Afterpulse prediction for SUBMET experiment

This paper presents a prediction method for PMT afterpulse rates in the SUBMET experiment that achieves approximately 20% precision, thereby enhancing the reliability of background predictions for the search of millicharged particles.

The Gist

Imagine you are trying to listen for a tiny, secret whisper in a very noisy room. This is essentially what the SUBMET experiment is doing. Scientists are hunting for "millicharged particles"—ghostly, tiny bits of matter that might make up dark matter. These particles are so weakly charged that they are incredibly hard to catch.

To catch them, the team built a detector at a giant particle accelerator in Japan (J-PARC). The detector is made of 160 long plastic bars (like giant glow sticks) connected to super-sensitive microphones called Photomultiplier Tubes (PMTs).

The Problem: The "Echo" Effect

Here is the trouble: When a high-energy particle hits the detector, it creates a massive, loud "bang" (a large electrical pulse) in the microphone. But, just like shouting in a canyon, the microphone doesn't just hear the bang and then go silent. It starts making echoes.

In the world of physics, these echoes are called afterpulses.

• The Real Signal: A tiny, single "click" from a dark matter particle (a Single Photoelectron or SPE).
• The Noise: The echoes from the big "bang."

The problem is that these echoes look exactly like the tiny clicks the scientists are looking for. If they can't tell the difference, they might think they found dark matter when it was just an echo. This creates a huge amount of "false alarms" (background noise).

The Solution: Predicting the Echoes

The scientists realized they couldn't just ignore the echoes; they had to learn to predict them. They asked: "If we know how loud the original 'bang' was, can we guess exactly how many echoes will follow and when they will happen?"

They developed a prediction recipe with two main ingredients:

1. The Size of the Bang (Area): They found that the bigger the initial pulse, the more echoes it creates. It's like hitting a drum harder; the louder the hit, the more the room vibrates afterward. They tested two ways to calculate this:

   • Linear: A straight-line relationship (Bigger hit = proportionally more echoes).
   • Exponential: A curve where a slightly bigger hit creates way more echoes.
   • Result: Both worked almost equally well.

2. The Timing (The Decay): They noticed the echoes don't happen all at once. They happen in a rush right after the bang and then slowly fade away, like a drumbeat that gets quieter and quieter over time. They measured exactly how fast this "fading" happens for each of the 160 detectors.

The Result: A Reliable Forecast

By combining these two ingredients, the team created a mathematical model that acts like a weather forecast for noise.

• How it works: When a big pulse happens, the model says, "Okay, based on the size of that pulse and the specific 'personality' of this detector, we expect about 130 echoes in the next few microseconds."
• The Accuracy: The model is surprisingly good. It predicts the number of echoes with about 20% precision.

Why This Matters

Think of the experiment like trying to find a specific coin in a pile of sand.

• Before: The "sand" (background noise) was so full of fake coins (echoes) that they couldn't find the real one.
• Now: With this prediction model, they can look at the pile and say, "We know 90% of these coins are fake echoes caused by that big rock we just dropped. Let's subtract those out."

This allows them to use more data. Previously, they might have thrown away any event that had a big pulse because it was too messy. Now, they can keep those events, subtract the predicted echoes, and look for the real dark matter signals hidden underneath.

In short: The scientists figured out how to mathematically "cancel out" the noise caused by their own equipment, making their search for the universe's most elusive particles much more reliable.

Technical Summary

1. Problem Statement

The SUB-Millicharge ExperimenT (SUBMET) at J-PARC aims to detect millicharged particles ($\chi$) with masses $m_\chi < 1.6 \text{ GeV}/c^2$ and charges $Q_\chi < 10^{-3}e$. The detector utilizes 160 modules, each consisting of an Eljen-200 plastic scintillator coupled to a Hamamatsu R7725 photomultiplier tube (PMT).

A critical challenge in this experiment is the presence of PMT afterpulses. These are delayed signals generated when photoelectrons ionize gas impurities between the photocathode and dynodes, creating secondary photoelectrons hundreds of nanoseconds later.

• The Issue: Afterpulses are indistinguishable from the target signal (Single Photoelectron or SPE pulses).
• The Context: The J-PARC beam consists of eight bunches separated by $\sim 600$ ns. Large pulses (height $> 140$ mV) from energetic particles in one bunch generate afterpulses that can overlap with SPE signals in subsequent bunches, significantly increasing the background rate.
• The Goal: To develop a predictive model for afterpulse rates based on measurable parameters to accurately estimate background contributions and improve the reliability of the experiment's data analysis.

2. Methodology

The authors developed a prediction model based on beam data collected in June 2024, utilizing a dedicated trigger delay to focus on the time window following the last beam bunch. The dataset consisted of 50,000 events, split evenly between model fitting and performance validation.

Key Observables and Assumptions

The model assumes the afterpulse rate ($dn/dt$) depends on:

1. Large Pulse Area ($A$): The integrated charge of the primary pulse generating the afterpulses.
2. Time Constant ($\tau$): The decay rate of the afterpulse probability over time.
3. Time Window: The analysis focuses on the window $t \in [720 \text{ ns}, 3475.2 \text{ ns}]$ after the large pulse. The first 720 ns (Region 1) are excluded due to baseline fluctuations.

Model Construction

The prediction framework involves two main components:

1. Dependence on Pulse Area ($A$):
   The total number of afterpulses ($n$) in a fixed time window was found to correlate positively with the large pulse area ($A$). Two functional forms were tested:

   • Linear Fit: $n_{pred}^{lin}(A) = p_0^{lin} + p_1^{lin} A$
   • Exponential Fit: $n_{pred}^{expo}(A) = \exp(p_0^{expo} + p_1^{expo} A)$

2. Time Structure:
   The distribution of the time difference ($\Delta t$) between the large pulse and the afterpulse follows an exponential decay: $N(\Delta t) \propto \exp(-\Delta t / \tau)$. The time constant $\tau$ was found to be independent of the pulse area $A$ and is measured individually for each of the 160 modules.

3. Prediction Formula:
   Combining the area dependence and time structure, the predicted number of afterpulses in an arbitrary time window $[t_i, t_f]$ is calculated as:
   $$n_{pred}(A, t_i, t_f) = \frac{1}{\tau} \int_{t_i}^{t_f} n_0(A) e^{-t'/\tau} dt'$$
   Where $n_0(A)$ is derived by normalizing the area-dependent fit ($n_{pred}(A)$) over the integration range $[t_0, t_1]$.

3. Key Contributions

• Dual-Model Framework: The paper presents two distinct predictive models (Linear and Exponential) linking large pulse area to afterpulse counts, validated against real beam data.
• Module-Specific Calibration: Recognizing that PMT characteristics vary, the authors measured the time constant $\tau$ and fit parameters ($p_0, p_1$) independently for all 160 detector modules.
• Background Mitigation Strategy: The method allows the experiment to include events containing "large pulses" (which were previously potentially discarded or treated as high-background) in the analysis by precisely subtracting the predicted afterpulse contribution.

4. Results

• Parameter Ranges:
  • Linear model parameters: $p_0 < 4$, $p_1 \in [3, 14] \times 10^{-5}$.
  • Exponential model parameters: $p_0 < 2$, $p_1 \in [1, 4] \times 10^{-5}$.
  • Mean time constant $\tau$: $\approx 1450$ ns (Standard Deviation: 140 ns).
• Model Performance:
  • Both the linear and exponential models reproduced the observed afterpulse rates with approximately 20% precision.
  • The reduced chi-squared ($\chi^2/ndf$) distributions for both models were comparable, with mean values of 0.731 (linear) and 0.750 (exponential).
  • The linear model was selected for further analysis due to its simplicity.
• Validation:
  • Figure 8 (in the paper) shows the total predicted vs. observed afterpulse counts for all 160 modules, demonstrating strong agreement within statistical uncertainties.
  • The model successfully predicts the time distribution of afterpulses, with the predicted counts falling within the $\pm 1\sigma$ uncertainty bands of the observed data.

5. Significance

• Data Utilization: Since more than 70% of collision events contain at least one large pulse, the ability to accurately predict and subtract afterpulses is crucial. Without this model, a vast majority of the collision data would be unusable due to high background uncertainty.
• Background Reliability: The method significantly improves the reliability of background predictions for the millicharged particle search, ensuring that potential signals are not obscured by misidentified afterpulses.
• General Applicability: The approach provides a robust framework for characterizing and correcting PMT afterpulse effects in other high-energy physics experiments utilizing similar scintillator-PMT readout systems.

In conclusion, this paper establishes a validated, module-specific prediction method that reduces afterpulse background uncertainty to ~20%, enabling the SUBMET experiment to maximize its sensitivity to millicharged particles in a previously unexplored parameter space.