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arxiv: 2606.03913 · v1 · pith:J5LN3RM4new · submitted 2026-06-02 · ✦ hep-ph

Probing Singlet Vector-Like Top Quarks in the Hadronic tZ Channel at the HL-LHC using Machine and Deep Learning Architectures

Haroon Sagheer , M. Tayyab Javaid , Ijaz Ahmed , Jamil Muhammad This is my paper

Pith reviewed 2026-06-28 09:03 UTC · model grok-4.3

classification ✦ hep-ph
keywords vector-like top quarkssinglet top partnerHL-LHCmachine learninggraph neural networkhadronic tZ channelsingle productionAsimov significance
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The pith

XGBoost and graph neural networks exclude vector-like singlet top partners with g* as low as 0.16 at 2σ in the hadronic tZ channel at HL-LHC.

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

The paper establishes projected sensitivities for single production of a vector-like singlet top partner T decaying to tZ in the fully hadronic final state at the 14 TeV high-luminosity LHC. Signal and background events are generated with standard Monte Carlo tools, passed through a hadronic pre-selection, and classified with jet-level features using both Extreme Gradient Boosting and a Graph Neural Network. A sympathetic reader would care because the resulting 2σ exclusion and 5σ discovery contours in the (g*, m_T) plane quantify how much parameter space can be probed or ruled out with 3000 fb^{-1} of data. The work compares results for two values of the parameter R_L and includes a 20% background systematic in the Asimov significance calculation.

Core claim

For R_L = 0 the analysis finds that 2σ exclusion is possible for g* in the interval [0.17, 0.49] with XGBoost and [0.16, 0.43] with the GNN across m_T from 1.8 to 2.7 TeV, while 5σ discovery reaches g* in [0.27, 0.44] and [0.26, 0.40] for m_T from 1.8 to 2.2 TeV; the corresponding intervals for R_L = 0.5 are shifted to slightly higher couplings but remain comparable in mass reach, with the GNN yielding marginally stronger and smoother limits in both cases.

What carries the argument

Extreme Gradient Boosting and Graph Neural Network classifiers trained on jet-level kinematic features after hadronic pre-selection (N_j ≥ 3, N_b ≥ 1, N_ℓ = 0) and optimized kinematic cuts in the tZ channel.

If this is right

  • For R_L = 0, 2σ exclusion of g* down to 0.16–0.17 is possible up to m_T = 2.7 TeV.
  • 5σ discovery is achievable for g* above 0.26–0.27 for m_T between 1.8 and 2.2 TeV.
  • The GNN produces slightly stronger limits than XGBoost across the scanned parameter space.
  • For R_L = 0.5 the 2σ exclusion window moves to g* ∈ [0.20, 0.48] up to m_T = 2.5 TeV.
  • All reaches incorporate a 20% background systematic uncertainty via the Asimov significance formula.

Where Pith is reading between the lines

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

  • Similar jet-level ML classifiers could be applied to other vector-like quark decay modes to improve overall search sensitivity.
  • The modest advantage of the GNN over XGBoost suggests that graph representations of jet correlations may become standard for fully hadronic final states.
  • Validation of the simulated background modeling against early HL-LHC data would be required before the projected reaches can be treated as reliable.
  • Combining the hadronic tZ channel with leptonic or multi-lepton channels could further extend the mass and coupling coverage.

Load-bearing premise

Monte Carlo generators and detector simulation correctly reproduce the kinematic distributions and rates of the dominant backgrounds, and the trained classifiers will perform similarly on real collision data.

What would settle it

A statistically significant mismatch between predicted and observed yields in a signal-depleted control region or after applying the ML working point to actual HL-LHC collision data would invalidate the quoted exclusion and discovery reaches.

Figures

Figures reproduced from arXiv: 2606.03913 by Haroon Sagheer, Ijaz Ahmed, Jamil Muhammad, M. Tayyab Javaid.

Figure 1
Figure 1. Figure 1: Branching ratio Br(T → tZ) in the (RL, mT ) plane. where i = 1, 3 denotes the generation index and ci = (c1, c3). The total width is obtained by summing over all accessible modes and generations, and the branching ratio for the signal channel is Br(T → tZ) = Γ(T → Zt) Γtot . (9) In the large-mT limit the overall factor (gg∗ ) 2 cancels in ratios, so Br(T → tZ) depends pri￾marily on RL and only weakly on mT… view at source ↗
Figure 2
Figure 2. Figure 2: Representative LO t-channel diagram for single production pp → T j in the 5FS with T → tZ, t → bW → bjj, and Z → νν¯. 4 The Machine and Deep Learning Methods for the Classifica￾tion The fully hadronic tZ topology with large missing transverse momentum exhibits correlated kinematic and angular structure that is difficult to capture with cut-based selections alone. To maximize signal sensitivity while contro… view at source ↗
Figure 3
Figure 3. Figure 3: Input variable distributions for XGBoost at the benchmark mass [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Input variable distributions for GNN at the benchmark mass [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Classifier score distributions for signal and background at the benchmark mass [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: ROC curves at mT = 2000 GeV for (a) XGBoost and (b) GNN [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Test AUC vs. mT for XGBoost and GNN. 11 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Significance vs. mT at the global threshold for (a) XGBoost and (b) GNN [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Exclusion and discovery contours in the ( [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Exclusion and discovery contours in the ( [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
read the original abstract

In this work, we study the single production of a vector-like singlet top partner \( T \) at the 14 TeV HL-LHC in the channel \( pp \to T j \) with \( T \to t Z \), \( t \to b W \to b j j \), and \( Z \to \nu \bar{\nu} \). Signal and background samples are generated with MadGraph5\_aMC@NLO v3.5.11, showered with Pythia 8, and passed through Delphes. The dominant backgrounds are \( t \bar{t} \), \( t Z j \), \( ZZ j j \), and \( W Z j j \) (including charge conjugates). A hadronic pre-selection (\( N_j \geq 3 \), \( N_b \geq 1 \), \( N_\ell = 0 \)) is imposed as trigger, followed by optimized kinematic cuts. We perform multivariate classification with Extreme Gradient Boosting (XGBoost) and a Graph Neural Network (GNN) based on jet-level features. Sensitivities at 3000 fb\(^{-1}\) are quoted using the Asimov significance, \( S / \sqrt{S + B} \), and an Asimov variant with a 20\% background systematic. The model parameters \( g^* \) and \( R_L \) are defined in Sec.~2, and a single global working point is used to avoid per-mass tuning bias. In the \( (g^*, m_T) \) scan, we present 2\(\sigma\) exclusion and 5\(\sigma\) discovery contours for \( R_L = 0 \) and \( R_L = 0.5 \). For \( R_L = 0 \), 2\(\sigma\) exclusion corresponds to \( g^* \in [0.17, 0.49] \) (\( 0.16, 0.43 \)) over \( m_T \in [1.8, 2.7] \) TeV, while 5\(\sigma\) discovery corresponds to \( g^* \in [0.27, 0.44] \) (\( 0.26, 0.40 \)) over \( m_T \in [1.8, 2.2] \) TeV for XGBoost and GNN respectively. For \( R_L = 0.5 \), the 2\(\sigma\) reach is \( g^* \in [0.21, 0.48] \) (\( 0.20, 0.43 \)) over \( m_T \in [1.8, 2.5] \) TeV, and the 5\(\sigma\) reach is \( g^* \in [0.33, 0.43] \) (\( 0.31, 0.49 \)) over \( m_T \in [1.8, 2.2] \) TeV, with the GNN yielding slightly stronger and smoother limits across the scan.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper studies single production of a singlet vector-like top partner T in the pp → Tj, T → tZ (hadronic) channel at the 14 TeV HL-LHC with 3000 fb⁻¹. Samples are generated with MadGraph5_aMC@NLO + Pythia 8 + Delphes; after hadronic pre-selection (Nj ≥ 3, Nb ≥ 1, Nℓ = 0) and kinematic cuts, XGBoost and a jet-based GNN are used for classification against tt̄, tZj, ZZjj, and WZjj backgrounds. Sensitivities are reported via the Asimov significance S/√(S+B) (with and without 20% background systematic) as 2σ exclusion and 5σ discovery contours in the (g*, m_T) plane for RL = 0 and RL = 0.5, with explicit numerical ranges given for each classifier.

Significance. If the Monte Carlo modeling of the fully hadronic final state is reliable, the work supplies concrete, up-to-date HL-LHC projections that incorporate modern jet-level classifiers (including a GNN) and a single global working point to reduce tuning bias. The explicit tabulation of g* intervals for both exclusion and discovery is a useful benchmark for experimental planning. The central results, however, rest entirely on the unvalidated simulation chain.

major comments (2)
  1. [multivariate classification section] The manuscript supplies no information on training/validation splits, hyperparameter optimization, or cross-validation procedure for the XGBoost and GNN classifiers (multivariate classification section). Because the quoted 2σ and 5σ reaches are obtained directly from the classifier output distributions via the Asimov formula, these details are required to assess whether the reported performance is robust or overfit.
  2. [simulation and background modeling section] No control-region closure tests, generator-variation studies, or data-driven background estimates are described for the dominant backgrounds (tt̄, tZj, ZZjj, WZjj) in the presence of MET (simulation and background modeling section). All sensitivity contours in the (g*, m_T) plane are derived exclusively from these simulated samples; any mismodeling in jet energy scale, b-tagging, or MET tails would directly shift the Asimov significances.
minor comments (1)
  1. [Abstract] The abstract states that kinematic cuts are 'optimized' but neither the optimization criterion nor the numerical cut values are given; these should be listed explicitly in the main text.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful review and constructive comments. We address each major comment below and indicate the revisions planned for the manuscript.

read point-by-point responses

  1. Referee: [multivariate classification section] The manuscript supplies no information on training/validation splits, hyperparameter optimization, or cross-validation procedure for the XGBoost and GNN classifiers (multivariate classification section). Because the quoted 2σ and 5σ reaches are obtained directly from the classifier output distributions via the Asimov formula, these details are required to assess whether the reported performance is robust or overfit.

    Authors: We agree that these methodological details are essential to evaluate robustness and potential overfitting. In the revised manuscript we will expand the multivariate classification section to specify the training/validation/test split (70/15/15), the hyperparameter optimization procedure (grid search combined with 5-fold cross-validation), and the cross-validation strategy used for both XGBoost and the GNN. These additions will allow readers to assess the reliability of the Asimov significances derived from the classifier outputs. revision: yes

  2. Referee: [simulation and background modeling section] No control-region closure tests, generator-variation studies, or data-driven background estimates are described for the dominant backgrounds (tt̄, tZj, ZZjj, WZjj) in the presence of MET (simulation and background modeling section). All sensitivity contours in the (g*, m_T) plane are derived exclusively from these simulated samples; any mismodeling in jet energy scale, b-tagging, or MET tails would directly shift the Asimov significances.

    Authors: This is a prospective HL-LHC projection study performed entirely with Monte Carlo samples, so data-driven background estimates and control-region closure tests with real data are not possible. In revision we will augment the simulation section with additional details on generator settings, a qualitative discussion of jet-energy-scale and b-tagging uncertainties, and an explicit statement of how the already-included 20% background systematic is intended to cover potential mismodeling. Generator-variation studies will be added where computationally feasible. revision: partial

standing simulated objections not resolved
  • Data-driven background estimates and control-region closure tests cannot be performed in the absence of actual HL-LHC collision data.

Circularity Check

0 steps flagged

No significant circularity in sensitivity projections

full rationale

The paper generates signal and background samples using external MC generators (MadGraph5_aMC@NLO, Pythia 8, Delphes), applies fixed pre-selections and kinematic cuts, trains XGBoost/GNN classifiers on jet-level features, and computes Asimov significances directly from the simulated yields to obtain the (g*, m_T) contours. No parameters are fitted to the target reaches, no self-citations justify uniqueness or ansatze, and no step reduces by construction to its own inputs. The derivation is self-contained forward simulation; the load-bearing assumptions concern MC fidelity rather than internal circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the accuracy of standard Monte Carlo tools for background modeling and on the assumption that ML performance on simulation transfers to data; no new free parameters are fitted to the target result.

axioms (1)
  • domain assumption Monte Carlo event generators and Delphes detector simulation accurately model signal and background kinematics and rates in the hadronic final state.
    Invoked implicitly when the paper uses generated samples to train classifiers and compute significances.
invented entities (1)
  • Singlet vector-like top partner T no independent evidence
    purpose: Signal hypothesis whose production and decay are simulated to set experimental reaches.
    The particle is postulated as an extension of the Standard Model; no independent evidence is provided within the paper.

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discussion (0)

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