Positron Transport System for Muonium-to-Antimuonium Conversion Experiment

This paper presents the design and simulation results of a positron transport system for the Muonium-to-Antimuonium Conversion Experiment (MACE), demonstrating high geometric acceptance, precise position resolution, and a time-of-flight capability that enables a $10^{-7}$ rejection factor for internal conversion backgrounds to facilitate the search for charged lepton flavor violation.

The Gist

Imagine you are trying to catch a very specific, tiny, and shy ghost (a positron) that appears only when two other ghosts collide and transform. But here's the catch: the room is absolutely packed with millions of other ghosts, some of which look almost exactly like the one you want, and they are much louder and faster.

This paper describes the design of a high-tech "ghost catcher" (called the Positron Transport System or PTS) for a massive physics experiment called MACE. The goal of MACE is to find a rare event where a "Muonium" atom (a hydrogen-like atom made of a muon and an electron) magically turns into "Antimuonium" (its anti-matter twin). This would prove that the laws of physics we thought were unbreakable are actually breakable, opening the door to "New Physics."

Here is how their "ghost catcher" works, explained in simple terms:

1. The Problem: The "Needle in a Haystack"

When the experiment runs, it creates a flood of particles.

• The Signal: A slow, low-energy positron (the "needle"). It's born with very little energy, like a sleepy baby.
• The Noise: Millions of high-energy positrons and electrons (the "haystack"). These are the "loud, fast ghosts" that can trick your detectors into thinking they are the signal.

If you just let them all fly into your detector, the signal will be completely drowned out. You need a way to sort the sleepy babies from the screaming toddlers.

2. The Solution: A Three-Stage Filter System

The authors designed a specialized tunnel (the PTS) that acts like a bouncer, a speed bump, and a maze all rolled into one.

Stage A: The "Wake-Up Call" (Electrostatic Accelerator)

The signal positrons are born with almost no energy (about 13.5 electron-volts). They are too weak to travel far.

• The Analogy: Imagine trying to push a heavy shopping cart up a hill, but the cart has no wheels.
• The Fix: The system uses an electric accelerator (a series of charged rings) to give the positron a gentle but firm push. It speeds them up to a few hundred electron-volts. This is just enough to get them moving through the tunnel without losing them, but not so much that they become indistinguishable from the noisy background.

Stage B: The "S-Shaped Maze" (The Solenoid)

Once moving, the particles enter a long tunnel wrapped in magnets that create a magnetic field.

• The Analogy: Think of a roller coaster track that twists in an "S" shape.
• How it works:
  • The Signal Positrons: Because they are light and slow, they hug the magnetic field lines tightly. They follow the "S" curve perfectly, like a snake slithering through a tube.
  • The Background Noise: The noisy, high-energy particles are heavy and fast. When they hit the curves of the "S," they can't turn sharp enough. They crash into the walls of the tunnel and get filtered out.
  • Why an "S"? If you only had one curve, the particles would drift off to the side. By using a symmetric "S" shape (one curve left, one curve right), the system cancels out the drift, ensuring the signal arrives exactly where it's supposed to.

Stage C: The "Hairnet" (The Collimator)

Even after the S-curve, some stubborn background particles might sneak through.

• The Analogy: Imagine a hairnet made of thin metal sheets with tiny gaps.
• How it works: The system places a special filter (collimator) in the middle of the tunnel. It consists of thin bronze sheets spaced very precisely (about 1.15 mm apart).
  • The signal positrons are spinning in tight circles (like a top) due to the magnetic field. They are small enough to wiggle through the gaps in the hairnet.
  • The background particles have too much "sideways" energy. They hit the metal sheets and get stopped.
  • The Precision: This is so sensitive that if the hairnet is tilted by just 0.13 degrees (less than the width of a pencil), the signal would be blocked entirely. The design accounts for this extreme precision.

3. The Result: Catching the Ghost

After passing through the accelerator, the S-maze, and the hairnet, the positrons arrive at a detector (a Microchannel Plate).

• The Scorecard: The simulation shows that this system catches 65.8% of the real signal (which is excellent for such a difficult task).
• The Cleanup: It rejects the background noise by a factor of 10 million (specifically $10^{-7}$). This means for every 10 million fake signals, only 1 gets through.
• The Timing: The system is so precise that it can measure when the particle arrives with an accuracy of a few nanoseconds. This allows scientists to double-check: "Did this particle arrive at the exact right time to be our signal?"

Why This Matters

This paper isn't just about building a machine; it's about creating a new paradigm for how we handle high-intensity particle beams. By combining an electric accelerator with a magnetic maze and a physical filter, the team has created a system that can see the "unseeable."

If MACE succeeds, it could rewrite the Standard Model of physics, proving that matter can spontaneously turn into anti-matter in a way we never expected. This "ghost catcher" is the key that unlocks that door.

Technical Summary

1. Problem Statement

The Muonium-to-Antimuonium Conversion Experiment (MACE) aims to detect the charged lepton flavor violation (cLFV) process $\mu^+ e^- \to \mu^- e^+$, which would indicate physics beyond the Standard Model (BSM).

• Signal Characteristics: The decay of antimuonium produces a high-energy Michel electron and a low-energy atomic positron (mean energy $\approx 13.5$ eV).
• Background Challenge: The primary background arises from Internal Conversion (IC) muon decays ($\mu^+ \to e^+ e^- e^+ \nu_e \bar{\nu}_\mu$). While the signal positrons are low energy, IC positrons typically have MeV-scale energies. However, a small fraction of IC positrons in the low-energy tail (keV region) can mimic the signal.
• The Challenge: With the high-intensity muon beam from the CiADS facility ($10^8\text{--}10^{10} \, \mu^+/\text{s}$), even a tiny background leakage rate could overwhelm the rare signal. The system requires a transport mechanism that can:
  1. Efficiently collect and transport extremely low-energy positrons (eV range).
  2. Precisely reconstruct the decay vertex.
  3. Suppress IC backgrounds by several orders of magnitude without losing the signal.

2. Methodology

The authors designed a Positron Transport System (PTS) comprising an electrostatic accelerator and a solenoid beamline. The design and optimization were validated using a multi-stage simulation approach:

• Field Simulation: Used COMSOL Multiphysics to model the electromagnetic fields (electrostatic and magnetic) and optimize coil currents to ensure field uniformity.
• Particle Transport Simulation: Used Geant4 (via the MACE offline software framework based on Mustard) to simulate particle trajectories, interactions, and detector responses, importing the field maps from COMSOL.
• Design Strategy:
  • Electrostatic Acceleration: To overcome the low initial energy of signal positrons, an internal electrostatic accelerator was designed to boost them to hundreds of eV.
  • S-Shaped Solenoid: A symmetric S-shaped solenoid configuration was adopted to transport positrons while acting as a momentum filter.
  • Collimation: A specialized collimator was integrated into the transport path to physically block high-transverse-momentum particles.

3. Key Contributions & System Design

The paper details the physical design of three critical subsystems:

A. Solenoid System (Magnetic Transport)

• Configuration: A symmetric S-shaped solenoid consisting of three straight segments ($T1, T2, T3$) and two counter-rotating $90^\circ$ toroids ($B1, B2$).
• Field Strength: Optimized to 0.1 T (longitudinal field). This strength is chosen to be low enough to avoid suppressing the muonium-to-antimuonium conversion rate (which is suppressed at fields $>1$ T) while high enough to guide low-energy positrons.
• Function:
  • Drift Cancellation: The symmetric S-shape cancels the transverse drift ($D = \frac{\pi}{2} \frac{p}{qB}$) that occurs in single-bend solenoids, improving vertex reconstruction precision.
  • Fringe Field Mitigation: Iron yokes and fine-tuned currents in segmented coils minimize fringe field distortions at the interfaces between the Michel electron Magnetic Spectrometer (MMS), the transport section, and the Positron Detection System (PDS).

B. Collimator (Momentum Filtering)

• Location: Integrated into the center of the $T2$ segment.
• Design: Composed of parallel bronze sheets with a pitch ($l$) of 1.15 mm and thickness ($d$) of 0.2 mm.
• Mechanism: The bending magnetic field induces a large Larmor radius for high-momentum background particles. The collimator blocks these particles based on their transverse momentum ($p_T$).
• Cut-off: Optimized to a transverse momentum cut of 14 keV/c, effectively filtering out the low-energy tail of the IC background while maintaining high signal acceptance.

C. Electrostatic Accelerator

• Location: Integrated inside the beam pipe at the center of the detector, covering the target region.
• Design: 11 circular electrodes creating a uniform electric field.
• Parameters:
  • Voltage: 500 V acceleration potential.
  • Length: 380 mm total (270 mm downstream of the target).
  • Purpose: Accelerates the 13.5 eV signal positrons to $\sim$500 eV to ensure efficient transport and minimize Time-of-Flight (TOF) spread.
  • Optimization: The 500 V / 270 mm configuration was chosen as a compromise to minimize TOF spread ($\Delta \text{TOF} \approx 24$ ns) while maintaining compatibility with the Microchannel Plate (MCP) detection efficiency.

4. Simulation Results

The simulations yielded the following performance metrics:

• Geometric Acceptance: The system achieves a signal acceptance of 65.81(4)%. This aligns with the theoretical estimate based on the collimator geometry ($\epsilon \approx 65\%$).
• Spatial Resolution: The system reconstructs the decay vertex with a precision of 88(1) $\mu$m $\times$ 102(1) $\mu$m in the $x$ and $y$ directions. The symmetric S-shape successfully recovers resolution lost during the first bend.
• Timing Performance:
  • Mean transit time: 322.4(1) ns.
  • Timing spread (standard deviation): 6.9(1) ns.
• Background Suppression:
  • Geometric Suppression: The collimator and S-shape reduce the geometric acceptance of IC backgrounds to $2.1 \times 10^{-6}$.
  • Total Suppression: By combining geometric selection with a TOF cut (window $[309.0, 337.9]$ ns), the total background rejection factor reaches $3.0 \times 10^{-7}$.
  • Signal Efficiency: The total signal efficiency (including acceptance and TOF cuts) is 62.4%.
  • Final Background Level: For a one-year run with $10^8$ muons on target, the expected background from IC decays is 0.29 events, effectively making MACE a background-free experiment.

5. Significance

• Paradigm Shift: This work offers a novel paradigm for internal transport systems in high-intensity frontier experiments. Unlike Mu2e or COMET, which transport muons, the MACE PTS transports positrons from a decay vertex, requiring unique solutions for low-energy handling and internal acceleration.
• Feasibility of MACE: The design demonstrates that it is physically possible to achieve the sensitivity required to improve the current limit on muonium-to-antimuonium conversion by more than two orders of magnitude.
• Engineering Roadmap: The paper identifies critical engineering challenges for future phases, specifically the precise alignment of the collimator (tolerance $<0.13^\circ$) and the integration of the electrostatic accelerator within the beam pipe. It sets the stage for technical design and prototype validation.

In conclusion, the proposed PTS design successfully balances high geometric acceptance for low-energy signals with extreme background rejection capabilities, providing a solid foundation for the next generation of cLFV searches.