Conceptual Design of the Muonium-to-Antimuonium Conversion Experiment (MACE)

This paper presents the theoretical framework and detailed experimental design of the Muonium-to-Antimuonium Conversion Experiment (MACE), which aims to discover or constrain charged lepton flavor violation by searching for muonium-to-antimuonium conversion with a sensitivity of approximately $10^{-13}$.

The Gist

The Big Idea: Catching a Ghostly Shape-Shifter

Imagine you have a tiny, invisible atom called Muonium. It's like a miniature hydrogen atom, but instead of a proton, it has a "muon" (a heavy cousin of an electron) orbiting a regular electron.

Now, imagine a magical rule in the universe that says: "Sometimes, this Muonium atom can spontaneously turn into its evil twin, Antimuonium." In this evil twin, the muon becomes an anti-muon, and the electron becomes a positron (anti-electron).

The Problem: This shape-shifting trick is incredibly rare. The last time scientists looked for it (in 1999), they didn't see it happen. They set a limit saying, "It happens less than once in every 100 billion tries."

The Goal: The MACE experiment (Muonium-to-Antimuonium Conversion Experiment) is a new, super-powered detective team designed to find this trick. They want to improve that limit by 100 times, looking for a signal in 100 trillion tries. If they find it, it proves that the "Standard Model" (our current rulebook of physics) is incomplete and that new, mysterious forces exist.

---

How the Experiment Works: The "Factory and Filter" Setup

To catch this rare event, the scientists have designed a massive, multi-stage machine. Think of it as a high-tech factory assembly line with three main stations.

1. The Factory: Making the Muonium

First, they need a steady stream of Muonium atoms.

• The Source: They use a giant particle accelerator (like a super-fast race car track) to shoot protons at a target. This creates a flood of muons.
• The Target: These muons are shot into a special silica aerogel target. Think of this aerogel as a super-light, porous sponge (like a cloud made of glass).
• The Magic: When a muon hits the sponge, it grabs an electron and becomes a Muonium atom. Because the sponge is full of holes, these new atoms can "diffuse" (drift) out of the sponge and into a vacuum chamber, where they are free to float around.

2. The Waiting Room: The Magnetic Spectrometer

Once the Muonium is floating in the vacuum, the team waits.

• The Trap: They surround the vacuum with a giant magnet and a high-tech camera system (a Drift Chamber).
• The Job: If a Muonium atom decays normally, it spits out a fast electron. The camera tracks this electron.
• The Twist: If the Muonium does the shape-shifting trick and turns into Antimuonium, it will eventually decay differently. It will spit out a fast electron AND a very slow, sleepy positron.

3. The Filter: Catching the "Sleepy Positron"

This is the hardest part. The fast electron is easy to see, but the positron from the shape-shifting event is incredibly slow (like a snail compared to a race car).

• The Transport System: The team uses a special Solenoid (a magnetic tube) that acts like a gentle, curved slide. It guides the slow positron away from the chaos of the factory.
• The Filter: This slide is designed so that only the "sleepy" positrons make it through. Any fast, energetic particles (which are just background noise) crash into the walls and get filtered out.
• The Finish Line: The positron arrives at a detector made of a Microchannel Plate (a tiny honeycomb of electron multipliers). When the positron hits it, it creates a flash of light (gamma rays) that is caught by a massive Calorimeter (a giant energy meter).

The Signal: A "Win" happens only if the camera sees the fast electron at the exact same time the honeycomb detector sees the slow positron. If they don't happen together, it's just noise.

---

Why is this so hard? (The Background Noise)

The biggest challenge isn't building the machine; it's ignoring the noise.

• The "Fake" Positrons: Muons naturally decay and sometimes spit out positrons. But these are usually fast and energetic.
• The Analogy: Imagine you are trying to hear a whisper (the signal) in a stadium full of people shouting (the background). The MACE team uses timing and speed filters to ignore the shouts. They only listen for the whisper that arrives at the exact right moment and has the exact right speed.

The "Phase-I" Side Quest

Before building the full machine, the team proposes a smaller version called Phase-I.

• The Goal: This smaller version will look for other rare "shape-shifting" tricks, like a muon turning into an electron and two photons (light particles).
• The Benefit: It acts as a "test drive" to make sure the detectors work perfectly before the full, expensive machine is built.

What Does This Mean?

The paper doesn't claim to have found new physics yet. Instead, it presents the blueprint for a machine that is ready to hunt for it.

• If they find it: It proves that nature has rules we don't know yet. It could explain why the universe has more matter than antimatter or what dark matter is.
• If they don't find it: They will have proven that the "shape-shifting" trick is even rarer than we thought, forcing physicists to rewrite their theories to explain why it's so hard to find.

In short, MACE is a high-precision trap designed to catch a ghost that might not even exist, but if it does, it will change our understanding of the universe forever.

Technical Summary

Technical Summary: Conceptual Design of the Muonium-to-Antimuonium Conversion Experiment (MACE)

1. Problem Statement and Physics Motivation

The Muonium-to-Antimuonium Conversion Experiment (MACE) addresses the search for charged lepton flavor violation (cLFV) in the $\Delta L_\ell = 2$ sector, specifically the spontaneous conversion of muonium ($M = \mu^+ e^-$) to antimuonium ($\bar{M} = \mu^- e^+$). Unlike $\Delta L_\ell = 1$ processes (e.g., $\mu^+ \to e^+ \gamma$), which are constrained by the Standard Model Effective Field Theory (SMEFT) to be distinct from $\Delta L_\ell = 2$ phenomena, muonium-to-antimuonium conversion probes new physics scales that may be inaccessible to other cLFV searches.

Current experimental limits, established by the MACS experiment at PSI in 1999, constrain the conversion probability to $P \lesssim 8.3 \times 10^{-11}$ at 90% confidence level. This limit has remained unchallenged for two decades. Theoretical models, including type-II hybrid seesaw models, axion-like particles, and $Z'$ bosons, predict this conversion at tree or one-loop levels. MACE aims to improve the sensitivity to the $O(10^{-13})$ level, potentially probing new physics scales of 10–100 TeV, comparable to or exceeding the reach of future high-energy muon colliders for specific operators.

2. Methodology and Experimental Design

The MACE conceptual design relies on a high-intensity surface muon beam, a specialized muonium production target, and a multi-component detector system optimized for the unique signature of antimuonium decay: a fast electron ($\sim$26 MeV) and a slow positron ($\sim$13.5 eV).

A. Beamline and Muon Source

MACE proposes utilizing the China initiative Accelerator Driven System (CiADS) linac, which will provide a high-intensity proton beam (up to 2.5 MW).

• Target: A free-surface liquid lithium target is designed to maximize surface muon production while minimizing heat density and positron background.
• Beam Transport: A solenoid-based beamline with Wien filters is employed to capture high-emittance muons and remove positrons. The design targets a surface muon flux of up to $1.5 \times 10^{10} \, \mu^+/\text{s}$.

B. Muonium Production Target

To maximize the yield of muonium atoms escaping into a vacuum (where conversion can occur without decoherence), the design utilizes perforated silica aerogel targets.

• Single-Layer Design: Optimization via Monte Carlo simulation suggests a perforated single-layer target with specific hole spacing and diameter can achieve a vacuum yield of $\sim$1%.
• Multi-Layer Design: A multi-layer silica aerogel concept is proposed to increase beam utilization and tolerate wider momentum spreads, potentially achieving a vacuum muonium yield of $\sim$3.8%.

C. Detector System

The detector system is divided into three main subsystems to identify the signal signature (energetic electron + slow positron) and reject backgrounds.

1. Michel Electron Magnetic Spectrometer (MMS):

   • Function: Detects the high-energy electron from antimuonium decay.
   • Components: A cylindrical drift chamber (CDC) with 21 layers of near-squared cells and a tiled timing counter (TTC) for triggering.
   • Magnet: Operates at a low magnetic field of $B = 0.1$ T to balance momentum resolution with the preservation of conversion probability (stronger fields suppress conversion).
   • Performance: Designed for 88.8% geometric acceptance and high spatial resolution to reconstruct the decay vertex.

2. Positron Transport System (PTS):

   • Function: Transports the low-energy ($\sim$13.5 eV) positron from the target to the detector while filtering out high-energy background positrons (e.g., from Michel decays).
   • Components: An S-shaped transport solenoid and an electrostatic accelerator (up to 780 V).
   • Mechanism: The S-shape acts as a momentum selector; high-energy particles collide with the solenoid walls, while low-energy positrons follow the field lines. The electrostatic accelerator boosts the positron energy to activate the downstream detector.
   • Performance: Achieves a transmission efficiency of $\sim$65.8% for signal positrons while suppressing high-energy backgrounds by orders of magnitude.

3. Positron Detection System (PDS):

   • Function: Detects the positron and its annihilation products.
   • Components: A Microchannel Plate (MCP) for position and timing, followed by a Goldberg-polyhedron Electromagnetic Calorimeter (ECAL).
   • ECAL Design: Composed of 622 modules (BGO, CsI:Tl, or LYSO crystals) arranged in a Goldberg polyhedron geometry to achieve $\sim$95% geometric acceptance.
   • Signal: The positron hits the MCP, producing secondary electrons and annihilating to produce two 511 keV gamma rays detected by the ECAL.

D. Background Suppression

The design addresses two primary background categories:

• Physical Backgrounds: Primarily the muon internal conversion decay $\mu^+ \to e^+ e^- e^+ \nu_e \bar{\nu}_e$. This is suppressed by kinematic cuts on the positron energy (selecting the $\sim$13.5 eV signal region) and the transverse momentum of the electron.
• Accidental Backgrounds: Coincidences between unrelated particles. Suppressed by precise time-of-flight (TOF) measurements, the S-shaped transport solenoid, and tight timing windows.

3. Key Results and Performance Estimates

• Sensitivity: Based on a baseline run of 1 year with a $10^8 \, \mu^+/\text{s}$ flux and a total signal efficiency of 6.6%, the single-event sensitivity (SES) is estimated at $1.3 \times 10^{-13}$.
• Upper Limit: Assuming a conservative background expectation of 1 event, MACE is projected to set an upper limit on the conversion probability of $P(M \to \bar{M}) \lesssim 3.8 \times 10^{-13}$ at 90% confidence level.
• New Physics Scale: This sensitivity corresponds to probing new physics scales of 10–100 TeV for $\Delta L_\ell = 2$ operators.
• Background Rates: Simulations estimate the total background rate to be less than 1 event per $10^8 \, \mu_{OT}/s \cdot \text{year}$, effectively enabling a background-free search.

4. MACE Phase-I Proposal

The paper proposes a Phase-I experiment to utilize a subset of the detector system (ECAL and an inner tracker) to search for other rare processes before the full construction of MACE.

• Targets:
  • $\mu^+ \to e^+ \gamma \gamma$ decay (currently limited to $BR < 7.2 \times 10^{-11}$).
  • Muonium decay $M \to \gamma \gamma$ (previously limited to $O(10^{-5})$).
• Detector Modifications: The Phase-I tracker includes a scintillating fiber (SciFi) tracker and a multigap resistive plate chamber (MRPC) hodoscope to improve timing and tracking for these specific signatures.

5. Significance and Claims

The paper claims that MACE represents a significant advancement in the search for cLFV by targeting the $\Delta L_\ell = 2$ sector, which is theoretically distinct from and potentially decoupled from $\Delta L_\ell = 1$ processes.

• Technological Innovation: The design introduces novel solutions, such as the liquid lithium target for high-intensity beams, the perforated multi-layer aerogel target for enhanced vacuum yield, and the S-shaped solenoid transport system for low-energy positron selection.
• Physics Impact: By improving the limit by two orders of magnitude, MACE will either discover a rare new physics process or significantly constrain the parameter space of models involving heavy neutral leptons, Higgs triplets, and flavor gauge bosons.
• Complementarity: The experiment is positioned to complement high-energy collider searches (like $\mu^+ e^- \to \mu^- e^+$ scattering at future muon colliders) and other low-energy cLFV experiments (like Mu3e and MEG II), providing a comprehensive probe of lepton flavor violation.

The authors emphasize that the observation of such a process would be a clear indicator of physics beyond the Standard Model, potentially shedding light on the origin of neutrino masses, matter-antimatter asymmetry, and dark matter.