Searching for EeV photons with Telescope Array Surface Detector and neural networks

Using 14 years of Telescope Array Surface Detector data and a neural network classifier fine-tuned on experimental data to distinguish between proton- and photon-induced events, the study reports no significant photon candidates and establishes an updated upper limit on the diffuse ultra-high-energy photon flux above $10^{19}$ eV of $3.0 \cdot 10^{-4} \, (\text{km}^2 \cdot \text{sr} \cdot \text{yr})^{-1}$.

The Gist

Imagine the Earth is constantly being pelted by invisible, super-fast bullets from deep space. These are Cosmic Rays, mostly protons (hydrogen nuclei) traveling at nearly the speed of light. But sometimes, scientists wonder: could some of these bullets actually be photons (particles of light) with energies so high they break the laws of physics as we know them?

This paper is the report card from the Telescope Array (TA), a giant cosmic ray detector in the Utah desert, on their 14-year hunt for these ultra-powerful "ghost" photons.

Here is the story of their hunt, explained simply.

1. The Detective's Dilemma: The Needle in the Haystack

The problem is that when a cosmic ray hits the atmosphere, it creates a massive "shower" of secondary particles hitting the ground.

• The Haystack: These showers are usually caused by protons (the common stuff).
• The Needle: Occasionally, a shower is caused by a photon (the rare, exotic stuff).

The trouble is, a proton shower can sometimes look exactly like a photon shower. It's like trying to tell the difference between a real diamond and a very high-quality fake glass just by looking at them in the dark. The "fake" protons are the background noise that drowns out the signal.

2. The New Tool: A Super-Intelligent AI Detective

In the past, scientists used simple rules to try to spot the difference. In this study, they upgraded to a Neural Network—a type of Artificial Intelligence that learns by example, much like a child learning to recognize a cat by seeing thousands of pictures.

How the AI was trained:

• The Classroom: They fed the AI millions of computer simulations of proton showers and photon showers.
• The "Fine-Tuning" Trick: Here is the clever part. Computer simulations are never 100% perfect; they are like a map that is slightly off. If you train a driver only on a bad map, they will crash in the real world.
  • The team took a small, safe subset of real data (events they were 100% sure were protons) and used it to "fine-tune" the AI.
  • Think of it as giving the AI a "field test" with real-world conditions before letting it go on the big hunt. This ensured the AI didn't get confused by the differences between the computer map and the real desert.

What the AI looked at:
Instead of just looking at the final result, the AI looked at the raw heartbeat of the event.

• The Waveforms: Every detector station in the desert records a "waveform"—a squiggly line showing how the signal changed over time (down to billionths of a second).
• The Pattern: The AI analyzed the shape of these waves and the pattern of which stations were hit, looking for the subtle "fingerprint" that says, "I am a photon," versus "I am just a proton."

3. The Hunt: 14 Years of Data

The Telescope Array has 507 detectors spread across 700 square kilometers (about the size of a large city). They collected data for 14 years.

They set a "blind" rule: They decided exactly how strict the AI should be before they looked at the final results. This is like a judge deciding the rules of a trial before hearing the evidence, to make sure they aren't biased.

The Results:

• The Verdict: The AI found a few "suspects" (events that looked like photons), but when they checked the math, the number of suspects was exactly what you would expect from random chance (statistical noise) in the proton background.
• The Conclusion: They found zero confirmed ultra-high-energy photons.

4. Why This Matters: Setting the "Speed Limit"

Even though they didn't find the "ghost photons," this is a huge success.

Think of it like setting a speed limit on a highway.

• Before this study, we knew the speed limit was "somewhere below 100 mph."
• Now, thanks to this 14-year hunt and the smart AI, they can say with 95% confidence: "The speed limit is definitely below 30 mph."

By not finding the photons, they have set the strictest limits yet in the Northern Hemisphere. This tells us:

1. Standard Physics is Safe: The "Ghost Particles" predicted by some exotic theories (like decaying Dark Matter) aren't showing up in the numbers we see.
2. The Map is Getting Clearer: We are getting closer to understanding the true composition of cosmic rays. If we don't see these photons, it means the cosmic rays are likely made of heavier stuff (like iron nuclei) rather than just protons.

Summary

The Telescope Array team built a super-smart AI detective, trained it on both computer simulations and real-world data to avoid mistakes, and spent 14 years scanning the Utah desert for the most energetic light particles in the universe.

They didn't find the "aliens" (the exotic photons), but by proving they aren't there, they have tightened the rules of the universe, helping scientists understand how the cosmos works and ruling out some wild theories about Dark Matter. It's a victory of precision over discovery, which is often how science moves forward.

Technical Summary

1. Problem Statement

Ultra-high-energy (UHE) photons ($E > 10^{18}$ eV) are critical for testing astrophysical models (via the Greisen-Zatsepin-Kuzmin or GZK mechanism) and Beyond-Standard-Model (BSM) scenarios, such as decaying super-heavy dark matter (SHDM) or Lorentz symmetry violation. However, detecting them is challenging because:

• Low Flux: The expected flux is extremely low, requiring massive exposure.
• Background Confusion: The primary background consists of hadronic cosmic rays (protons and nuclei). Hadron-induced air showers can fluctuate to produce a dominant electromagnetic component (e.g., via $\pi^0 \to \gamma\gamma$ decay), making them indistinguishable from primary photon showers using traditional reconstruction methods.
• Detector Limitations: While fluorescence detectors offer excellent discrimination via shower depth ($X_{max}$), they have a low duty cycle. Surface Detectors (SD) operate continuously but struggle to distinguish the muon-to-electromagnetic ratio, which is the key discriminator between hadrons and photons.

The Telescope Array (TA) experiment seeks to improve upon previous limits using its Surface Detector data, specifically addressing the discrepancy between Monte Carlo (MC) simulations and real experimental data that often biases machine learning classifiers.

2. Methodology

The analysis utilizes 14 years of TA SD data (2008–2022) and employs a novel machine learning pipeline.

A. Data Preparation & Simulation

• Dataset: 14 years of TA SD data (507 scintillator stations, 1.2 km spacing).
• Monte Carlo (MC): Simulations using CORSIKA 7.7420 and GEANT4.
  • Protons: Simulated with three hadronic interaction models (QGSJET-II-04, EPOS-LHC, Sibyll 2.3d) to test model dependence.
  • Photons: Simulated with QGSJET-II-04, accounting for geomagnetic pair production (PRESHOWER code).
• Event Selection: Strict quality cuts applied (zenith $< 55^\circ$, $\ge 7$ triggered stations, core within array, $\chi^2/d.o.f. < 5$). Lightning-correlated events were excluded.
• Balancing: Proton and photon events were mixed in equal numbers across energy bins to prevent the neural network from using energy as a proxy for particle type.

B. Neural Network Architecture

The authors developed a hybrid Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) architecture with three main components:

1. Spatial Station Bundle: Treats the activated stations as a $6\times6$ "image" centered on the shower core. Uses Conv2D layers to analyze geometric patterns (coordinates, charge, arrival time, front curvature).
2. Temporal Station Bundle: Processes stations ordered by activation time.
   • Waveform Encoder: Uses Conv1D and LSTM layers to extract features from raw time-resolved waveforms (128 time bins) from upper and lower scintillator layers.
   • Sequence Analysis: A Bidirectional LSTM processes the sequence of stations to capture the shower's temporal evolution.
3. Combined Analysis: Concatenates features from spatial and temporal bundles with reconstructed physical parameters (zenith, azimuth, $S_{800}$, Linsley curvature). The final output is a confidence score $\xi \in [0, 1]$ (0 = proton-like, 1 = photon-like).

C. Training & Fine-Tuning (Key Innovation)

To mitigate biases where MC simulations do not perfectly match reality:

• Weighted Training: Proton events were weighted 5:1 against photons to minimize the false-positive rate (protons misidentified as photons).
• Focal Loss: Used to force the network to focus on "hard-to-classify" events.
• Fine-Tuning with Burn Sample: After initial training on MC, the network was fine-tuned on a subset of experimental data confidently identified as protons ($\xi \le 0.2$). This "burn sample" allows the network to learn real-world detector nuances without using the data intended for the final flux limit calculation.
• Blind Optimization: The classification threshold ($\xi_{cut}$) was optimized on MC data to minimize the expected upper limit on the photon flux before unblinding the experimental data.

3. Key Contributions

1. Novel Fine-Tuning Strategy: The introduction of a "burn sample" to fine-tune the neural network on real experimental data significantly reduced the discrepancy between MC and data predictions (reducing the mean asymmetric ratio from 5.1 to 1.2). This ensures the classifier's reliability in the signal region.
2. Hybrid Architecture: Successfully combining spatial geometry, raw time-resolved waveforms, and reconstructed parameters in a single deep learning model to maximize discrimination power.
3. Model Dependence Analysis: Demonstrated that while hadronic interaction models affect proton predictions at very high energies ($>10^{19.5}$ eV), the network's performance for photon-like events ($\xi > 0.5$) remains robust across different models.
4. Validation: Confirmed the network's ability to identify known electromagnetic cascades (e.g., Terrestrial Gamma-Ray Flashes and lightning-induced events) as photon-like, validating its physics understanding.

4. Results

• Observation: No significant excess of photon candidates was found above the expected hadronic background. The observed candidates were consistent with statistical fluctuations.
• Upper Limits (95% CL): The study set the most stringent limits on the diffuse photon flux in the Northern Hemisphere to date:
  • $\Phi_\gamma (E > 10^{19} \text{ eV}) < 2.3 \times 10^{-3} \, (\text{km}^2 \cdot \text{sr} \cdot \text{yr})^{-1}$
  • $\Phi_\gamma (E > 10^{20} \text{ eV}) < 3.0 \times 10^{-4} \, (\text{km}^2 \cdot \text{sr} \cdot \text{yr})^{-1}$
• Improvement: These limits represent an improvement of approximately a factor of three over previous TA results (using Boosted Decision Trees) at $10^{18.5}$ eV and $10^{20}$ eV.
• Comparison: The limits approach the theoretical upper edge of GZK photon predictions (assuming pure proton composition) but remain above the predictions for the TA best-fit composition model. They are competitive with Pierre Auger Observatory limits for Super-Heavy Dark Matter (SHDM) decay scenarios, despite TA not observing the Galactic Center.

5. Significance

• Constraint on BSM Physics: The results provide tight constraints on models involving decaying dark matter and Lorentz symmetry violation, ruling out large portions of the parameter space for super-heavy dark matter lifetimes.
• Methodological Advancement: The paper establishes a robust framework for using neural networks in UHECR physics, specifically demonstrating how to bridge the "sim-to-real" gap via fine-tuning. This approach is likely to be adopted by future experiments (e.g., AugerPrime, TAx4) to enhance sensitivity.
• Northern Hemisphere Coverage: By complementing the Southern Hemisphere limits set by the Pierre Auger Observatory, this work provides a more complete global picture of the UHE photon sky, crucial for distinguishing between isotropic GZK production and anisotropic BSM sources.