Pulse shape discrimination for $\alpha$ event rejection in BEGe-type high-purity germanium detectors

This study demonstrates that pulse shape discrimination classifiers trained exclusively on gamma-ray data can effectively identify and reject alpha events in high-purity germanium detectors, offering a robust background suppression strategy for next-generation neutrinoless double beta decay searches like LEGEND where dedicated alpha training data is insufficient.

The Gist

Imagine you are trying to listen for a single, perfect whisper in a very noisy room. This is essentially what scientists do when they search for a rare event called "neutrinoless double beta decay." They use incredibly sensitive microphones made of pure germanium crystals (detectors) to catch these whispers.

However, the room is full of other noises:

1. The "Bad" Noise: Sometimes, gamma rays (a type of radiation) bounce around the room multiple times before stopping. These are like people clapping their hands in different corners of the room. The scientists want to ignore these.
2. The "Intruder" Noise: Sometimes, alpha particles (tiny, heavy radioactive specks) land right on the surface of the microphone. These are like someone tapping the microphone directly with a finger. They create a sound that looks very similar to the "whisper" the scientists are hunting for, potentially tricking them into thinking they found something when they didn't.

The Problem

Usually, to teach a computer how to ignore the "Bad Noise" (gamma rays), scientists show it thousands of examples of those sounds. But for the "Intruder Noise" (alpha particles), there's a catch: in real experiments, these intruders are so rare that there aren't enough of them to teach the computer what they look like.

The big question this paper asks is: Can we teach the computer to spot the "Intruder" just by showing it the "Bad Noise" (gamma rays), without ever showing it an actual Intruder?

The Experiment

The researchers set up a high-tech germanium detector (a "BEGe" type) and did two things:

1. Training: They bombarded the detector with gamma rays (using a Thorium source) to teach two different computer programs (a "Multilayer Perceptron" and a "Projective Likelihood" classifier) how to tell the difference between a single bounce (good) and multiple bounces (bad).
2. Testing: They then placed a source of Polonium (an alpha emitter) directly on the detector's surface. This created thousands of "Intruder" events. They asked the computer: "Hey, you learned from the gamma rays. Can you now spot and reject these alpha particles?"

The Results

The computer programs were surprisingly good at this.

• The "Smart" Filter: The best method, a type of Artificial Neural Network (called a Multilayer Perceptron or MLP), acted like a super-smart bouncer.
• Keeping the Good: It kept over 80% of the "whispers" (the single-site gamma events that look like the signal they want).
• Rejecting the Bad: It threw out over 80% of the "clapping" (the multi-site gamma events).
• Kicking Out the Intruders: Most importantly, it rejected the alpha particles with incredible efficiency. It filtered out more than 27,000 alpha particles for every one that slipped through.

The Analogy

Think of the detector as a security camera.

• Gamma rays are like people walking through a door; sometimes one person walks through (good), sometimes a group walks through together (bad). The camera learns to spot the groups.
• Alpha particles are like someone trying to climb through a window right next to the door.
• The paper shows that by learning to spot the "groups" at the door, the camera also learned to spot the "climber" at the window, even though it never saw a climber during its training.

The Conclusion

The paper concludes that you don't need a massive library of rare "intruder" examples to teach your detector how to reject them. By training the system only on the more common "bad noise" (gamma rays), the machine learning algorithms naturally learn to spot the "intruders" (alpha particles) as well.

This is a huge win for future experiments (like the LEGEND project mentioned in the text) because it means they can build detectors that are cleaner and more sensitive without needing to wait years to collect enough rare alpha events to train their software. The "smart filter" works out of the box, using only the data they already have.

Technical Summary

Technical Summary: Pulse Shape Discrimination for $\alpha$ Event Rejection in BEGe-type HPGe Detectors

Problem Statement
High-purity germanium (HPGe) detectors are central to rare-event searches, particularly the search for neutrinoless double beta decay ($0\nu\beta\beta$) in $^{76}\text{Ge}$ (e.g., the LEGEND experiment). While these detectors offer excellent energy resolution and intrinsic purity, they remain susceptible to background events. A specific challenge is the rejection of $\alpha$ particles emitted by surface contaminants such as $^{210}\text{Po}$ and $^{226}\text{Ra}$. If these emitters are located on the thin $p^+$ contact of the detector, $\alpha$ particles can deposit a fraction of their energy within the active volume, creating signals that may mimic the region of interest (ROI) around the $Q_{\beta\beta}$ value of 2039 keV.

Standard Pulse Shape Discrimination (PSD) techniques are effective at distinguishing single-site events (SSEs, signal-like) from multi-site events (MSEs, background-like $\gamma$ rays). However, $\alpha$ events are also typically SSE-like, making them difficult to reject using standard $\gamma$-based PSD cuts. Furthermore, in low-background experiments, the total number of observed $\alpha$ events over the experiment's lifetime is often too low to train dedicated classifiers specifically for $\alpha$ rejection. The core problem addressed is whether a PSD classifier trained exclusively on high-statistics $\gamma$-ray data (SSE vs. MSE) can effectively identify and reject $\alpha$ events without requiring dedicated $\alpha$ training data.

Methodology
The study utilized a point-contact Broad Energy Germanium (BEGe) detector. Two measurement campaigns were conducted on the surface:

1. Low-Statistics (LS): Using a $^{209}\text{Po}$ source ($\sim$0.1 Bq), yielding $\sim 1.36 \times 10^5$ $\alpha$ events.
2. High-Statistics (HS): Using a $^{210}\text{Po}$ source ($\sim$1 Bq), yielding $\sim 1.87 \times 10^6$ $\alpha$ events.

In both campaigns, a gold foil with deposited polonium was placed directly on the detector's $p^+$ contact to simulate surface contamination. Calibration runs with a $^{228}\text{Th}$ source provided the training data for the PSD classifiers.

Two machine learning (ML) approaches were investigated:

• Projective Likelihood (PLK): A Naive Bayesian classifier assuming statistical independence among input features.
• Multilayer Perceptron (MLP): A feed-forward artificial neural network with six dense layers (dimensions: 64-32-16-8-4-1), using ReLU activation for hidden layers and sigmoid for the output.

Input Features and Training:

• The input consisted of 64 points from the rising edge of the raw waveform (32 samples before, 1 at, and 31 after the current maximum).
• Training datasets were constructed from $^{228}\text{Th}$ calibration runs, selecting specific energy regions to define SSE (Double Escape Peaks, Compton Edge) and MSE (Single Escape Peaks, Full Energy Peaks, Multi-Compton Scattering) classes.
• Six different training configurations (TC1–TC6) were tested, varying the specific peaks used for SSE and MSE definitions.
• A traditional A/E (Amplitude/Energy) classifier was used as a benchmark.

Key Results
The classifiers were evaluated based on three metrics: SSE survival (signal efficiency), MSE rejection (background suppression), and $\alpha$-rejection factor.

1. Performance on $\gamma$ Background: Both ML methods successfully separated SSE and MSE events. Configurations trained on Double Escape Peaks (DEP) generally outperformed those trained on the Compton Edge (CE). The MLP achieved SSE survival fractions $>80\%$ and MSE survival fractions $<20\%$, consistent with or exceeding previous results from GERDA and LEGEND.
2. Performance on $\alpha$ Rejection: Crucially, classifiers trained only on $\gamma$ data demonstrated strong capability in rejecting $\alpha$ events.
   • MLP: Achieved the best overall performance. For the HS run (TC2 configuration), it yielded an $\alpha$-rejection factor $> 2.71 \times 10^4$ (at 90% confidence level) while maintaining high signal efficiency.
   • PLK: Also effective, though slightly less performant than the MLP in terms of the lower limit on the rejection factor.
   • A/E: The traditional A/E method showed significantly weaker $\alpha$ rejection (factor $\sim 54$), with residual $\alpha$ peaks remaining visible in the spectra.
3. Waveform Analysis: The study observed that $\alpha$ events generally cluster at lower MLP scores than the signal band. However, a secondary cluster of $\alpha$ events (approx. 1% of total) appeared closer to the signal band, likely due to events occurring near the edges of the contact. Despite this, the optimal cut value maximized the Figure of Merit (FoM) while suppressing the vast majority of $\alpha$ events.

Significance and Claims
The paper claims that robust pulse shape discrimination for HPGe detectors can be achieved using training information derived solely from $\gamma$ events. This finding is significant because it offers a practical strategy for next-generation $0\nu\beta\beta$ experiments (like LEGEND) where dedicated $\alpha$ training data is unavailable due to the rarity of such events.

The authors conclude that:

• It is not necessary to develop separate, dedicated classifiers for $\alpha$ rejection.
• A single PSD cut, optimized on $\gamma$ data, can simultaneously suppress multi-site $\gamma$ backgrounds and surface $\alpha$ backgrounds with high efficiency.
• The MLP approach is superior to both the PLK and the traditional A/E method for this dual-purpose rejection.

The study acknowledges limitations, including the surface-level measurement conditions (higher muon background) and the specific detector configuration (JFET replacement between campaigns). The authors suggest that repeating the experiment underground would further reduce background, potentially allowing for an $\alpha$-rejection factor in the order of $10^5$.