High-Resolution Timing for Vertex-Reconstructed Muon-Spin Spectroscopy Using Plastic Scintillators and MuTRiG

This paper demonstrates that integrating plastic scintillator detectors read out by the MuTRiG ASIC into the MuSiP spectrometer overcomes the timing limitations of silicon pixel detectors, enabling high-rate vertex-reconstructed muon-spin spectroscopy with sub-300 ps resolution and the ability to resolve precession frequencies exceeding 50 MHz.

The Gist

Imagine you are trying to take a high-speed photograph of a firefly buzzing around in a dark room. You have two main challenges:

1. Where is it? You need to know exactly which leaf the firefly landed on (Spatial Resolution).
2. When did it happen? You need to know the exact split-second it flashed (Timing Resolution).

For a long time, scientists studying tiny magnetic particles inside materials (using a technique called Muon-Spin Spectroscopy or µSR) had a dilemma. They had a super-sharp camera that could tell them exactly where a particle stopped, but it was a slow camera that couldn't capture the speed of the action. Conversely, they had fast cameras that could capture the speed, but they were blurry and couldn't tell where the action happened.

This paper describes a brilliant "hybrid" solution that combines the best of both worlds.

The Problem: The "Slow Shutter"

The scientists were using a high-tech system called MuSiP, which uses silicon pixel detectors (like the sensor in a super-advanced digital camera) to track muons (subatomic particles).

• The Good: It could pinpoint exactly where a muon stopped on a tiny sample with incredible precision.
• The Bad: The "shutter speed" was too slow (about 16 nanoseconds). It was like trying to photograph a hummingbird's wings with a camera that takes a photo every second. You'd just see a blur. This meant they couldn't study fast-moving magnetic phenomena.

The Solution: Adding a "Speed Sensor"

To fix this without throwing away their amazing "location camera," the team added a new layer of detectors made of plastic scintillators.

• The Analogy: Think of the silicon pixels as a GPS tracker that tells you the exact address of a car. The new plastic scintillators act like a high-speed stopwatch that tells you exactly when the car passed a specific point.
• The Tech: They used special plastic blocks that glow when a particle hits them. To read this glow incredibly fast, they used a custom chip called MuTRiG (originally designed for a different experiment).

How They Made It Work

The team had to overcome a few engineering hurdles:

1. Vacuum Survival: The detectors had to work inside a vacuum chamber (a space with no air). Usually, electronics hate vacuums, but they successfully made the MuTRiG chip survive there.
2. The "Time-Walk" Problem: Imagine a race where runners start at different times based on how loud they shout. If a runner shouts loudly (a strong signal), the timer starts early. If they whisper (a weak signal), the timer starts late. This is called "time-walk."
   • The team wrote a clever software correction (a lookup table) to adjust the timing based on how "loud" the signal was, ensuring every runner was timed fairly.
3. The Result: After fixing the timing issues, they achieved a resolution of under 300 picoseconds. To put that in perspective: A picosecond is to a second what a second is to 31,000 years. They went from a "slow shutter" to a "super-speed shutter."

The Proof: Catching the "Fast Dance"

To prove their new system worked, they tested it on a sample of glass (SiO2).

• Inside the glass, muons form a tiny atom called "muonium" that spins and wobbles incredibly fast (about 50 million times a second).
• The old silicon-only system was too slow to see this wobble; it just looked like static noise.
• The new hybrid system (Silicon + Plastic Scintillators) clearly saw the wobble. It was like finally seeing the individual blades of a spinning fan instead of just a blur.

Why This Matters

This isn't just about taking better pictures; it's about unlocking new science.

• Small Samples: Because the system is so precise, scientists can now study tiny, uneven samples (like a speck of dust or a tiny chip) that were previously too small to measure accurately.
• High Speed: They can now study materials where magnetic changes happen at lightning speed.
• Scalability: They proved this system works in a vacuum and can be scaled up.

In summary: The team took a high-precision location tracker and glued a high-speed stopwatch to it. By teaching the stopwatch to ignore its own timing errors, they created a machine that can see exactly where and exactly when subatomic particles are dancing, opening the door to discovering new secrets in quantum materials.

Technical Summary

Here is a detailed technical summary of the paper "High-Resolution Timing for Vertex-Reconstructed Muon-Spin Spectroscopy Using Plastic Scintillators and MuTRiG".

1. Problem Statement

Vertex-reconstructed muon-spin spectroscopy (vx-µSR) using silicon pixel detectors (specifically the MuSiP spectrometer) has recently achieved unprecedented lateral resolution and the ability to operate at high muon stop rates (>400 kHz). However, a critical bottleneck remains: timing resolution.

• Current Limitation: The MuPix11 silicon pixel chips used in MuSiP provide a time resolution of approximately 16 ns.
• Consequence: This resolution is insufficient to resolve fast muon-spin precession frequencies (typically >10 MHz) and restricts measurements on samples with fast relaxation rates.
• Gap: State-of-the-art conventional µSR spectrometers using scintillators achieve sub-nanosecond timing, but they lack the spatial (vertex) resolution of pixel detectors. Developing new pixel chips with both low material budget and high timing performance is currently not feasible.

2. Methodology

The authors pursued a hybrid approach: integrating Plastic Scintillator Detectors (PSDs) read out by the MuTRiG ASIC into the existing MuSiP spectrometer to complement the spatial data from silicon pixels with high-precision timing.

• Detector Configuration:
  • Three PSDs were installed: a Muon counter (M), a backward positron detector (B), and a forward positron detector (F).
  • Material: High-efficiency, fast-timing EJ-212 plastic scintillators.
  • Geometry:
    • M: 17 mm diameter, 200 µm thick.
    • B: 85 × 45 × 4 mm³ with a central 17 mm hole to allow muons to pass.
    • F: 40 × 40 × 4 mm³.
  • Readout: Each scintillator is read out at both ends by arrays of five series-connected Advansid NUV3S-P SiPMs (Silicon Photomultipliers).
• Electronics (MuTRiG):
  • The SiPMs are coupled to the MuTRiG ASIC, a 32-channel mixed-signal chip originally developed for the Mu3e experiment.
  • Key Features: MuTRiG offers intrinsic timing resolution of ~50 ps and supports hit rates up to 1 MHz per channel.
  • Integration: A custom high-voltage AC-coupling adapter was designed to interface the SiPMs with the MuTRiG. The readout board was installed inside the vacuum vessel, marking the first successful operation of MuTRiG in a vacuum environment.
• Data Processing:
  • Time-Walk Correction: A significant challenge in scintillator-SiPM systems is "time-walk" (where signal amplitude affects timing). The authors implemented a lookup-table approach using Time-over-Threshold (ToT) measurements to correct the time offset on an event-by-event basis.
  • Coincidence Logic: Events were validated by requiring coincident hits on both ends of a scintillator to suppress dark counts and noise.

3. Key Contributions

• First Vacuum Operation: Demonstrated the stable operation of the MuTRiG ASIC inside a vacuum vessel, a critical step for integration into particle physics spectrometers.
• Hybrid Architecture: Successfully integrated fast timing detectors (PSDs) with spatial tracking detectors (Si pixels) without compromising the high-rate capability or spatial resolution of the MuSiP system.
• Custom Electronics Integration: Developed and validated a custom AC-coupling solution for high-voltage SiPMs with the MuTRiG ASIC, enabling seamless data acquisition within the existing MuSiP infrastructure.
• Performance Benchmarking: Established that the hybrid system can resolve frequencies far beyond the capabilities of silicon pixels alone.

4. Results

• Timing Resolution:
  • After applying time-walk corrections, the system achieved single-detector time resolutions (RMS) of:
    • M Counter: 278 ps
    • B Detector: 268 ps
    • F Detector: 227 ps
  • These values represent an improvement of nearly two orders of magnitude over the 16 ns resolution of the MuPix11 chips.
  • The results are comparable to established scintillator-based µSR instruments and consistent with offline measurements using a radioactive alpha source.
• µSR Performance Demonstration:
  • Standard transverse-field µSR measurements were performed on a SiO₂ (Suprasil) sample in a ~3.5 mT magnetic field.
  • The system successfully resolved muonium precession frequencies at 46.22 MHz and 47.31 MHz.
  • This confirms the system can handle fast oscillations (~50 MHz) that are entirely inaccessible to silicon pixel detectors alone.

5. Significance

This work establishes a viable, scalable path toward next-generation vx-µSR instruments that combine:

1. High Lateral Resolution: Provided by silicon pixel detectors for vertex reconstruction and background suppression.
2. High Timing Precision: Provided by MuTRiG-readout plastic scintillators for resolving fast spin dynamics.
3. High Rate Capability: The system maintains the ability to operate at muon rates exceeding 400 kHz.

Impact: This hybrid approach removes the timing bottleneck of current vertex-reconstructed µSR, enabling new experiments on small, spatially inhomogeneous quantum materials and fast-relaxing magnetic systems. It proves that existing pixel-based spectrometers can be upgraded to state-of-the-art timing performance without requiring a complete redesign of the detector geometry. Future work will focus on highly segmented PSDs to handle even higher rates and utilizing the timing layers for coarse tracking in magnetic fields.