and that at 3000 fb–1 the leptonic channel with BDT keeps Z_A > 5σ (after a 20% systematic uncertainty) up to m_T ≈ 5 TeV for g* ∈ [0.10, 0.50]. The authors also report a crossover: the hadronic channel dominates at intermediate masses (2–3 TeV) because of the larger T→Wb branching ratio, while the leptonic channel is more resilient at the kinematic frontier because of its cleaner ba

What carries the argument

The argument is carried by a simulation chain with Monte Carlo event generation, parton showering, and fast detector simulation for the processes μ−p → νμ T b̄ with T→Wb, against Standard Model backgrounds (single top, W+jets, Z+jets, multijet). Two final states are analyzed separately: hadronic bjj and leptonic blν, with sequential cuts on jet/lepton pT, multiplicities, b-tags, missing transverse momentum, and angular separations. The key discriminating variables are reconstructed mass peaks M_bjj and M_blν, missing transverse energy, and helicity angles. Four multivariate classifiers—boosted decision trees, gradient-boosted decision trees, multilayer perceptrons, and likelihood—are trained

Load-bearing premise

Each reported significance is the maximum over four classifiers chosen on the same test sample, with no trial-factor correction; if a single classifier had been fixed in advance, the quoted Z values would likely be lower.

What would settle it

Recompute the significances with a strictly pre-specified classifier (for instance, the BDT chosen before seeing any test events) or with a nested cross-validation that separates classifier selection from significance estimation. If the Z values for the claimed boundary points—such as 4 TeV hadronic at 100 fb–1 or 5 TeV leptonic at 3000 fb–1—drop below 5σ, the central discovery claim fails. Alternatively, a single run on an independent Monte Carlo sample with the same selection would provide a direct check.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • At √s = 9.16 TeV, a future muon–proton collider would have >5σ discovery sensitivity for single vector-like T production at 100 fb–1 for masses up to 4 TeV, well beyond the current LHC mass limits.
  • With 3000 fb–1, the leptonic channel with a BDT classifier would maintain 5σ sensitivity up to m_T ≈ 5 TeV for couplings g* ≥ 0.10, enabling a search far beyond the HL-LHC's pair-production reach.
  • The hadronic channel, with its larger branching fraction, provides the strongest early sensitivity for m_T around 2–3 TeV, making it the natural first-look channel.
  • The crossover between hadronic and leptonic dominance as a function of m_T gives a two-stage discovery strategy: hadronic for first evidence, leptonic for confirmation at the high-mass frontier.
  • The saturation of Asimov significance at high luminosity quantifies when systematic uncertainties, not statistics, limit the search, meaning further luminosity after that point yields little new reach.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The claimed reach assumes the best of four classifiers is chosen per mass point without a trial-factor correction; if a single pre-specified classifier were required, the effective significance at the quoted mass boundaries would be lower. A re-analysis with a fixed classifier or with a correction for the number of classifiers tried would test how much of the 5σ claim depends on this selection.
  • The crossover effect suggests an empirical prediction: in a real detector, the hadronic channel should reveal a broad excess in the 2–3 TeV region first, while the leptonic channel should show a narrower, higher-purity excess near 5 TeV if the T exists and couples as assumed.
  • The paper stops at T→Wb; extending the same framework to T→tZ and T→tH would test the Goldstone-boson-equivalence prediction that these branching ratios become comparable at high mass, providing a model-discriminating cross-check.
  • If the 9.16 TeV energy is not achievable, the results imply that energy is the dominant lever: the 5.29 TeV configuration loses sensitivity above 3 TeV, suggesting that investing in higher beam energy rather than luminosity is the efficient path to multi-TeV search reach.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper presents a Monte Carlo feasibility study of single production of a vector-like singlet top quark (T) at a future muon-proton collider with sqrt(s) = 5.29, 6.48, and 9.16 TeV, focusing on the T -> Wb decay in fully hadronic (bjj) and leptonic (blnu) final states. Signal and background samples are generated with MadGraph5, PYTHIA8, and Delphes3, and four TMVA classifiers (BDT, BDTG, MLP, Likelihood) are trained per mass point. The central quantitative claims are the statistical significances in Tables VIII-X and the resulting g*-mT reach plots: the abstract states that 9.16 TeV gives >5 sigma up to 4 TeV with 100 fb^-1 and that at 3000 fb^-1 the hadronic/leptonic channels reach mT up to 4-5 TeV for g* in [0.10, 0.50].

Significance. If the quoted significances were reliable, the paper would provide a useful phenomenological benchmark for VLQ searches at a future muon-proton collider. The paper has clear strengths in scope and execution of the simulation chain: full LO event generation with showering and fast detector simulation, multiple decay channels, and several ML classifiers with overtraining checks. However, the load-bearing statistical results are internally inconsistent. Tables IX and X are numerically identical despite differing by a factor of six in luminosity, and multiple entries have Asimov significance larger than the Gaussian significance, which is incompatible with a 20% systematic uncertainty that should reduce sensitivity. These issues directly undermine the abstract and conclusion claims. The best-classifier-per-mass-point selection on the same test sample also introduces an uncontrolled trial factor. The central quantitative claims cannot be considered supported by the presented results.

major comments (4)
  1. [Tables IX and X] Tables IX (L=500 fb^-1) and X (L=3000 fb^-1) are numerically identical for every mass point, classifier, channel, and energy: all Z and Z_A entries are exactly the same. Since S and B scale linearly with luminosity, Eq. (8) requires Z to grow by sqrt(3000/500)=sqrt(6)≈2.45 in the statistical limit. The absence of any change means the 3000 fb^-1 results were not obtained from the stated calculation. All conclusions quoting 3000 fb^-1 numbers (e.g., Z_A = 42.23 at 2.5 TeV hadronic, Z_A = 30.76 at 4 TeV leptonic) are unsupported.
  2. [Table VIII, Z_A > Z entries] The Asimov significance Z_A is supposed to include a 20% background systematic and should therefore be no larger than the Gaussian significance Z. Many entries violate this, e.g., Table VIII, 5.29 TeV hadronic 2000 GeV: Z=16.62, Z_A=21.83; Table VIII, 9.16 TeV hadronic 4500 GeV: Z=21.28, Z_A=36.60. This is not a small rounding effect and indicates that either the event yields, the systematic treatment, or the definition of Z_A used to produce the tables is not the one described in Sec. IV.D.
  3. [Sec. IV.D and Tables VIII-X] For each mass point the quoted significance is the maximum over four classifiers (BDT, BDTG, MLP, Likelihood), with the best classifier chosen on the same simulated test sample used to evaluate the significance. This is a form of selection on the test set: the maximum of four positively correlated statistics is biased upward relative to any pre-specified classifier. No trial-factor correction is applied or discussed. Since the reach conclusions are based on these maxima, the quoted discovery potential is systematically optimistic.
  4. [Fig. 11 and Sec. IV.E] The g* parameter in the reach maps is never defined in terms of the Lagrangian in Eq. (1), which uses kappa_W, kappa_Z, kappa_H and V4i. No cross-section formula or scaling relation is given, so the g*-mT exclusion and discovery regions cannot be reproduced or checked. This is a load-bearing omission because the abstract and conclusion state reach specifically as a function of g*.
minor comments (3)
  1. [Sec. III.B] The text says 'T ransverse Mass' and 'Heliciy Angle'; these typos should be corrected. Also 'amd' in Sec. IV.A.
  2. [Tables IX-X] In Table IX, 2500 GeV, 5.29 TeV leptonic, the classifier is listed as 'Leptonic', which is a channel name, not a classifier. In Table X the same entry says 'Like'. This inconsistency makes the tables harder to interpret.
  3. [References] Several references are duplicated (e.g., DELPHES3 refs [11], [46], [61]; CMS leptonic VLQ refs [29], [44], [57]). The reference list would benefit from deduplication.

Circularity Check

0 steps flagged

No significant circularity; the central Monte Carlo projections are independent. Internal numerical inconsistencies (Table X = Table IX, Z_A > Z) undermine the 3000 fb^-1 claims but are correctness issues, not derivation-circularity.

full rationale

The paper does not present a derivation chain in which an output quantity is defined in terms of the quantity it claims to predict. Signal/background samples are generated with MadGraph/PYTHIA/Delphes, classifiers are trained with TMVA, and significances are computed from Eq. (8), Z = S/sqrt(S+B). The g* reach maps scan an input coupling parameter, which is a standard phenomenological scan rather than a fitted-input-called-prediction. The self-citations (e.g., Refs. [40,41] by authors Ahmed and Muhammad) are used only as examples of multivariate collider studies and are not load-bearing for the VLQ reach claims. However, two internal inconsistencies should be flagged as correctness risks, not circularity: (1) Table X at L=3000 fb^-1 is numerically identical to Table IX at L=500 fb^-1 for every listed Z and Z_A value, despite the paper's own statement that Gaussian significance follows Z ∝ sqrt(L) and Eq. (8)'s linear scaling of S and B with luminosity; the conclusion's quoted values Z_A = 42.23 and 30.76 from Table X are therefore unsupported by the stated calculation. (2) Multiple entries have Z_A > Z (e.g., Table VIII, 5.29 TeV hadronic 2000 GeV: Z=16.62, Z_A=21.83), which is inconsistent with the described 20% systematic uncertainty reducing significance. Additionally, the practice of choosing the best-performing classifier per mass point on the same simulated test sample used to evaluate significance introduces an optimistic bias, but it is a statistical selection effect rather than a reduction of the result to its inputs. These issues affect the reliability of the quoted discovery reach but do not make the derivation circular.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central claims rest on Monte Carlo simulation, assumed beam parameters, an undefined coupling parameter g*, and repeated use of significance formulas. The ledger lists the assumptions and hand-chosen inputs that the projected reach depends on.

free parameters (3)
  • g* (heavy-state coupling) = 0.10–0.50 (scanned, undefined)
    Appears in sensitivity maps and conclusions, but no relation to κW,Z,H in Eq. (1) is given.
  • 20% background systematic = 0.20
    Assumed for Asimov significance; no derivation or covariance model is provided.
  • TMVA hyperparameters = not listed
    Manually tuned in Sec. IV.A; not reported, so classifier performance and significance cannot be independently reproduced.
axioms (4)
  • domain assumption MadGraph5+Pythia8+Delphes give a faithful description of signal and backgrounds at LO/fast-simulation level
    No validation against data, NLO corrections, or detailed detector performance is shown; all efficiencies depend on this.
  • domain assumption The effective singlet-VLQ Lagrangian (Eq. 1) and branching-ratio formula (Eq. 2) define the signal model
    Standard framework, but it does not define g* or relate it to κW,Z,H.
  • domain assumption A muon-proton collider with √s=5.29, 6.48, 9.16 TeV and up to 3000 fb^{-1} is a meaningful facility assumption
    These parameters are taken as given; no accelerator design or running-time justification is provided.
  • domain assumption Z=S/√(S+B) and the Asimov significance procedure are valid for the quoted event counts
    Used in Sec. IV.D; no validity conditions (e.g., S<<B, Gaussian approximation) are checked, and the tables violate expected scaling.

pith-pipeline@v1.3.0-alltime-deepseek · 18666 in / 15767 out tokens · 156147 ms · 2026-08-03T05:48:10.821546+00:00 · methodology

0 comments
read the original abstract

In this work, we explore the discovery potential of Vector-Like Singlet Top quarks ($T$) at a future $\mu p$ collider with center-of-mass energies of 5.29, 6.48, and 9.16 TeV, providing a unique environment to probe beyond Standard Model limits. We analyze the $T \to Wb$ decay mode in both fully hadronic ($bjj$) and leptonic ($bl\nu$) final states, offering a multi-channel assessment of $T$-quark sensitivity across a mass range of 2 to 5 TeV. Our methodology employs multivariate classifiers such as Boosted Decision Trees (BDTs) and Multi-Layer Perceptrons (MLP) to optimize signal-to-background discrimination in complex final states. The results demonstrate that the 9.16 TeV benchmark acts as a definitive discovery machine; even with 100 fb$^{-1}$ of data, the statistical significance exceeds $5\sigma$ up to 4 TeV masses. We identify a crossover effect where hadronic channels provide superior reach at intermediate masses due to higher branching ratios, while leptonic channels offer robustness at 5 TeV where purity limits detection. Incorporating a 20\% systematic uncertainty via Asimov significance ($Z_A$), we quantify the transition from fluctuation-dominated to systematic-dominated regimes at high luminosities. At 3000 fb$^{-1}$, regions with $g^{*} \in [0.20, 0.50]$ and $m_T$ up to 4 TeV are discoverable via the hadronic channel with MLP, and regions with $g^{*} \in [0.10, 0.50]$ and $m_T$ up to 5 TeV are accessible through the leptonic channel with BDT, highlighting the collider's potential to probe new physics beyond the Standard Model.

Figures

Figures reproduced from arXiv: 2602.01010 by Haroon Sagheer, Ijaz Ahmed, Jamil Muhammad, M. Danial Farooq, M. Tayyab Javaid, Mudassar Hussain.

Figure 1
Figure 1. Figure 1: FIG. 1: Representative leading-order (LO) Feynman diagram for the single production of a vector [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Representative leading-order (LO) Feynman diagram for single production of a vector-like [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The Hadronic and Leptonic Signal efficiency [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The Output Distribution Score and Overtraining Evaluation of all ML Classifiers (BDTs, [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The Output Distribution Score and Overtraining Evaluation of all ML Classifiers (BDTs, [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The Comparison of AUC (Area Under the Curve) vs [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The Comparison of AUC (Area Under the Curve) vs [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The reconstruction of all [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The Reconstruction of all [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The illustration of (a) Hadronic and (b) Leptonic signal significances at [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: The Exclusion and Discovery capabilities using MLP for the (a) Hadronic and BDT [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗

discussion (0)

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Forward citations

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