Improving sensitivity of vectorlike top partner searches with jet substructure

This paper enhances the sensitivity of searches for vectorlike top partners produced with a Standard Model top quark by employing a multivariate analysis that leverages jet substructure techniques and event shape observables across both fixed and dynamically varying jet radii to effectively handle boosted decay scenarios.

The Gist

Imagine you are a detective trying to find a very specific, rare criminal hiding in a massive, chaotic city square. This city square is the Large Hadron Collider (LHC), a giant machine that smashes particles together at incredible speeds. The "criminal" you are looking for is a Vectorlike Top Partner—a heavy, exotic particle that doesn't exist in our everyday world but might explain why the universe is the way it is.

Here is a simple breakdown of what the authors of this paper did, using everyday analogies.

1. The Mission: Finding the "Ghost" Particle

The Standard Model of physics is like a rulebook for how the universe works. But it has holes in it. It can't explain why things have mass or why the universe is stable. Scientists think there are "new rules" (New Physics) involving heavy particles like the Top Partner.

Think of the Top Partner as a heavy twin of the top quark (the heaviest known particle). If we can find this twin, it might solve the mystery of why the universe doesn't collapse.

2. The Problem: The "Crowded Market"

When the LHC smashes particles, it creates a chaotic explosion of debris.

• The Signal: The rare Top Partner decaying into specific pieces (like a heavy jet, a lepton, and missing energy).
• The Background: Millions of ordinary particles (Standard Model junk) flying around that look almost exactly like the signal.

It's like trying to find a specific, rare red balloon in a stadium filled with millions of red balloons, plus a few blue ones, and a lot of confetti. The "noise" is so loud that the "signal" gets drowned out.

3. The Old Tool: The "Fixed-Size Net"

To catch these particles, physicists use "jets" (clumps of debris). Traditionally, they use a fixed-radius algorithm.

• The Analogy: Imagine trying to catch fish in a river with a net that is always exactly 1 meter wide.
  • If the fish is small, the net works fine.
  • If the fish is huge and spreads out, the net might cut off its tail.
  • If the fish is tiny and tight, the net catches a lot of extra water and mud (noise) along with it.

In the LHC, when particles are moving super fast (high energy), they spread out like a giant, fluffy cloud. A fixed-size net often misses parts of this cloud or catches too much garbage.

4. The New Tool: The "Smart, Stretchy Net"

This paper introduces a new method called Dynamic Radius (DR) Jet Clustering.

• The Analogy: Instead of a rigid 1-meter net, imagine a smart, stretchy net that can change its size.
  • If the particle is small and tight, the net shrinks to fit it perfectly, ignoring the surrounding mud.
  • If the particle is huge and spread out (like a "fat jet" from a heavy Top Partner), the net stretches wide to catch the whole thing without losing any pieces.

The authors tested this "smart net" against the old "fixed net" to see which one was better at finding the Top Partner.

5. The Investigation: How They Did It

The team simulated a collision event on a computer:

1. The Setup: They created a scenario where a Top Partner is produced alongside a normal top quark.
2. The Decay: The Top Partner breaks apart into four possible combinations (like a top quark + a W boson, or a top quark + a Higgs boson, etc.).
3. The Filter: They looked for events with:
   • One "fat jet" (the big, spread-out debris from the heavy particle).
   • One "b-tagged jet" (a specific type of debris from a bottom quark).
   • One lepton (an electron or muon).
   • Missing energy (invisible particles like neutrinos).
4. The Substructure: They didn't just look at the whole net; they looked inside the net. They used tools like Soft Drop (trimming off the fuzzy edges of the net) and N-subjettiness (checking if the debris inside looks like it came from 2 or 3 distinct sources, which is a signature of a heavy particle).

6. The Results: The Smart Net Wins

After running thousands of simulations and using a "brain" (a machine learning algorithm called a Boosted Decision Tree) to sort the good events from the bad ones, they found:

• In the "High-Speed" Zone: When the particles were moving very fast (high energy), the Dynamic Radius (smart net) was significantly better.
• Why? It captured the full shape of the heavy particle's debris more accurately, while the fixed net either cut off pieces or included too much background noise.
• The Outcome: Using the smart net allowed them to set tighter limits on where this Top Partner could be hiding. It means they can rule out more possibilities and get closer to finding the real thing.

Summary

Think of this paper as a guide for detectives. The authors said: "We are looking for a rare, heavy criminal in a chaotic city. The old way of searching (using a fixed-size net) works okay, but when the criminal is running very fast and spreading out, we need a better tool. We tested a new 'smart, stretchy net' (Dynamic Radius clustering), and it caught the criminal's clues much better than the old net, especially in the high-speed chase scenarios."

This improvement is crucial for future experiments, like the High-Luminosity LHC, where the collisions will be even more energetic and the particles even faster. The "smart net" will be essential for finding the new physics hiding in the chaos.

Technical Summary

1. Problem Statement

The search for Beyond the Standard Model (BSM) physics, specifically Vector-Like Quarks (VLQs), is a primary goal of the Large Hadron Collider (LHC). Vector-like top partners ($T$) are motivated by their ability to stabilize the electroweak vacuum and address the hierarchy problem.

• The Challenge: Detecting heavy $T$ quarks (masses $\gtrsim 1.8$ TeV) is difficult due to overwhelming Standard Model (SM) backgrounds, particularly $t\bar{t} + \text{jets}$ and QCD multijet events.
• The Kinematic Regime: In high-mass scenarios, the decay products of the $T$ quark (e.g., $T \to bW, tZ, th, tg$) are highly boosted. This causes the decay products to merge into single, large-radius "fat jets."
• Limitation of Current Methods: Traditional jet clustering algorithms use a fixed radius ($R$). In highly boosted regimes, a fixed $R$ may be too small to capture all decay products of a massive particle (leading to lost energy) or too large (incorporating excessive pile-up and underlying event noise), degrading mass resolution and substructure discrimination.
• Objective: To evaluate the efficacy of a Dynamic-Radius (DR) jet clustering algorithm compared to standard fixed-radius clustering for improving the sensitivity of $T$ partner searches in the $bW$ decay channel.

2. Methodology

A. Signal and Background Modeling

• Signal Model: The study focuses on the associated production of a SM top quark and a heavy vector-like top partner ($pp \to T\bar{t} + X$) mediated by chromomagnetic coupling. The top partner decays via four channels: $bW$, $tZ$, $th$, and $tg$.
  • Benchmark Point: $M_T = 2.2$ TeV, mixing angles $\theta_{L,R} = 0.06$ rad, and coupling scale $\Lambda = 8$ TeV.
  • Focus: The analysis prioritizes the $bW$ decay mode in the one-fat-jet final state ($1\ell + 1 \text{ fat jet} + \geq 1 b\text{-jet} + E_T^{\text{miss}}$) to maximize the signal-to-background ratio.
• Simulation:
  • Signal: Generated using MadGraph5_aMC@NLO (LO), showered with Pythia8 (CMS Tune MonashStar), and simulated with Delphes (fast detector simulation). Pile-up ($\langle \mu \rangle \approx 20$) is included.
  • Background: Utilizes high-statistics CMS Open Data samples for $t\bar{t}$, $tW$, $W/Z$+jets, and QCD multijets. These undergo full Geant4 simulation with realistic pile-up.

B. Jet Algorithms and Substructure

• Clustering:
  • Fixed-Radius (FR): Standard anti-$k_T$ algorithm with $R=0.8$ (fat jets) and $R=0.4$ (narrow jets).
  • Dynamic-Radius (DR): An algorithm where the jet radius $R_d$ adapts based on the internal kinematics of the proto-jet. The radius modifier $\sigma_i$ is derived from Energy Correlation Functions (ECFs), specifically $C_1^{(2)} - (C_1^{(1)})^2$. This allows the radius to expand for wide-angle decays (heavy bosons/tops) and contract for narrow QCD jets.
• Substructure Techniques:
  • Soft Drop Grooming: Removes soft, wide-angle radiation to mitigate pile-up and underlying event effects.
  • N-subjettiness: Ratios $\tau_{32}$ and $\tau_{21}$ used to distinguish 3-prong (top) and 2-prong ($W/Z$) structures from QCD backgrounds.
  • Event Shape Variables: Sphericity, Aplanarity, and Fox-Wolfram moments ($H_{10}$) are included to characterize global event topology.

C. Analysis Strategy

• Event Selection: Requires exactly one isolated lepton ($e/\mu$), missing transverse momentum ($p_T^{\text{miss}} > 30$ GeV), at least one $b$-tagged narrow jet, and exactly one fat jet ($p_T > 200$ GeV).
• Multivariate Analysis (MVA): A Boosted Decision Tree (BDT) is trained to separate signal from background.
  • Inputs: Lepton kinematics, jet kinematics, substructure variables ($m_{SD}, \tau_{32}, \tau_{21}$), and event shapes.
  • Training: 70/30 split for training/validation. Overtraining checks (Kolmogorov-Smirnov test) confirm robustness.
  • Optimization: Selection thresholds on BDT scores are optimized using the Punzi Figure-of-Merit (FOM).

3. Key Contributions

1. First Realistic DR Study: While DR algorithms have been studied in zero-pile-up scenarios, this paper provides a comprehensive analysis under realistic LHC Run-II conditions (including $\sim 20$ pile-up interactions per event).
2. Comparative Performance: It directly compares FR and DR clustering for a specific BSM process ($T\bar{t}$ production), demonstrating that DR clustering is superior in the highly boosted regime ($p_T^{\text{fat jet}} \gtrsim 750$ GeV).
3. Improved Reconstruction: The study shows that DR clustering better captures the full decay products of boosted $W/Z$ bosons and top quarks, leading to higher selection efficiencies (e.g., 41.1% vs 38.3% for boosted $W/Z$ at high $p_T$).
4. Systematic Understanding: The paper addresses the trade-offs, noting that while DR improves signal capture, it may increase sensitivity to Jet Energy Resolution (JER) uncertainties due to the accumulation of more particles within the adaptive radius.

4. Results

• Signal Sensitivity: The DR algorithm significantly outperforms the fixed-radius method in the high-$p_T$ tail of the phase space.
  • ROC Curves: For tight $p_T$ thresholds, the DR BDT performance degrades less rapidly than FR.
  • Significance: The signal significance ($S/\sqrt{S+B}$) and Punzi FOM are consistently higher for DR clustering when $p_T^{\text{fat jet}} \geq 750$ GeV.
• Exclusion Limits: The study derives expected 95% CL upper limits on the chromomagnetic coupling ($C_{tR}/\Lambda$) for top partner masses between 1.4 and 3.0 TeV.
  • Outcome: The DR approach yields tighter exclusion limits (smaller coupling values) compared to FR. The improvement is most pronounced at a fat jet $p_T$ threshold of 900 GeV.
• Robustness: The analysis remains robust against variations in substructure parameters (e.g., Soft Drop $\beta$ and $z_{cut}$).

5. Significance and Outlook

• Physics Impact: This work validates the use of dynamic-radius clustering as a critical tool for future heavy resonance searches. As top partners become heavier, their decay products become more collimated, making fixed-radius algorithms increasingly inefficient.
• Future Colliders: The authors project that DR clustering will be even more essential at the High-Luminosity LHC (HL-LHC) and future 100 TeV colliders (FCC-hh), where the boost of heavy particles will be extreme.
• Future Directions: The paper suggests integrating DR jets with Machine Learning (ML) based tagging (e.g., Graph Neural Networks) and optimizing pile-up mitigation specifically for adaptive radii to further enhance sensitivity.

In summary, this paper demonstrates that Dynamic-Radius jet clustering is a superior technique for reconstructing highly boosted vector-like top partners, offering a statistically significant improvement in discovery potential and exclusion limits over traditional fixed-radius methods in the high-energy regime.