Construction and characterization of a muon trigger detector for the PSI muEDM experiment

This paper presents the design, construction, and beam test results of the Muon Trigger Detector (MTD) for the PSI muEDM experiment, demonstrating through experimental data and Geant4 simulations that the system successfully identifies storable muons to enable a sensitivity improvement of over three orders of magnitude in the muon electric dipole moment measurement.

The Gist

Imagine you are trying to catch a specific type of rare, fast-moving butterfly (a muon) in a giant, swirling garden (a magnetic solenoid) to study its secrets. But here's the catch: the garden is full of millions of other insects, and you only want to catch the ones that are perfectly healthy and ready to stay in the center. If you catch the wrong ones, or if you miss the right ones, your experiment fails.

This paper is about building a super-fast, ultra-smart gatekeeper (called the Muon Trigger Detector or MTD) to solve this problem for a giant science experiment at the Paul Scherrer Institute in Switzerland.

Here is the breakdown of how they did it, using simple analogies:

1. The Mission: Catching the "Perfect" Butterfly

The scientists want to measure something called the Electric Dipole Moment (EDM) of the muon. Think of this as checking if the butterfly has a tiny, hidden imbalance in its wings. Finding this imbalance would prove that our current understanding of the universe (the Standard Model) is missing a huge piece of the puzzle.

To do this, they need to trap these muons in a magnetic "cage" and watch them spin. But the muons are moving incredibly fast (like bullets). They need a system to:

• Spot a muon coming in.
• Decide in a split second if it's a "keeper" (one that will stay in the cage).
• Fire a magnetic "net" to trap it before it flies away.

2. The Problem: Too Many False Alarms

The beam of muons coming in is like a firehose spraying water. Only 0.4% of that water is the "good stuff" (the storable muons). The other 99.6% are "bad" muons that will crash into the walls or fly out of the cage.

If the gatekeeper isn't perfect, it will waste its energy trapping the wrong muons, or worse, miss the right ones. The system needs to be so precise that it rejects the bad muons 98% of the time and catches the good ones 95% of the time.

3. The Solution: The "Gate" and the "Aperture"

The scientists built a two-part detector that acts like a bouncer at an exclusive club:

• Part A: The "Gate" (The Thin Door):
  This is a super-thin sheet of plastic (0.1 mm thick), like a piece of tissue paper. It's the first thing the muon hits. Its job is to say, "Hey, someone is here!" It's so thin that it doesn't slow the muon down much; it just waves hello.
• Part B: The "Aperture" (The Thick Wall):
  Behind the Gate is a thick block of plastic (5 mm thick) with a hole cut in it. This is the "Active Aperture."
  • The Hole: If a muon is on the perfect path, it flies through the hole without touching the wall.
  • The Wall: If a muon is on a bad path (too wide or at a bad angle), it smashes into the thick wall and stops.

The Magic Logic (The Anti-Coincidence):
The detector uses a simple rule: "If you hit the Gate BUT NOT the Wall, you are a VIP. Let you in!"

• Gate Hit + Wall Hit: You are a "bad" muon. Stop! (Vetoed).
• Gate Hit + No Wall Hit: You are a "good" muon. TRIGGER! (Fire the magnetic net).

4. The Construction: High-Tech Eyes

To see these muons, they didn't use cameras. They used plastic scintillators (plastic that glows when hit by a particle) and SiPMs (Silicon Photomultipliers).

• Think of the SiPMs as super-sensitive eyes that can see a single photon of light.
• When a muon hits the plastic, it flashes. The SiPMs see the flash and send a signal to the computer.
• The whole system is built with CNC machines (robotic cutters) to make the hole in the thick plastic perfectly precise, down to the width of a human hair.

5. The Test: The "Dry Run"

In late 2024, they took this detector to a test beam at PSI. They couldn't use the full-power machine yet, so they scaled it down:

• They used a weaker beam.
• They tested it in the air instead of a vacuum (like testing a car on a dirt road before taking it to the racetrack).
• They even used positrons (sister particles to electrons) to simulate the muons' paths.

The Results:
They ran millions of particles through the detector.

• Did it work? Yes! The detector correctly identified the "good" muons and rejected the "bad" ones.
• Did the computer simulation match reality? They built a virtual version of the detector in a computer (using software called Geant4). At first, the computer was too optimistic, thinking it caught more muons than it actually did.
• The Fix: They realized they needed to simulate the light itself—how it bounces off the shiny aluminum coating inside the detector and hits the "eyes" (SiPMs). Once they added this "light physics" to the simulation, the computer's predictions matched the real-world results with 97% accuracy.

6. Why This Matters

This paper proves that the "Gatekeeper" is ready for the big show.

• It's fast enough to catch the muons before they escape.
• It's smart enough to ignore the trash muons.
• The scientists now understand exactly how it works, down to the behavior of individual light particles.

In short: They built a high-tech, light-speed bouncer that can tell the difference between a VIP muon and a regular one in a fraction of a nanosecond. This is a crucial step toward discovering new physics that could change how we understand the universe.

Technical Summary

1. Problem Statement

The PSI muEDM experiment aims to measure the muon Electric Dipole Moment (EDM) with a sensitivity improvement of over three orders of magnitude beyond the current limit set by the BNL Muon $g-2$ experiment. A critical challenge in this measurement is the efficient and selective storage of muons within a solenoid.

• Low Acceptance: Only a tiny fraction (approx. 0.4%) of the incoming muon beam (120 kHz) falls within the specific phase space required for storage.
• Timing Constraints: The system must rapidly identify "storable" muons and trigger a magnetic kicker pulse within 140 ns to confine them.
• Rate Limitations: The pulsed power supply has a maximum repetition rate of 2 kHz. If the trigger system fails to reject non-storable muons (background) with high efficiency, the system will be overwhelmed, exceeding the kicker's operational limits.
• Requirement: A detector is needed that can distinguish storable muons from the background with an acceptance rate ($\epsilon_a$) $\ge$ 95% and a rejection rate ($\epsilon_r$) $\ge$ 98%, while introducing minimal perturbation to the beam trajectory.

2. Methodology

The authors developed, constructed, and tested an upgraded Muon Trigger Detector (MTD) prototype.

A. Detector Design

The MTD utilizes an anti-coincidence logic scheme consisting of two plastic scintillator subsystems:

1. Gate Detector (GD): A thin (0.1 mm) plastic scintillator (Eljen EJ-200) that detects all incoming muons. It is read out by four Silicon Photomultipliers (SiPMs).
2. Active Aperture Detector (AAD): A thick (5 mm) CNC-machined plastic scintillator slab. It acts as a veto; muons hitting this detector are "out-of-acceptance" and are stopped/vetoed. It is read out by six SiPMs connected in parallel.

• Trigger Logic: A valid trigger is generated only if the Gate detects a hit AND the Aperture detects NO hit.
• Readout: Fast electronics generate a Low-Voltage Transistor-Transistor Logic (LVTTL) signal in $<10$ ns.

B. Simulation and Optimization

• Tools: The design was optimized using Geant4 frameworks (G4Beamline for beam dynamics and musrSim for detector response).
• Optimization: A surrogate model optimization algorithm (Polynomial Chaos Expansion) was used to determine the optimal aperture geometry to maximize storage efficiency ($\epsilon_s$) while meeting $\epsilon_a$ and $\epsilon_r$ constraints.
• Modeling: The simulation included detailed optical photon transport, SiPM response modeling, and specific surface treatments (aluminum nano-coating on the Aperture to prevent crosstalk and maximize light collection).

C. Experimental Setup (Test Beam 2024)

• Location: PSI $\pi$E1 beamline (October 2024).
• Conditions: Due to logistical constraints, the test used scaled-down conditions:
  • Beam: 22.5 MeV/c $\mu^+$ (primary) and 7 MeV/c $e^+$ (secondary) beams.
  • Magnetic Field: Reduced or off (compared to the nominal 3 T).
  • Environment: Air (instead of vacuum).
• DAQ: WaveDream Board (WDB) digitizer was used to record waveforms from all SiPM channels. Five trigger patterns were defined to analyze different event topologies (e.g., Gate-only, Aperture-only, Coincidence, Anti-coincidence).

3. Key Contributions

1. Prototype Construction: Successful fabrication of a compact (diameter $\le$ 200 mm, length $\le$ 150 mm) MTD prototype using thin/thick scintillators and SiPMs, featuring a custom 3D-printed holder and optimized light guides.
2. Advanced Simulation Framework: Development of a high-fidelity Geant4 simulation that incorporates optical photon transport and SiPM response. This goes beyond simple "truth-level" simulations (which only track energy deposition) to model realistic signal generation, including threshold effects and light collection efficiency.
3. Validation of Anti-Coincidence Logic: Experimental demonstration that the anti-coincidence scheme effectively selects storable muons while vetoing background, even under non-nominal beam conditions.

4. Results

• Detector Response:
  • The Gate showed a Landau distribution (characteristic of thin scintillators) with peaks of 15–20 photoelectrons (p.e.).
  • The Aperture showed a truncated Gaussian distribution (due to online thresholds) as muons were fully stopped in the 5 mm slab.
• Event Topology:
  • Approximately 75% of events satisfied the anti-coincidence condition (Gate hit, Aperture no hit).
  • Only ~4% of events hit the Aperture (vetoed), consistent with the higher momentum beam having less scattering than the design baseline.
• Simulation vs. Measurement:
  • Truth-level simulation (energy deposition only) failed to reproduce the data, underestimating anti-coincidence rates by >20% and predicting a 0% rate for "No Aperture & No Exit" events.
  • Optical simulation (including photon transport and thresholds) achieved ~97% agreement with measured data.
  • The optical simulation correctly predicted the "No Aperture & No Exit" topology at ~4%, matching the measurement, whereas the truth-level simulation predicted ~0%.
• Performance Metrics: The system demonstrated a rejection efficiency well above the critical 98% threshold required for the final experiment, validating the core design concept.

5. Significance

• Readiness for Phase-1: The results validate the MTD design and confirm its readiness for deployment in the full muEDM Phase-1 setup.
• Methodological Advance: The study highlights the critical importance of optical modeling in detector simulation. Relying solely on truth-level simulations leads to significant errors in predicting trigger rates, whereas modeling the full optical chain (scintillation yield, reflection, SiPM PDE) is essential for accurate performance prediction.
• Physics Impact: By ensuring high-efficiency storage of muons and effective background rejection, the MTD enables the muEDM experiment to reach its target sensitivity of $6 \times 10^{-23} e\cdot cm$, offering a powerful probe for CP violation and new physics beyond the Standard Model.