⚛️ phenomenology

Boosted top tagging via lepton-in-jet topology for vector-like quark searches in FCC-hh

This paper presents a machine-learning-based framework for identifying highly boosted, leptonically decaying top quarks at the 100 TeV FCC-hh, demonstrating that both variable-based and constituent-based taggers achieve comparable performance and enabling a search for vector-like $B'$ quarks with a discovery reach of up to 10 TeV.

Original authors: Sanchari Bhattacharyya, Biplob Bhattacherjee, Kirana K. K., Swagata Mukherjee

Published 2026-10-06

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CC BY 4.0

Original authors: Sanchari Bhattacharyya, Biplob Bhattacherjee, Kirana K. K., Swagata Mukherjee

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is built from a small set of fundamental particles that interact through forces, a framework known as the Standard Model. This model has been incredibly successful, predicting the behavior of matter with extreme precision and confirming the existence of the Higgs boson. Yet, it leaves major questions unanswered, such as the nature of dark matter and why neutrinos have mass. To find answers, physicists look for new, heavier particles that do not fit into the current model. These hypothetical particles, if they exist, would be too massive to be created by today's most powerful particle collider. To see them, scientists are planning a future machine called the Future Circular Collider, which will smash protons together at energies far beyond what is currently possible.

When these new, heavy particles are created in such a collision, they are expected to decay almost instantly into lighter, known particles. One promising candidate for a new heavy particle is a vector-like quark, a type of matter that behaves differently from the quarks making up our everyday world. If such a particle exists, it might decay into a top quark and a W boson. The top quark is the heaviest known particle, and when it is produced with immense energy, it moves so fast that its decay products are squashed together into a single, narrow stream. This creates a unique challenge: the top quark decays into a bottom quark, a neutrino, and a charged particle like an electron or muon. Because the top quark is moving so fast, the charged particle ends up trapped inside the stream of debris, making it difficult to distinguish from the background noise of the collision.

A team of researchers has developed a new method to identify these specific, high-speed top quarks using machine learning. They focused on a scenario where a heavy vector-like quark decays into a top quark and a W boson, with both particles eventually producing charged particles. In this event, one charged particle comes from the W boson and is isolated, while the other comes from the top quark and is buried inside a jet of particles. The researchers trained two different types of artificial intelligence to spot this buried particle. One system looked at a list of calculated properties, such as the energy and position of the particles, while the other system examined the individual particles themselves, much like a human would look at the details of a photograph. They tested these systems against various types of background noise, including jets made of bottom quarks and other heavy particles that also contain charged particles.

The results showed that both machine learning approaches were highly effective at finding the buried top quarks. The system that examined individual particles performed slightly better at lower energies, while the system using calculated properties performed just as well at the highest energies. This is significant because it proves that even when particles are so compressed that they are hard to separate, the overall pattern of energy and movement still holds the key to identification. The researchers then used these tools to simulate a search for the heavy vector-like quark at the future collider. They found that with enough data, the collider could discover this new particle if it weighs up to seven trillion electron volts, a mass far beyond what current machines can reach. If the particle is slightly wider or less stable, the search could extend to ten trillion electron volts.

The study also addressed a practical concern for future experiments: the presence of "pile-up," where many extra collisions happen at the same time and create a mess of extra particles. The researchers tested whether their method would still work if they ignored the softer, slower particles that pile-up tends to produce. They found that the identification power remained strong even when focusing only on the most energetic tracks. This suggests that the method is robust enough to handle the chaotic environment of a future high-energy collider. By combining these advanced tagging tools with a broader analysis of the entire collision event, the team demonstrated a clear path to discovering new physics. Their work provides a concrete strategy for how scientists might finally see these elusive, heavy particles when the next generation of colliders comes online.

Technical Summary: Boosted Top Tagging via Lepton-in-Jet Topology for Vector-Like Quark Searches in FCC-hh

Problem Statement
The search for Beyond the Standard Model (BSM) physics, specifically Vector-Like Quarks (VLQs), at the Future Circular Collider in hadron-hadron mode (FCC-hh) operating at $\sqrt{s} = 100$ TeV faces a unique challenge: the extreme kinematic regime. When heavy resonances (e.g., a bottom-like VLQ, $B'$ ) decay into top quarks ( $B' \to tW$ ), the resulting top quarks are highly boosted. In this regime, the decay products of the top quark ( $t \to b\ell\nu$ ) become highly collimated, often merging into a single jet. Specifically, the charged lepton from the top decay is embedded within the top-jet cone, failing standard isolation criteria. This "lepton-in-jet" topology complicates the identification of leptonic top jets against backgrounds such as hadronic top jets, heavy-flavor ( $b$ and $c$ ) jets containing non-isolated leptons from semileptonic decays, and light-flavor jets. Furthermore, the neutrino escapes detection, limiting kinematic reconstruction. The paper investigates whether constituent-based machine learning (ML) architectures retain their discrimination power in this ultra-boosted regime compared to traditional variable-based approaches.

Methodology
The study employs a two-tiered ML framework to identify boosted leptonic top jets and perform a full event-level search for single $B'$ production ( $pp \to B'j \to tWj$ ).

Theoretical Framework and Benchmarking:
- The analysis focuses on a $SU(2)$ singlet bottom-like VLQ ( $B'$ ) with quantum numbers $(3, 1, -1/3)$ .
- The model is defined by two free parameters: the coupling strength $\tilde{g}$ and the mixing parameter $R_L$ (governing coupling to 1st vs. 3rd generation quarks).
- A benchmark point is selected ( $\tilde{g}=0.07, R_L=1.0$ ) to satisfy the width constraint $\Gamma_{B'}/m_{B'} < 25\%$ while maximizing the single-production cross-section.
- Signal events are generated using MadGraph5_aMC@NLO and PYTHIA 8, interfaced with Delphes 3.5.0 using an FCC-hh detector card.
Leptonic-Top Jet Tagger (Object-Level):
- Signal Definition: Jets containing a high- $p_T$ non-isolated lepton ( $p_T > 100$ GeV) originating from $t \to b\ell\nu$ .
- Backgrounds: Hadronic top jets ( $t_{had}$ ), $b$ -jets, and $c$ -jets.
- Approaches: Two complementary classifiers are trained separately in seven lepton $p_T$ $p_{T}$ bins (0.1 TeV to $>3$ $> 3$ TeV):
  - Variable-based DNN: Uses a set of physics-motivated high-level observables, including lepton kinematics, track-based variables (displaced tracks, impact parameters), tower-based isolation variables, and jet substructure (N-subjettiness, jet mass).
  - Constituent-based Particle Transformer (ParT): Operates directly on individual jet constituents (lepton, tracks, calorimeter towers) using a transformer architecture with self-attention mechanisms to learn correlations between particles.
- Training: The taggers distinguish the signal class ( $t_{lep}$ ) from the three background classes.
Event-Level Analysis:
- A second DNN is employed for signal-background discrimination at the event level.
- Input Features: Global kinematic variables ( $H_T$ , $E_T^{miss}$ , dilepton invariant mass), lepton-specific kinematics, and the output scores from the object-level jet taggers.
- Topology: Events are selected with exactly one isolated lepton (from $W$ ) and one non-isolated lepton (from $t$ ), plus significant missing transverse energy.
- Backgrounds: Standard Model processes including $t\bar{t}$ , $tW$ , $VV$ , $W$ +jet, and heavy-flavor production.

Key Contributions

Validation of Constituent-Based ML in Ultra-Boosted Regimes: The paper demonstrates that constituent-based architectures (ParT) remain highly effective even when decay products are collimated, achieving performance comparable to or exceeding engineered variable-based DNNs.
Comprehensive Feature Set: The development of a specific set of variables (including displaced tracks and tower isolation) tailored for the "lepton-in-jet" signature, which is distinct from standard top tagging.
Robustness Checks: The study includes sensitivity analyses regarding soft track activity (simulating pile-up effects) and comparisons with Graph Neural Networks (GNNs) restricted to track-only inputs.
Anomaly Detection Application: The authors explore the use of pre-trained ParT representations in a DeepSVDD framework for one-class anomaly detection, showing potential for identifying unusual jet topologies without explicit background training.

Results

Jet Tagger Performance:
- Both DNN and ParT achieve high tagging efficiencies for leptonic tops (93–97%).
- ParT generally outperforms the DNN at lower and intermediate $p_T$ (AUC 0.994–0.997 vs. 0.981–0.996).
- At very high $p_T$ ( $>2$ TeV), the DNN's mistag rates for backgrounds become slightly lower than ParT's, suggesting that engineered observables retain significant power in the ultra-boosted limit where constituent resolution is challenging.
- In track-only comparisons, ParT (AUC 0.981) significantly outperforms GNN (0.964) and DNN (0.942), highlighting the value of attention mechanisms in capturing track correlations.
Event-Level Sensitivity:
- The event-level DNN achieves an AUC of 0.994 for distinguishing the $B'$ signal ( $m_{B'}=5$ TeV) from SM backgrounds.
- The analysis assumes an integrated luminosity of 30 ab $^{-1}$ .
- Discovery Reach:
  - Under the width constraint $\Gamma_{B'}/m_{B'} < 25\%$ , a $5\sigma$ discovery is achievable for $B'$ masses up to ~7 TeV (even with 10% background systematic uncertainty).
  - Relaxing the width constraint to $\Gamma_{B'}/m_{B'} \lesssim 50\%$ extends the discovery reach to ~10 TeV.
- At $m_{B'} = 10$ TeV, the minimum cross-section required for $5\sigma$ discovery is 0.054 fb (statistics-only) and 0.28 fb (with 10% systematics).

Significance and Claims
The paper claims that the proposed framework provides a realistic and effective strategy for discovering multi-TeV vector-like quarks at the FCC-hh. By successfully identifying the specific "lepton-in-jet" topology, the authors bridge the gap between standard top-tagging techniques and the extreme kinematics of future colliders. The work emphasizes that while constituent-based ML (ParT) offers superior performance in capturing complex correlations, physics-motivated variable-based approaches remain robust and competitive, particularly at the highest energy scales. The integration of object-level tagging with event-level classification allows for the suppression of dominant SM backgrounds (like $t\bar{t}$ and $tW$ ) to a level where heavy resonances can be discovered, even in the presence of systematic uncertainties. The study also highlights the utility of these ML tools for anomaly detection, offering a less model-dependent avenue for new physics searches.

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