Deep learning approaches to top FCNC couplings to photons at the LHC

This paper demonstrates that transformer-based deep learning architectures significantly outperform traditional cut-based analyses in detecting top quark flavor-changing neutral current interactions with photons at the LHC, enabling the exploration of rare branching ratios as low as $10^{-6}$ at the high-luminosity phase.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. It smashes protons together at nearly the speed of light to create a chaotic storm of subatomic particles. Usually, these particles follow the "rulebook" of physics known as the Standard Model. But physicists suspect there's a secret chapter in the rulebook they haven't found yet—New Physics.

This paper is a detective story about finding a very specific, very rare clue in that chaotic storm: a Top Quark (the heaviest known particle) suddenly changing its identity and spitting out a photon (a particle of light).

Here is the breakdown of the paper using everyday analogies:

1. The Crime Scene: The "Top Quark" and the "Forbidden Switch"

In the Standard Model, a Top Quark is like a shy celebrity who only hangs out with specific friends (the bottom quark and the W boson). It is extremely rare for a Top Quark to suddenly switch friends and hang out with an Up or Charm quark while flashing a photon. This is called a Flavor-Changing Neutral Current (FCNC).

• The Analogy: Imagine a strict bouncer at a club (the Standard Model) who only lets a VIP guest (the Top Quark) dance with a specific partner. If you see the VIP suddenly dancing with a stranger and flashing a strobe light (the photon), it's a huge red flag. It suggests someone broke the rules.
• The Problem: This "dance" is so rare that in the current rulebook, it happens maybe once in a trillion tries. But if "New Physics" exists, it might happen a million times more often. The LHC is looking for these rare dances.

2. The Old Detective Method: "Cut-Based Analysis"

For decades, physicists have looked for these rare events using a method called "Cut-Based Analysis."

• The Analogy: Imagine you are looking for a specific person in a crowded stadium. The old method is like handing out a checklist: "If the person is wearing a red hat, check. If they are taller than 6 feet, check. If they are holding a hot dog, check."
• The Flaw: This is too rigid. You might miss the person because they are wearing a blue hat but are holding a hot dog. You are throwing away too much data by being too strict with simple rules. You end up with a lot of noise (fake signals) and miss the real signal.

3. The New Detective Method: "Deep Learning"

The authors of this paper decided to hire a team of super-smart AI detectives using Deep Learning. Instead of a rigid checklist, they used three different types of AI brains to look at the data:

• The MLP (Multi-Layer Perceptron): Think of this as a very smart student who looks at a list of numbers (speed, angle, energy) and tries to guess if it's a signal. It's good, but it treats every number as a separate fact, missing how they relate to each other.
• The GAT (Graph Attention Network): This is like a detective who looks at the relationships between people. Instead of just looking at the VIP, it looks at how the VIP is standing relative to the photon, the jets, and the missing energy. It builds a map of connections.
• The Transformer: This is the "Super Detective" (the same technology behind AI chatbots like me). It looks at the entire event as a "cloud" of particles. It uses a mechanism called Self-Attention to ask: "Out of all these particles, which ones are actually talking to each other to tell a story?" It dynamically weighs the importance of every particle in the crash.

4. The Results: The "Super Detective" Wins

The team simulated millions of particle crashes and tested these AI models against the old "checklist" method.

• The Outcome: The Transformer and GAT models were vastly superior. They didn't just look at the numbers; they understood the story the particles were telling.
• The Analogy: If the old method was like trying to find a needle in a haystack by only checking the color of the straw, the new AI method is like having a metal detector that can sense the needle's shape, weight, and magnetic field simultaneously.
• The Improvement: The new AI methods improved the sensitivity by a factor of five. This means they can spot the "forbidden dance" much more clearly against the background noise.

5. The Future: Seeing the Invisible

Because these AI models are so much better at filtering out the noise, the LHC can now look for much rarer events.

• The Goal: The paper predicts that with the upcoming "High-Luminosity" phase of the LHC (where they will smash more particles than ever before), these AI tools could detect these rare Top Quark decays happening as rarely as 1 in a million.
• Why it matters: Finding this rare decay would be like finding a fingerprint of a new, unknown force of nature. It would prove that our current rulebook (the Standard Model) is incomplete and open the door to understanding dark matter, extra dimensions, or other mysteries of the universe.

Summary

This paper is essentially saying: "Stop using a ruler to measure a cloud. Use a smart AI that understands the shape of the cloud."

By teaching computers to look at the complex relationships between particles rather than just simple rules, physicists can now hunt for the most elusive secrets of the universe with unprecedented precision. The "Transformer" AI is the new super-sleuth that might finally crack the case of the Top Quark's secret identity.

Technical Summary

1. Problem Statement

The paper addresses the challenge of detecting Flavor-Changing Neutral Current (FCNC) interactions involving the top quark and a photon ($t \to q\gamma$ and $qg \to t\gamma$). In the Standard Model (SM), these processes are highly suppressed (branching ratios $\sim 10^{-17}$ to $10^{-12}$) due to the GIM mechanism. However, various Beyond the Standard Model (BSM) scenarios predict enhancements up to $10^{-4}$.

Current experimental limits from the LHC (Run 2) are in the range of $10^{-5}$ to $10^{-3}$. As the LHC moves toward the High-Luminosity phase (HL-LHC) with integrated luminosities up to $3000 \text{ fb}^{-1}$, there is a critical need to improve analysis sensitivity to probe branching ratios down to $10^{-6}$. Traditional cut-based analyses struggle with this task because they rely on linear cuts and fail to exploit complex, non-linear correlations in high-dimensional kinematic feature spaces, leading to low signal purity in the presence of large SM backgrounds (e.g., $t\bar{t}\gamma$, $t\gamma$, $W\gamma$, $Z\gamma$).

2. Methodology

Theoretical Framework

• Effective Field Theory (SMEFT): The authors use the Standard Model Effective Field Theory to model BSM effects via dimension-six operators. They focus on operators inducing dipole couplings between the top quark, a photon, and a light up-type quark ($u$ or $c$).
• Processes Studied:
  1. Single Top Production: $qg \to t\gamma$ (where $t$ decays leptonically).
  2. Top Pair Production: $pp \to t\bar{t}$, where one top decays via SM ($t \to bW$) and the other via FCNC ($t \to q\gamma$).
• Simulation: Signal and background events were generated using MadGraph5_aMC@NLO at Leading Order (LO). Detector effects were simulated using MadAnalysis 5 with a Simplified Fast Simulation (SFS) module.

Analysis Strategies

The study compares three distinct analysis approaches:

1. Cut-Based Strategy: A traditional approach applying sequential kinematic cuts (e.g., $p_T$, $\eta$, isolation, $\Delta R$) to isolate signal events.
2. Deep Learning (DL) Strategies: Three architectures were trained to perform binary classification (Signal vs. Background) using low-level and high-level kinematic variables:
   • Multi-Layer Perceptron (MLP): Treats events as fixed-size vectors of 29 features (e.g., $p_T$, $\eta$, $\phi$, $E$, $\Delta R$, $\Delta \phi$, $H_T$, $m_{eff}$). It learns non-linear boundaries but ignores intrinsic event topology.
   • Graph Attention Network (GAT): Represents events as graphs where nodes are final-state objects (jets, photon, lepton, MET, reconstructed top) and edges represent relationships. It uses an attention mechanism to dynamically weight the importance of neighboring nodes, capturing local topological structures.
   • Transformer: Treats events as unordered sets (point clouds) of particles. It utilizes self-attention mechanisms to evaluate the global context and relevance of each particle relative to all others, preserving permutation invariance.

Training Setup

• Data: Signal samples for $t\gamma$, $t\bar{t} \to u\gamma$, and $t\bar{t} \to c\gamma$ were combined with dominant backgrounds ($t\bar{t}\gamma$, $t\gamma$, $W\gamma$, $Z\gamma$).
• Optimization: Hyperparameters were tuned via random grid search. Models were trained using PyTorch and PyTorch Lightning with AdamW optimizers and Cosine Annealing schedulers.
• Evaluation: Performance was measured using Receiver Operating Characteristic (ROC) curves, Area Under the Curve (AUC), and confusion matrices. Statistical significance was calculated using the $CL_s$ method.

3. Key Contributions

• Systematic Comparison of Architectures: The paper provides a rigorous benchmark of MLPs, GATs, and Transformers for top FCNC searches, demonstrating that attention-based architectures (GAT and Transformers) significantly outperform traditional MLPs and cut-based methods.
• Handling Event Topology: It highlights the advantage of representing collider events as graphs or sets rather than fixed vectors. Transformers and GATs effectively capture the complex correlations between final-state particles that MLPs miss.
• Quantitative Sensitivity Projections: The study provides updated exclusion limits for the LHC Run 3 ($500 \text{ fb}^{-1}$) and the HL-LHC ($3000 \text{ fb}^{-1}$), translating model performance into constraints on SMEFT Wilson coefficients and branching ratios.
• Flavor Dependence: The analysis explicitly compares sensitivity to up-quark ($u$) vs. charm-quark ($c$) FCNC couplings, noting that while up-quark production rates are higher due to PDFs, the charm channel benefits from distinct kinematic features in the pair-production mode.

4. Results

Classification Performance

• Cut-Based: Achieved a signal significance of $S \approx 20.3$ (assuming 0% background uncertainty) but with low signal purity ($\sim 10\%$).
• MLP: Improved discrimination with an AUC of 0.928 for single top and $\sim 0.78$ for top pair production. Feature importance analysis showed $H_T$, $\Delta R(b, \ell)$, and $p_T^\gamma$ were the most critical variables.
• GAT: Achieved an AUC of 0.973 (single top) and $\sim 0.92$ (top pair).
• Transformer: Achieved the highest performance with an AUC of 0.985 (single top) and $\sim 0.935$ (top pair). The self-attention mechanism successfully identified subtle, non-linear correlations between particles.

Exclusion Limits

The deep learning models significantly improved the expected exclusion limits on the anomalous couplings ($f^\gamma_{tq}/\Lambda$) and branching ratios ($BR$):

• At $139 \text{ fb}^{-1}$ (Run 2):
  • MLP: $BR(t \to u\gamma) \lesssim 1.0 \times 10^{-5}$, $BR(t \to c\gamma) \lesssim 2.4 \times 10^{-5}$.
  • Transformer/GAT: Improved limits by factors of 1.5 to 2.6, reaching $BR(t \to u\gamma) \approx 3.6 \times 10^{-6}$ and $BR(t \to c\gamma) \approx 4.7 \times 10^{-6}$.
• At $500 \text{ fb}^{-1}$ (Run 3):
  • Transformer models can probe $BR(t \to u\gamma)$ down to $\sim 3.6 \times 10^{-6}$ and $BR(t \to c\gamma)$ down to $\sim 4.7 \times 10^{-6}$.
• At HL-LHC ($3000 \text{ fb}^{-1}$):
  • The study projects that branching ratios as low as $10^{-6}$ can be excluded at 95% confidence level using Transformer-based classifiers.
  • Coupling limits reach down to $\sim 2 \times 10^{-3} \text{ TeV}^{-1}$.

5. Significance

This work demonstrates that attention-based deep learning architectures are essential tools for the next generation of LHC physics. As data volumes increase and signals become rarer, traditional cut-based and simple MLP approaches become suboptimal.

• Physics Impact: The ability to probe branching ratios at the $10^{-6}$ level opens the door to testing a wide range of BSM models (e.g., Two-Higgs-Doublet Models, Supersymmetry, Composite models) that were previously inaccessible.
• Methodological Impact: The paper validates the use of Transformers and Graph Neural Networks in high-energy physics, showing that treating collider events as structured data (graphs or sets) rather than unstructured vectors yields a factor of 5 improvement in exclusion limits compared to traditional methods.
• Future Outlook: The results suggest that future experimental analyses at the HL-LHC should prioritize attention-based models to maximize discovery potential in top quark sectors.