Letter Of Intent for a future $μ^+ \to \mathrm{e}^+ γ$ experiment at the High Intensity Muon Beam facility at PSI

This Letter of Intent outlines a proposal to develop a future $\mu^+ \to \mathrm{e}^+ \gamma$ experiment at the High-Intensity Muon Beam facility at PSI, aiming to improve current sensitivity by over an order of magnitude within the next decade to maintain leadership in searching for charged lepton flavor violation.

The Gist

The Great Cosmic Hunt: Catching a Ghost in the Machine

Imagine you are trying to find a specific, incredibly rare event in a crowded stadium. In the world of particle physics, this event is a muon (a heavy, unstable cousin of the electron) spontaneously turning into a positron (anti-electron) and a flash of light (a photon) all at once.

According to our current rulebook of the universe, the Standard Model, this should never happen. It's like a magician trying to turn a rabbit into a bicycle without any tools; the laws of physics say it's impossible. But if we do see it happen, it means there is a new, hidden rulebook (New Physics) that we haven't discovered yet.

This document is a Letter of Intent—essentially a bold proposal from a team of scientists at the Paul Scherrer Institute (PSI) in Switzerland. They want to build a super-powered microscope to catch this "impossible" event.

Here is the plan, broken down into simple concepts:

1. The Problem: The Needle in a Haystack

Currently, the best experiment (called MEG II) is looking for this needle. They are very good, but the "haystack" (background noise) is huge.

• The Noise: Most of the time, muons decay in boring, normal ways. Sometimes, they decay in a way that looks like the rare event we want, just by pure coincidence.
• The Limit: To find the needle, we need to look at more muons. But if we just turn up the volume (beam intensity), the noise gets louder too, drowning out the signal.

2. The Solution: A New Kind of Camera

The team proposes a new experiment (let's call it MEG3) that changes how they "see" the light.

• Old Way (The Flashbulb): Previous experiments used a giant tank of liquid xenon to catch the photon. It's like trying to catch a firefly in a dark room with a camera that has a slow shutter speed. You know the light hit, but you aren't sure exactly when or where with perfect precision.
• New Way (The Trap): The new plan is to use a "conversion layer." Imagine the photon hits a thin sheet of special crystal and instantly splits into an electron and a positron (like a billiard ball hitting a cushion and bouncing off in two directions).
  • By tracking these two new particles with extreme precision, they can reconstruct the original photon's path, energy, and timing with much better accuracy.
  • The Analogy: Instead of guessing where the firefly was based on a blurry photo, they are now catching the firefly in a net, measuring its wingspan, and timing its flight down to the nanosecond.

3. The Two-Step Strategy (The "Staged" Approach)

Building this machine is like building a Formula 1 car. You don't just build the final car on day one; you build a prototype, test it, and then upgrade.

• Phase 0 (The Proof): Before building the big machine, they will run small tests to prove that their new "crystal trap" actually works. They will shoot particles at crystals to see if they can measure the split perfectly.
• Phase I (The Prototype - Early 2030s): They will build a smaller version of the experiment using current technology. It won't be the ultimate machine, but it will be 10 times better than what exists today. This is their "safety net" to ensure the big idea works before spending billions on the final version.
• Phase II (The Ultimate Machine - Late 2030s): This is the grand finale. They will use a massive new beam of muons (100 times stronger than before) and the full, upgraded detector. This is where they hope to either discover the new physics or set the strictest limits on the universe ever.

4. The Challenges: Fighting the "Traffic Jam"

The main enemy is noise.

• If you have too many muons hitting the target at once, the detectors get confused. It's like trying to hear a whisper in a rock concert.
• The Fix: They need incredibly fast "cameras" (detectors) that can take pictures in picoseconds (trillionths of a second). They are developing new silicon chips and gas detectors that are so thin and fast they can separate the signal from the noise, even when the "concert" is at full volume.

5. Why Does This Matter?

If they find this decay, it's a smoking gun. It would prove that the Standard Model is incomplete and open the door to understanding:

• Why there is more matter than antimatter in the universe.
• What dark matter is.
• The true nature of gravity and the forces that hold the universe together.

Summary

Think of this proposal as a team of detectives saying: "We have a hunch that a crime is happening, but our current magnifying glass isn't strong enough to see the clues. We want to build a super-magnifying glass, test it on a smaller case first, and then use it to solve the biggest mystery in physics."

They are asking for the green light and funding to start building this machine, aiming to revolutionize our understanding of the universe by the late 2030s.

Technical Summary

1. Problem Statement

Physics Motivation:
Charged Lepton Flavor Violation (cLFV) is strictly forbidden in the Standard Model (SM) (branching ratio $\sim 10^{-54}$) but is predicted at measurable rates by many New Physics (NP) models. The decay $\mu^+ \to e^+ \gamma$ is a "golden channel" because it is a clean probe; any observation would be unequivocal evidence of physics beyond the SM.

Current Limitations:

• MEG II Status: The current leading experiment, MEG II at PSI, has set a limit of $B(\mu^+ \to e^+ \gamma) < 1.5 \times 10^{-13}$ and aims for $\sim 6 \times 10^{-14}$.
• Competition: Other experiments (Mu3e, Mu2e, COMET) are targeting $\mu^+ \to e^+ e^+ e^-$ and $\mu^- N \to e^- N$ conversion with sensitivities comparable to or better than MEG II.
• Theoretical Discrimination: Different NP models contribute differently to these channels (e.g., dipole vs. four-fermion interactions). To distinguish between competing models if a signal is found, the sensitivity of the $\mu^+ \to e^+ \gamma$ channel must be comparable to the other channels.
• The Bottleneck: Simply increasing the muon beam rate ($R_\mu$) without improving detector resolution does not improve sensitivity significantly at high rates because the accidental background scales with $R_\mu^2$. A new experimental concept with superior resolution and background rejection is required to exploit the upcoming HIMB facility (up to $10^{10} \, \mu^+/\text{s}$).

2. Methodology and Experimental Concept

The proposal outlines a staged approach (Phase-0, Phase-I, Phase-II) to develop a next-generation detector capable of reaching a branching ratio sensitivity of $\sim 10^{-15}$.

A. Core Innovation: Photon Conversion Spectrometer

Unlike MEG II, which uses a Liquid Xenon (LXe) calorimeter, the baseline concept for the future experiment is a photon conversion pair spectrometer.

• Mechanism: Photons are converted into $e^+e^-$ pairs in a thin, active converter layer. The resulting pair is tracked in a magnetic field to reconstruct the photon's energy, direction, and timing.
• Advantages:
  • Energy Resolution: Potentially superior to calorimetry ($\sigma_E/E \approx 0.3\%$ vs. $\sim 1\%$).
  • Direction Resolution: The reconstructed tracks allow for a standalone measurement of the photon direction ($\sim 150$ mrad), enabling vertex compatibility checks with the positron to suppress accidental backgrounds.
  • Active Converter: The converter itself (likely LYSO crystals) measures ionization energy loss to correct for energy fluctuations, acting as both a converter and a timing detector (target resolution $\sim 20-30$ ps).

B. Positron Reconstruction

• Phase-I ($R_\mu \sim 2 \times 10^8 \, \mu^+/\text{s}$): Utilizes a conventional gaseous drift chamber (similar to MEG II) or an upgraded version, potentially reusing the MEG II COBRA magnet.
• Phase-II ($R_\mu \ge 10^9 \, \mu^+/\text{s}$): Requires ultra-thin silicon pixel sensors (High Voltage Monolithic Active Pixel Sensors - HVMAPS) to handle high rates and minimize material budget (to reduce Multiple Coulomb Scattering). This leverages technology developed for the Mu3e experiment.

C. Magnetic Field Configurations

Two geometries are proposed:

1. Single Solenoid: Both positron and photon spectrometers share a single solenoid field. This minimizes material in front of the photon detector but requires a complex field gradient to sweep away low-momentum positrons.
2. Solenoid-Toroid: The positron spectrometer is in a central solenoid, while the photon conversion detectors are in an external toroidal field. This allows independent tuning of fields but introduces more material (coils) in front of the photon detector.

D. Staged Roadmap

• Phase-0 (Proof-of-Concept): Beam tests to validate the conversion technique, active converter timing, and TPC tracking performance using tagged photon beams.
• Phase-I (Early 2030s): Operates on a conventional beam line ($R_\mu \approx 2 \times 10^8 \, \mu^+/\text{s}$). Uses a reduced number of converter layers and existing/modified magnets (e.g., COBRA). Goal: Reach $\sim 1.5 \times 10^{-14}$ sensitivity and validate the system.
• Phase-II (Late 2030s): Full-scale experiment at the HIMB facility ($R_\mu \ge 10^9 \, \mu^+/\text{s}$). Utilizes the full multi-layer converter, advanced silicon trackers, and dedicated magnets. Goal: Reach $\sim 2\text{--}3 \times 10^{-15}$ sensitivity.

3. Key Contributions

• New Detector Paradigm: Proposes shifting from calorimetric photon detection to a conversion-based spectrometer to overcome the resolution limits of LXe detectors at high beam rates.
• Active Converter Technology: Introduces the concept of using LYSO crystals as active converters to measure energy loss and provide precise timing, correcting for the energy resolution limitations of passive converters.
• Scalable Architecture: A realistic, staged roadmap that allows for risk mitigation. Phase-I serves as a technical and physics bridge, ensuring the feasibility of the high-rate Phase-II before full commitment.
• Integration with Mu3e: The proposal explicitly coordinates with the Mu3e experiment, utilizing its silicon pixel technology and scheduling to avoid resource conflicts while maximizing the physics return of the HIMB facility.

4. Results and Sensitivity Estimates

Based on simulations and projected detector performance (Table 1 in the LOI):

• Detector Performance Targets:
  • Photon Energy Resolution: 200 keV ($\sim 0.4\%$).
  • Photon Timing: 30 ps.
  • Positron Momentum Resolution: 100 keV/c.
  • Geometrical Acceptance: Up to 85% (36% if using MEG II COBRA magnet constraints).
• Projected Sensitivity (90% C.L.):
  • Phase-I: With a beam rate of $2 \times 10^8 \, \mu^+/\text{s}$ and a single conversion layer, sensitivity reaches $1.5 \times 10^{-14}$. This is already significantly better than the final MEG II sensitivity.
  • Phase-II: With a beam rate of $> 10^9 \, \mu^+/\text{s}$ and four conversion layers, sensitivity improves to $(2\text{--}3) \times 10^{-15}$.
• Physics Impact:
  • This sensitivity level ensures that the $\mu^+ \to e^+ \gamma$ channel remains competitive with $\mu \to e$ conversion and $\mu \to 3e$ searches across a wide range of New Physics models (dipole and four-fermion interactions).
  • It allows for the discrimination of NP models should a signal be discovered in any of the cLFV channels.

5. Significance

This Letter of Intent represents a strategic plan to maintain PSI's leadership in the search for Charged Lepton Flavor Violation. By proposing a radical upgrade in detector technology (conversion spectrometers) and a staged implementation strategy, the group aims to push the sensitivity of the $\mu^+ \to e^+ \gamma$ search by more than one order of magnitude beyond current limits.

The success of this project is critical for the global cLFV program. Without a competitive $\mu^+ \to e^+ \gamma$ search, the community risks losing the ability to distinguish between different theoretical explanations of any potential New Physics signal found in other channels. The proposed experiment leverages the unique capabilities of the upcoming HIMB facility, ensuring that the next decade of muon physics yields definitive answers regarding the nature of physics beyond the Standard Model.