Performance of an LYSO-Based Active Converter for a Conversion Spectrometer aiming for 52.8 MeV photon detection in Future $\mu^+ \to e^+ \gamma$ Search Experiments

This paper reports the successful development and test-beam validation of a prototype LYSO-based active converter for future $\mu^+ \to e^+ \gamma$ experiments, demonstrating a time resolution of 25 ps and a light yield of $10^4$ photoelectrons that significantly exceed the design requirements for detecting 52.8 MeV photons.

The Gist

Imagine you are trying to catch a ghost. In the world of particle physics, this "ghost" is a rare event where a muon (a heavy cousin of the electron) spontaneously turns into a positron (anti-electron) and a photon (light particle). This shouldn't happen according to our current rulebook of physics (the Standard Model), so if we catch it, it proves there are new, hidden rules of the universe.

The problem? This event is incredibly rare, and it's buried under a mountain of "noise" from other common particle interactions. To find this needle in the haystack, we need a detector that is not just sensitive, but incredibly precise in two ways: time (knowing exactly when the event happened) and energy (knowing exactly how much energy the particles carried).

This paper describes the development and testing of a new "super-sniffer" designed specifically for this job. Here is how it works, broken down into simple concepts:

1. The Problem with the Old "Passive" Trap

In the past, scientists used a "passive" converter to catch these photons. Think of this like throwing a ball at a thick, dark curtain. When the ball (the photon) hits the curtain, it breaks into two smaller balls (an electron and a positron). The scientists then try to guess the original ball's speed by measuring the two smaller balls.

The flaw: As the smaller balls travel through the curtain, they rub against the fabric, losing some energy (like friction). Because the curtain is "passive" (it doesn't talk back), the scientists can't measure exactly how much energy was lost. This makes their guess about the original speed a bit fuzzy.

2. The New "Active" Converter: A Talking Curtain

The team in this paper built an active converter. Imagine the curtain is now made of a special, glowing crystal (called LYSO) that lights up whenever something bumps into it.

• How it works: When the photon hits the crystal, it splits into an electron and a positron. As these two particles zip through the crystal, they make it glow. The crystal measures exactly how much light is produced (which tells us how much energy was lost) and the exact moment the light was emitted.
• The Benefit: By adding the "lost energy" (measured by the glow) to the speed of the particles, the scientists can reconstruct the original photon's energy with much higher precision. It's like the curtain whispering, "Hey, I lost 5% of your energy, so you were actually moving faster than you thought!"

3. The Design: Slicing the Cake

To make this work perfectly, the team had to figure out the right size for these glowing crystals.

• Too thick: The particles get stuck or lose too much energy, and the "glow" gets messy.
• Too thin: The photon might pass right through without breaking apart.
• The Solution: They simulated millions of scenarios and found the "Goldilocks" size: a crystal slice that is 3 millimeters thick, 5 millimeters wide, and 50 millimeters long. They also cut these crystals into many small segments (like slicing a loaf of bread) to prevent confusion if multiple particles hit at once.

4. The Test Drive: The 3-GeV Electron Beam

To see if their "talking curtain" actually worked, they took their prototype crystals to a particle accelerator at KEK in Japan. They shot a beam of electrons (acting as stand-ins for the particles they expect to see) at the crystals.

They tested the crystals under different conditions:

• Different angles: Shooting the beam straight on vs. at a slant.
• Different thicknesses: Testing a 3mm slice and a thinner 1.5mm slice.
• Different sensors: Trying different types of light detectors (SiPMs) to see which one caught the glow best.

5. The Results: Smashing the Goals

The team had set a very high bar for their detector:

• Time Goal: They needed to measure time within 40 picoseconds (a picosecond is one-trillionth of a second).
• Energy Goal: They needed to detect enough light to measure energy precisely.

What they found:

• Time: Their prototype was super fast, measuring time with a resolution of 25 picoseconds. This is significantly better than their goal. It's like hitting a target with a bullseye when you only needed to hit the outer ring.
• Light: The crystals were incredibly bright, producing about 10,000 units of light (photoelectrons) for a standard particle hit. Their goal was only 700. They had more than enough "signal" to make precise measurements.

6. Why This Matters

The paper concludes that this new design is a "home run." Because the crystals are so fast and so bright, the new detector can distinguish the rare "ghost" event from the background noise much better than previous experiments.

If they build the full-scale machine using these crystals, they hope to reach a sensitivity level of 1 in 10^15. This means they could finally catch the decay that proves physics beyond our current understanding.

In short: They built a super-fast, super-bright crystal detector that acts like a high-speed camera and a precise scale simultaneously. They tested it, and it works better than they ever hoped, paving the way for a new generation of experiments to hunt for the secrets of the universe.

Technical Summary

Technical Summary: Performance of an LYSO-Based Active Converter for a Conversion Spectrometer

Problem and Motivation
Future searches for the charged lepton flavor-violating decay $\mu^+ \to e^+ \gamma$ aim for a branching-ratio sensitivity of $O(10^{-15})$, necessitated by the High-Intensity Muon Beam (HIMB) project at the Paul Scherrer Institute (PSI). Achieving this sensitivity requires suppressing accidental background events, which scale with the square of the muon beam rate and the resolutions of photon energy ($\Delta E_\gamma$), timing ($\Delta t_\gamma$), and angular measurements. Current and near-future experiments like MEG II target sensitivities of $10^{-14}$, but the next generation requires unprecedented detector performance: specifically, an energy resolution of $\Delta E_\gamma < 200$ keV and a timing resolution of $\Delta t_\gamma < 30$ ps for 52.8 MeV photons.

Conventional conversion spectrometers, which reconstruct photon energy solely from the momenta of $e^+e^-$ pairs produced in passive converters, are fundamentally limited by unmeasured energy losses (ionization and bremsstrahlung) within the converter material. To overcome this, the authors propose an active converter design. In this concept, a crystal scintillator serves as the converter, allowing for the direct measurement of energy deposition ($E_{dep}$) by the $e^+e^-$ pair in addition to the momentum measurement. This integration aims to significantly enhance energy resolution beyond the capabilities of passive systems.

Methodology
The study employs a two-pronged approach: simulation-based design optimization followed by experimental validation using electron beam tests.

1. Simulation and Design Optimization (Geant4):

   • Material and Thickness: The team simulated various materials and thicknesses to maximize signal efficiency ($\epsilon_{sig}$). They identified LYSO (Lutetium-Yttrium Oxyorthosilicate) as the optimal material due to its high density and scintillation properties. A thickness of 3 mm was selected as the baseline, balancing conversion probability against energy leakage from bremsstrahlung.
   • Segmentation: To mitigate topological inefficiencies (where $e^+e^-$ tracks re-enter the same crystal cell after a half-turn or more, causing energy overestimation) and pile-up effects, the converter was segmented. Simulations determined a baseline segmentation of 5 mm (azimuthal) $\times$ 50 mm (longitudinal) $\times$ 3 mm (radial) to maintain a topological efficiency ($\epsilon_{topo}$) of 95.6% while suppressing high-energy tails in the background spectrum.
   • Light Yield Requirements: To achieve the target energy resolution of 200 keV, simulations indicated a requirement of at least 2,500 photoelectrons (p.e.) for a 10 MeV energy deposit.

2. Experimental Validation:

   • Setup: Prototypes consisting of Ce-doped LYSO crystals (specifically the "Ce:FTRL" fast-response variant) were tested at the KEK PF-AR test beamline using a 3 GeV electron beam.
   • Configuration: The prototypes were instrumented with Silicon Photomultipliers (SiPMs) in various readout schemes (single-sided, double-sided, series-connected, and individual readout) to evaluate timing and light yield performance.
   • Analysis: Time resolution was evaluated by comparing the prototype timing against reference counters, correcting for time-walk effects. Light yield was determined by calibrating the SiPM gain and correcting for pixel saturation non-linearities.

Key Results
The experimental results demonstrated performance significantly exceeding the design requirements:

• Time Resolution: The prototypes achieved a single-MIP time resolution of 25 ps (for a 3 mm thick crystal). This is well within the design goal of 40 ps for a single conversion particle, which translates to a total photon time resolution of better than 30 ps when combining electron and positron measurements. The resolution remained stable across various beam hit positions, incident angles, and SiPM types.
• Light Yield: The measured light yield was on the order of $10^4$ photoelectrons for typical Minimum Ionizing Particle (MIP) energy deposits. This exceeds the minimum requirement of 700 p.e. (scaled from the 2,500 p.e. requirement for 10 MeV) by more than an order of magnitude.
• Position Dependence: While a position-dependent variation in time offset (up to 50 ps) and light yield (approx. 15%) was observed within single crystals, the authors note these can be corrected using reconstructed track positions.
• Readout Schemes: Comparisons between different SiPM models and readout topologies (series vs. individual) showed consistent timing performance, though series-connected readout was favored to reduce channel count without sacrificing resolution.

Significance and Claims
The paper concludes that the LYSO-based active converter is a highly promising technology for next-generation $\mu^+ \to e^+ \gamma$ experiments. The primary significance lies in the demonstration that the stringent performance requirements for the HIMB-era experiments are achievable:

1. Feasibility of High Resolution: The study confirms that an active converter can provide the necessary timing (25 ps) and light yield ($10^4$ p.e.) to support a photon energy resolution of 200 keV and a timing resolution of 30 ps.
2. Statistical Dominance: Due to the high light yield, the contribution of photon statistics to the energy resolution is estimated to be negligible (below 50 keV). This implies that the ultimate energy resolution will be limited by the tracking precision of the pair-tracker and calibration quality, rather than the converter's photon statistics.
3. Scalability: The authors argue that while a full-scale detector would require $\sim 10^5$ readout channels, the performance margins (e.g., 25 ps vs. 40 ps requirement) allow for potential design simplifications, such as single-sided readout or electrical signal combining, to manage channel counts while maintaining performance.

The work establishes the technical viability of the LYSO active converter concept, providing a robust foundation for the development of the conversion spectrometer required to probe physics beyond the Standard Model at the $O(10^{-15})$ sensitivity level.