Suppression of Neutron Background using Deep Neural Network and Fourier Frequency Analysis at the KOTO Experiment

The KOTO experiment at J-PARC successfully suppressed neutron background by a factor of $5.6\times10^5$ while maintaining 70% signal efficiency for the rare $K^0_L\rightarrow\pi^0\nu\bar{\nu}$ decay search by employing deep convolutional neural networks and Fourier frequency analysis to distinguish neutrons from photons based on their distinct cluster and pulse shapes in the undoped CsI electromagnetic calorimeter.

The Gist

Imagine you are a detective trying to solve a very rare crime. The "criminal" is a specific type of particle decay called $K_L^0 \to \pi^0 \nu \bar{\nu}$. This event is so rare that it happens only about 3 times out of every 100 billion attempts. To catch this criminal, scientists at the KOTO experiment in Japan built a massive, high-tech trap.

However, there's a problem: the trap is full of "look-alikes." These are innocent bystanders (neutrons) that accidentally trip the alarm and look exactly like the criminal. If the scientists can't tell the difference, they will be flooded with false alarms and never find the real crime.

This paper is about how the scientists invented two new, super-smart "lie detectors" to filter out the noise and find the signal.

The Setting: The CSI Calorimeter

The KOTO detector uses a giant wall made of 2,716 crystals (like a giant grid of ice cubes) called the CsI Calorimeter. When a particle hits this wall, it leaves a "splash."

• The Signal (Photons): When the rare decay happens, it creates two photons. They hit the wall and make a splash that looks like two perfect, round, symmetrical puddles.
• The Background (Neutrons): Neutrons are the troublemakers. They bounce around inside the wall and can accidentally create two splashes that look like the photons. But if you look closely, the neutron splashes are messy, asymmetrical, and have a different "texture."

The Problem

In the past, scientists used simple rules to tell the difference (like "is the splash round?"). But the neutrons were getting better at faking the look. They needed a smarter way to distinguish the real deal from the fakes.

The Solution: Two New Super-Tools

The paper introduces two advanced techniques, like giving the detectives a pair of high-tech glasses and a super-ear.

1. The "AI Eye" (Deep Neural Network)

The Analogy: Imagine you are trying to tell the difference between a photo of a cat and a photo of a dog. You could look at the ears or the tail, but a computer is better at looking at the whole picture at once.

• How it works: The scientists fed thousands of photos of "splash patterns" (called clusters) into a Convolutional Neural Network (CNN). This is a type of Artificial Intelligence that acts like a super-observant artist.
• The Trick: The AI didn't just look at the size of the splash; it looked at the tiny details of the energy distribution and timing across the grid of crystals. It learned that photon splashes are usually "cleaner" and more symmetrical, while neutron splashes are "jagged" and messy.
• The Result: The AI became an expert judge. It could look at a splash and say, "99% sure this is a photon," or "99% sure this is a neutron."

2. The "Super-Ear" (Fourier Frequency Analysis)

The Analogy: Imagine you are listening to two people speak. One speaks with a smooth, clear voice (the photon). The other speaks with a voice that has a long, rattling echo at the end (the neutron). Even if they say the same words, the sound is different.

• How it works: When a particle hits a crystal, it creates an electrical pulse (a wave). The scientists used Fourier Frequency Analysis to break these waves down into their musical notes (frequencies).
• The Trick: They found that neutron pulses have a "long tail" (a slow fade-out) compared to the sharp, clean pulses of photons. By analyzing the "frequency" of the sound, they could mathematically prove which particle made the noise.
• The Result: This method acted like a high-quality noise-canceling headphone, filtering out the "rattling" neutron sounds and keeping only the "clear" photon sounds.

The Grand Finale: The Combined Power

The scientists didn't just use one tool; they used both together.

• The AI Eye looked at the shape of the splash.
• The Super-Ear listened to the sound of the splash.

When they combined these two methods, the results were incredible. They were able to block out 99.9998% of the neutron background (a suppression factor of 560,000).

Think of it like this: If you had a bucket of water with 560,000 drops of mud (neutrons) and 1 drop of gold (the signal), these new techniques allowed them to scoop out all the mud so perfectly that only the gold remained, without losing any of the gold in the process.

Why Does This Matter?

By cleaning up the data so effectively, the KOTO experiment can now search for that incredibly rare particle decay with much higher confidence. They aren't just guessing anymore; they have a much clearer view of the universe's secrets. This paper proves that using modern AI and advanced math can solve some of the oldest and hardest problems in physics.

Technical Summary

1. Problem Statement

The KOTO experiment at J-PARC aims to detect the ultra-rare decay $K^0_L \to \pi^0\nu\bar{\nu}$, a process with a Standard Model branching ratio of approximately $3.00 \times 10^{-11}$. The primary challenge in this search is distinguishing the signal from background events, specifically beam-halo neutrons.

• Signal Signature: The decay produces two photons from $\pi^0 \to \gamma\gamma$, detected as two isolated energy clusters in a Cesium Iodide (CsI) crystal calorimeter (CSI).
• Background Mechanism: A single halo neutron can interact within the CSI, scattering and producing two "photon-like" hits separated by a distance. These events mimic the signal topology (two isolated clusters) but lack the intermediate track of a charged particle.
• The Challenge: Traditional discrimination methods based on simple cluster shape or pulse shape were insufficient to suppress this background to the level required for the 2016–2018 data analysis, necessitating more advanced techniques.

2. Methodology

The authors developed two distinct analysis techniques to exploit the physical differences between electromagnetic (photon) and hadronic (neutron) interactions in the undoped CsI calorimeter.

A. Cluster Shape Discrimination (CSD) using Deep Neural Networks

• Concept: Photons interact via electromagnetic showers, creating circular and symmetric energy/timing distributions in the CsI grid. Neutrons interact via hadronic processes, creating asymmetric and irregular shapes.
• Implementation:
  • Input: The energy and timing distributions of the CsI crystals were treated as 2D images. The input included three types of cluster configurations based on crystal size (small, large, or mixed).
  • Architecture: A Convolutional Neural Network (CNN) was employed. The network consisted of:
    • Input Layer: Cluster images (16×16 or 12×12 pixels) plus incident particle direction ($\theta, \phi$) and energy ($E$).
    • Hidden Layers: Four convolutional layers (using 32 filters of size 3×3) followed by six dense layers (2048 neurons each).
    • Regularization: L2 regularization ($\lambda=0.001$) and 10% dropout were used to prevent overfitting.
  • Training: The model was trained on Monte Carlo (MC) simulated photon events and real neutron data (collected during special runs with an aluminum scatterer). Data augmentation (mirroring and angle randomization) was applied to improve generalization.
  • Output: A probability score (0 to 1), where values near 1 indicate photon-like and near 0 indicate neutron-like.

B. Pulse Shape Discrimination (PSD) using Fourier Frequency Analysis

• Concept: Neutron-induced pulses in CsI have longer tails compared to the faster, cleaner pulses produced by photons due to differences in hadronic vs. electromagnetic interaction timescales.
• Implementation:
  • Transformation: Discrete Fourier Transform (DFT) was applied to the digitized pulse waveforms (28 samples per event).
  • Feature Extraction: The amplitudes of the lowest five frequency sinusoids ($A_0$ to $A_4$) were extracted, as the pulse tail is dominated by low-frequency components.
  • Template Matching: Templates of Fourier amplitudes were created for each crystal and energy bin.
  • Likelihood Calculation: A likelihood ratio ($R$) was calculated for each cluster by comparing the observed Fourier amplitudes against photon and neutron templates.
  • Output: A PSD score ($R$) ranging from 0 (neutron-like) to 1 (photon-like).

C. Combined Performance Estimation

• Event-Weighted Method: To estimate the residual background without relying solely on rare signal-region data, the authors calculated a survival probability ($W$) for individual neutron clusters based on their energy ($E$) and incident angle ($\theta$).
• Calculation: For a neutron event with two clusters, the total survival probability is the product of the individual cluster probabilities ($W_1 \times W_2$). The expected number of background events ($N_{Est}$) is the sum of these weights over all neutron events in a defined "Wide Signal Box" (WSB).

3. Key Contributions

1. Novel Application of Deep Learning: First application of a CNN to classify cluster shapes in the KOTO experiment, significantly improving discrimination over traditional cut-based methods.
2. Fourier Analysis for Pulse Shapes: Introduction of DFT-based frequency analysis to discriminate pulse shapes, which proved approximately twice as effective as previous time-domain methods.
3. Robust Background Estimation: Development of an event-weighted method that accurately predicts background suppression factors using data from the Wide Signal Box, validated by the agreement between predicted and observed neutron counts.
4. Data Augmentation Strategy: Implementation of specific augmentation techniques (mirroring, angle randomization) to handle the geometric symmetries of the detector and variations in incident angles.

4. Results

The combined application of CSD and PSD yielded significant improvements in background rejection while maintaining high signal efficiency:

• Suppression Factor: The combined techniques suppressed the neutron background by a factor of $5.6 \times 10^5$.
  • CSD alone suppressed neutrons by a factor of ~150 (at 90% photon acceptance).
  • PSD alone suppressed neutrons by a factor of ~6.5 (at 90% photon acceptance).
  • The combination provided a multiplicative effect.
• Signal Efficiency: The efficiency for detecting the $K^0_L \to \pi^0\nu\bar{\nu}$ signal was maintained at 69.9% (approx. 70%).
• Validation: In the 2016–2018 data analysis, with CSD and PSD thresholds set at 0.985 and 0.5 respectively:
  • The predicted number of remaining neutron events in the signal region was $0.0106 \pm 0.0002$.
  • The observed number of neutron events was 0.
  • This confirmed the reliability of the background estimation method.

5. Significance

This work represents a critical advancement in the search for $K^0_L \to \pi^0\nu\bar{\nu}$. By suppressing the dominant beam-halo neutron background by a factor of $5.6 \times 10^5$ while retaining ~70% of the signal, the KOTO experiment significantly improved its sensitivity.

• Impact on Physics: This suppression allowed the experiment to set a tighter upper limit on the branching ratio ($B < 3.0 \times 10^{-9}$ at 90% CL) and reduced the background uncertainty, which is essential for future discoveries of physics beyond the Standard Model (BSM).
• Methodological Legacy: The successful integration of CNNs for spatial pattern recognition and Fourier analysis for temporal signal processing in high-energy physics detectors provides a blueprint for future experiments dealing with complex background discrimination.