Enhancing di-jet resonance searches via a final-state radiation jet tagging algorithm

This paper demonstrates that using an event-level deep neural network to tag final-state radiation jets significantly improves di-jet resonance search sensitivity at the LHC and HL-LHC by enhancing mass resolution and achieving over 10% sensitivity gains with minimal background sculpting.

The Gist

Imagine you are a detective trying to solve a mystery at a massive, chaotic party called the Large Hadron Collider (LHC).

The Mystery: The "Heavy Guest"

At this party, scientists are looking for a rare, heavy guest (let's call him Mr. Heavy) who might be a new type of particle from a hidden world beyond our current understanding. When Mr. Heavy shows up, he doesn't stay long; he immediately splits into two energetic "runners" (jets of particles) that zoom away in opposite directions.

The detectives' job is to find Mr. Heavy by catching these two runners and measuring their combined energy. If the energy adds up to a specific number, they know, "Aha! Mr. Heavy was here!"

The Problem: The "Noise" at the Party

The problem is that the party is incredibly loud and messy.

1. The Crowd (Background): There are millions of ordinary party-goers (Standard Model particles) running around, creating a huge amount of noise that looks exactly like Mr. Heavy's runners.
2. The Clutter (Radiation): Sometimes, when Mr. Heavy splits, he accidentally drops a third, smaller item (a "Final State Radiation" or FSR jet) as he runs away. It's like a heavy backpack falling off a runner.
3. The Confusion: The detectives usually only look at the two main runners. But because that third item fell off, the two runners don't seem to have enough energy to add up to Mr. Heavy's true weight. It's like trying to weigh a person by only looking at their legs, but they dropped their heavy coat on the floor. The math doesn't add up, and the "signal" gets blurry.

The Old Way vs. The New Way

The Old Way: The detectives just ignore the dropped coat. They calculate the weight based on the two runners. Because of the missing coat, their calculation is often wrong, and the "peak" where Mr. Heavy should be is wide and fuzzy. It's hard to tell if a bump in the data is a real discovery or just a random fluctuation.

The New Way (This Paper): The authors of this paper invented a smart AI detective (a Deep Neural Network). Instead of ignoring the third item, this AI is trained to spot it and ask: "Did this third item fall off Mr. Heavy (FSR), or is it just a random stranger from the crowd (ISR or background)?"

How the AI Detective Works

The AI doesn't need to know the complex physics of how the particles were made. It just looks at the shape and position of the three jets (the two runners and the third item).

Think of it like this:

• If Mr. Heavy drops a backpack, the backpack lands right next to him.
• If a random stranger throws a rock at the party, the rock lands somewhere else.

The AI learns these patterns. It looks at the three jets and says:

• "Ah, this third jet is right next to the main runners. It's the dropped backpack! Let's pick it up and add its weight back into the calculation."
• "No, this third jet is far away. It's just noise. Ignore it."

The Results: Sharper Vision

Once the AI successfully picks up the "dropped backpack" (the FSR jet) and adds it to the calculation, something amazing happens:

1. The Picture Becomes Clear: The fuzzy peak of Mr. Heavy's weight suddenly becomes a sharp, distinct spike. It's like switching from a blurry photo to a high-definition 4K image.
2. Better Detection: Because the signal is so much clearer, the scientists can spot Mr. Heavy much more easily, even if he's hiding in a crowd of noise. The paper shows this improves their chances of finding him by more than 10%.
3. No False Alarms: The AI is smart enough not to pick up random rocks from the crowd. It doesn't mess up the background noise, so the scientists don't get confused by fake signals.

Why This Matters

The LHC is getting ready for a "High-Luminosity" upgrade, which means the party is going to get even bigger and louder. Finding rare particles will be harder than ever.

This new AI tool is like giving the detectives super-powered glasses. It allows them to:

• See the "dropped backpacks" that were previously invisible.
• Reconstruct the true weight of the heavy particles with incredible precision.
• Find new physics that might otherwise be lost in the noise.

In short, this paper teaches us that by using a smart algorithm to catch the "forgotten" pieces of the puzzle, we can solve the mystery of the universe much faster and more accurately.

Technical Summary

1. Problem Statement

The search for heavy resonances decaying into two jets (di-jet searches) is a cornerstone of Beyond the Standard Model (BSM) physics at the Large Hadron Collider (LHC). However, current strategies face specific limitations:

• Incomplete Mass Reconstruction: Standard searches rely on the invariant mass ($m_{jj}$) of the two leading jets. However, heavy particle decays often emit Final State Radiation (FSR) jets. If the hardest FSR jet is not included in the mass calculation, the reconstructed mass peak is smeared and shifted away from the true resonance mass ($m_{Y^0}$), degrading mass resolution.
• Background Contamination: Simply adding the third jet to the mass calculation is not a viable solution because the third jet could be Initial State Radiation (ISR) or a soft jet from the QCD background. Including these incorrectly introduces a high-mass tail and broadens the distribution, reducing sensitivity.
• Trigger Constraints: While ISR-tagging strategies exist for lower mass regions, there is a need for a robust method to identify and utilize FSR jets in the high-mass region ($>1$ TeV) to improve sensitivity without introducing significant biases to the background estimation.

2. Methodology

The authors propose a machine learning-based approach using a Deep Neural Network (DNN) to tag the hardest FSR jet in an event.

A. Dataset Generation

• Signal: A simplified dark matter model with a spin-0 mediator ($Y^0$) decaying to quarks. Training data covers $m_{Y^0} \in [1000, 3000]$ GeV; testing extends to $[3500, 5000]$ GeV.
• Background: Standard Model QCD multi-jet production. To avoid kinematic biases, the background is sampled from three $p_T$-sliced datasets (450, 900, and 1350 GeV).
• Simulation: Generated with MadGraph5 aMC@NLO, showered with Pythia 8, and reconstructed with Delphes 3 (CMS geometry, anti-$k_t$ algorithm, $R=0.4$).
• Labeling Strategy: To distinguish ISR from FSR, the authors use Pythia status codes. A jet is labeled as ISR or FSR based on the ratio of the scalar sum of $p_T$ of associated ISR particles to FSR particles ($\Sigma p_T^{ISR} / \Sigma p_T^{FSR}$).

B. Algorithm Architecture

• Network Type: A feed-forward deep neural network with 12 input nodes, four hidden layers (30-60-30-12 nodes), and ReLU activation.
• Input Features: The algorithm uses only kinematic variables of the leading three jets that are dimensionless or ratios, ensuring minimal dependence on the absolute mass scale ($m_{jj}$).
  • Angular variables: $\eta$ and $\phi$ for jets 1, 2, and 3.
  • Ratios: Jet mass to $p_T$ ($m_j/p_{T,j}$) and relative $p_T$ fractions ($p_{T,3}/p_{T,1}$, etc.).
• Output Classes: A 4-class classification problem:
  1. Signal FSR ("sig-fsr")
  2. Signal ISR ("sig-isr")
  3. Background FSR ("bkg-fsr")
  4. Background ISR ("bkg-isr")
• Discriminant: A custom discriminant $D^f_s$ is constructed to balance efficiency and false positive rates:
  $$D^f_s = \log \frac{p^f_s}{(f^i_s \cdot p^i_s + f^f_b \cdot p^f_b + (1 - f^i_s - f^f_b) \cdot p^i_b)}$$
  Where $p$ represents the network output probabilities for each class, and hyperparameters $f^i_s$ and $f^f_b$ are tuned to minimize background sculpting.

C. Application Strategy

If the third jet is identified as "sig-fsr" with a high $D^f_s$ score, the event's invariant mass is recalculated using the tri-jet invariant mass (leading two jets + tagged FSR jet) instead of the standard di-jet mass.

3. Key Contributions

1. FSR Tagging via ML: Development of a specialized algorithm that successfully isolates the hardest FSR jet from ISR and background jets using only basic kinematic variables.
2. Mass Resolution Improvement: Demonstrated that correcting the mass with the tagged FSR jet significantly sharpens the signal peak, shifting the median closer to the true mass and reducing the spread.
3. Background Preservation: The algorithm is designed to introduce minimal mass sculpting to the QCD background. The background mass spectrum remains smoothly falling, which is critical for data-driven background estimation methods (e.g., functional fits).
4. Model Independence: By avoiding low-level features (like track multiplicity) and using mass-independent ratios, the algorithm maintains applicability across a broad mass range and different BSM scenarios.

4. Results

• Sensitivity Gain: The method improves the search sensitivity (significance $N_s/\sqrt{N_b}$) by 10% to 14% for signal masses between 1.5 and 3 TeV. The authors note potential gains up to 20% depending on the fit model.
• Classification Performance:
  • The algorithm achieves a ~40% identification efficiency for signal FSR jets.
  • The fake rate (misidentifying ISR or background jets as signal FSR) is kept at the ~20% level.
  • The Area Under the Curve (AUC) for distinguishing signal FSR from signal ISR is 0.70, and from background ISR is 0.70.
• Mass Resolution: For a 1.5 TeV signal, the FSR-corrected mass distribution shows a significantly narrower peak compared to the original di-jet mass. The median shifts toward the true mass, and the interquartile range shrinks.
• Generalization: The algorithm was tested on unseen mass points (3.5 TeV to 5 TeV) and showed consistent performance gains, confirming its robustness across the mass spectrum.

5. Significance

• Enhanced Discovery Potential: As the LHC moves toward the High-Luminosity (HL-LHC) era, maximizing sensitivity is crucial. This method offers a systematic way to recover signal events that would otherwise be lost due to poor mass resolution.
• Complement to Existing Strategies: Unlike ISR-tagging strategies used for low-mass triggers, this FSR-tagging approach is optimized for the high-mass resonance region where the di-jet mass is the primary observable.
• Flexibility: The multi-class output allows the algorithm to be re-optimized for different goals (e.g., prioritizing mass resolution over sensitivity, or vice versa) by adjusting the discriminant hyperparameters.
• Future Outlook: The authors suggest that while the current model uses only 4-momenta, future iterations could incorporate lower-level features (charged tracks, calorimeter deposits) to exploit color connections, though this would require careful evaluation of detector and showering dependencies.

In conclusion, this work proves that identifying and utilizing FSR jets via deep learning is a viable and effective strategy to enhance the discovery potential of di-jet resonance searches at the LHC and HL-LHC.