Reconstruction of the Effective Energy-deposition Vertex of Muon Showers using PMT Waveform in a Large-scale Liquid Scintillator Detector

This paper proposes a novel waveform-based method that isolates shower components from muon tracks to reconstruct energy-deposition vertices in large-scale liquid scintillator detectors with high precision and efficiency, thereby enabling effective localized spatial vetoes to suppress cosmogenic backgrounds in experiments like JUNO.

The Gist

Imagine you are trying to listen to a very quiet whisper (a neutrino signal) in a giant, dark swimming pool filled with special glowing water (liquid scintillator). The problem is that occasionally, a giant, noisy rock (a cosmic muon) falls into the pool from the sky. When this rock hits the water, it doesn't just make a splash; it explodes into a chaotic storm of smaller rocks and bubbles (a particle shower).

These "bubbles" create radioactive particles that look exactly like the whispers you are trying to hear. If you don't know exactly where the explosion happened, you have to turn off the whole pool for a long time to be safe, which means you miss a lot of the whispers.

This paper presents a new, clever way to find the exact center of the explosion so you can only turn off a tiny bubble around it, leaving the rest of the pool open to listen.

Here is the breakdown of their solution using simple analogies:

1. The Problem: The "Messy" Rock

In big underground detectors like JUNO (a massive tank of glowing liquid), cosmic rays hit the detector. Most of the time, a muon just swims straight through like a fish. But sometimes, it hits something hard and creates a shower—a burst of energy radiating out like a firework.

• The Issue: These fireworks create radioactive "ghosts" (isotopes) that mimic the signals scientists want to find.
• The Old Way: If you see a firework, you assume the whole pool is contaminated and shut it down for a while. This wastes a lot of time.
• The Goal: We need to pinpoint the center of the firework so we can only block that specific spot.

2. The Challenge: Seeing in the Dark

In a clear water tank, you can see the path of the fish (the muon track) easily. But in this glowing liquid, the light scatters in all directions, like trying to see the shape of a firework through thick fog. It's very hard to tell where the main explosion happened just by looking at the light.

3. The Solution: The "Subtraction Trick"

The authors came up with a brilliant method to isolate the "explosion" from the "swimming path."

• The Analogy: Imagine you are listening to a song, but there is a constant hum in the background (the muon's path). You want to hear the sudden crash of a cymbal (the shower).
• The Method:
  1. Record the Song: The detector records the light waves (waveforms) from the muon.
  2. Predict the Hum: The scientists use math to calculate exactly what the "swimming path" (the hum) should look like if there were no explosion.
  3. Subtract: They subtract the "hum" from the "song."
  4. The Result: What's left is the pure sound of the cymbal crash (the shower). Now, they can see exactly where the crash happened.

4. Finding the Center: The "Flashlight Game"

Once they have isolated the "crash," they need to find its center.

• The Setup: The detector is covered in thousands of light sensors (PMTs), like eyes looking into the dark pool.
• The Game: The scientists ask, "If the explosion happened here, when would the light hit each eye?"
• The Iteration: They guess a spot, check the timing, and see how wrong they are. Then they move the guess a little bit and try again. They do this over and over (like a GPS recalculating your route) until the guess is perfect.
• The Speed: They found that doing this "recalculation" about four times is enough to get the location incredibly precise.

5. The Results: Pinpoint Accuracy

The results are impressive:

• Precision: They can find the center of the explosion within about 15 to 26 centimeters (roughly the length of a ruler). That is incredibly precise for a tank the size of a football field!
• Success Rate: They succeed in finding the spot more than 96% of the time.
• Why it Matters: Because they know the spot so well, they can draw a tiny circle (a "veto") around just the explosion. This stops the radioactive "ghosts" from messing up the data, but keeps the rest of the detector open to catch the precious neutrino whispers.

Summary

Think of this paper as inventing a super-precise GPS for particle explosions. Instead of shutting down the whole city because of one traffic accident, they can now pinpoint the exact intersection where the crash happened and only close that one block. This allows the "JUNO" experiment to listen to the universe's quietest secrets with much less noise and much more time.

Technical Summary

Here is a detailed technical summary of the paper "Reconstruction of the Effective Energy-deposition Vertex of Muon Showers using PMT Waveform in a Large-scale Liquid Scintillator Detector."

1. Problem Statement

In deep-underground low-background experiments, such as the Jiangmen Underground Neutrino Observatory (JUNO), cosmogenic muons induce radioactive isotopes (e.g., $^9$Li, $^8$He, $^{11}$C) via spallation. These isotopes constitute a significant background for neutrino and dark matter searches.

• The Challenge: While standard muon veto strategies (vetoing a volume around the muon track) work well for "through-going" muons, they are inefficient for shower muons. Shower muons (muons that induce hadronic or electromagnetic showers) account for only 20% of all muon events but generate **88% of all muon-induced isotopes**.
• The Specific Difficulty: In large-scale Liquid Scintillator (LS) detectors, the isotropic nature of light emission makes it difficult to reconstruct the detailed profile of a shower compared to detectors like LArTPC. Existing methods struggle to precisely locate the "energy-deposition centroid" of the shower, which is the critical point for effective background rejection.

2. Methodology

The authors propose a novel waveform-based reconstruction algorithm specifically designed for 20-kiloton LS detectors. The core logic involves isolating the shower signal from the muon track signal and using photon timing to reconstruct the vertex.

A. Definitions and Simulation

• Shower Vertex: Defined as the energy-deposition-weighted centroid of voxels within a 2-meter radius. This range captures the majority of shower energy.
• Shower Muon: A muon depositing >1.8 GeV of energy (excluding minimum ionization) within a 2m sphere.
• Simulation: A Geant4-based framework simulates muons traversing the JUNO detector geometry. It includes detailed optical processes (scintillation, Cherenkov, scattering) and electronics response (PMT single photoelectron waveforms, transit time spread, dark noise).

B. Waveform Subtraction Strategy

The fundamental innovation is the isolation of the shower component from the total PMT waveform:

1. Track Subtraction: The waveform contribution from the muon's minimum ionizing track is calculated analytically or derived from non-shower muon events with similar trajectories. This "track component" is subtracted from the raw shower muon waveform.
2. Isolation: The residual waveform contains peaks primarily attributable to the shower energy deposition.
3. Peak Selection: Peaks in the subtracted waveform exceeding 60% of the maximum amplitude are selected as candidates for vertex reconstruction.

C. Reconstruction Algorithm

The algorithm reconstructs the vertex position by minimizing a $\chi^2$ function based on photon time-of-flight (ToF):

• Objective Function: Minimize $\chi^2 = \sum (\frac{T_{pre} - T_{obs}}{\sigma})^2$, where $T_{pre}$ is the predicted peak time and $T_{obs}$ is the observed peak time.
• Time Prediction Model: $T_{pre}$ is calculated as the sum of:
  • Muon incident time ($t_{incident}$).
  • Muon time-of-flight ($t_{muon\_tof}$).
  • Photon time-of-flight ($t_{photon\_tof}$), accounting for complex optical propagation (refractive index, scattering).
  • Electronic delays ($t_{delay}$) and waveform offset ($t_{offset}$).
• Iterative Optimization:
  1. An initial vertex is estimated using the charge centroid method.
  2. The $\chi^2$ is minimized to find a refined vertex.
  3. The process is repeated iteratively (up to 4 times). The paper finds that convergence is achieved by the 4th iteration, with negligible gains thereafter.
• Quality Control: Events with a $\chi^2$/NDF > 10 are flagged as reconstruction failures.

3. Key Contributions

1. First Comprehensive Study: This is the first detailed study of shower muon reconstruction in a 20-kiloton LS detector, addressing a gap in current JUNO analysis capabilities.
2. Waveform Subtraction Technique: The paper introduces a robust method to analytically subtract the muon track component from the total waveform, effectively isolating the shower signal in a medium where light is isotropic.
3. Definition of Effective Vertex: It establishes the "energy-deposition-weighted centroid" (within 2m) as the optimal reference point for background vetoing, showing that 84% of isotopes are produced within 3m of this vertex.
4. Iterative Optimization Framework: A specific $\chi^2$ minimization scheme using PMT peak times and photon propagation models is developed and validated.

4. Results

The performance was evaluated using simulated data for single and double shower events.

• Spatial Resolution (68% percentile):
  • X-axis: 0.16 m
  • Y-axis: 0.15 m
  • Z-axis: 0.26 m
  • Total Distance (Vertex): 0.49 m
  • Longitudinal ($d_L$): 0.40 m (larger due to forward-peaking shower profile).
  • Transverse ($d_T$): 0.17 m.
• Reconstruction Efficiency:
  • Exceeds 96.7% for single shower events with energies > 3 GeV (specifically for 100 GeV initial muon energy).
  • Efficiency drops for double-shower events but remains high (~100% for the first vertex in the 5–9 GeV range).
• Robustness:
  • The algorithm remains effective even when the input muon track is smeared (simulating realistic reconstruction uncertainties of $\sigma=20$ cm), keeping the vertex deviation within 1 m.
  • Performance is stable for vertices within 15 m of the detector center; degradation occurs near the periphery due to energy leakage and boundary effects.
• Background Suppression Potential: Since 84% of isotopes are within 3 m of the shower vertex, reconstructing this vertex allows for a localized spherical veto that significantly reduces background while minimizing dead time compared to full-detector vetoes.

5. Significance

• For JUNO: This method provides the critical technical foundation for implementing localized spatial vetoes against muon-induced backgrounds. By precisely locating the shower vertex, JUNO can reject the dominant source of $^9$Li/$^8$He backgrounds without sacrificing excessive live time, thereby enhancing the sensitivity to neutrino mass ordering and other rare events.
• For Future Experiments: The methodology is applicable to other large-scale, low-background LS detectors (e.g., future multi-kiloton experiments) that record PMT waveforms. It offers a solution to the challenge of shower reconstruction in isotropic media, potentially aiding in dark matter searches and neutrino physics.
• Strategic Impact: The paper suggests a hybrid veto strategy combining cylindrical track vetoes with spherical shower vertex vetoes, optimizing the trade-off between background rejection and detector live time.