Muon collider experiments as electron/positron beam sources: case studies of new light-particle searches

This paper demonstrates the feasibility of utilizing decay electrons and positrons from future muon colliders (IMCC and $\mu$TRISTAN) as high-energy, high-repetition-rate beams for new light-particle searches, proposing complementary strategies to probe dark matter and axion-like particles beyond the reach of current experiments.

The Gist

Here is an explanation of the paper, translated into simple language with creative analogies.

The Big Idea: Turning "Trash" into Treasure

Imagine you are building a massive, high-speed race track for tiny particles called muons. These muons are like super-fast, heavy electrons. Scientists want to smash them together to discover new secrets of the universe (like finding new heavy particles).

However, there's a problem: Muons are unstable. They are like over-ripe fruit that naturally rots (decays) very quickly. When a muon rots, it doesn't just disappear; it spits out a shower of other particles, including electrons and positrons (the antimatter version of electrons) and invisible neutrinos.

In the past, scientists treated these spitting particles as garbage. They worried they would damage the delicate equipment (like magnets and detectors) and create a "mess" of radiation. They built thick walls to block them.

This paper proposes a radical new idea: Instead of blocking this "garbage," let's catch it and use it.

The authors suggest that the electrons and positrons spitting out of the decaying muons are actually a free, high-energy beam that we can harvest. It's like realizing that the exhaust fumes from a race car engine aren't just pollution, but actually contain enough energy to power a second, smaller car driving alongside the track.

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How It Works: The "Curved Track" Trick

To understand how they catch these particles, imagine the muon race track is a giant circle. To keep the muons running in a circle, you need giant magnets that bend their path, just like a banked turn on a racetrack keeps a car from flying off.

1. The Heavy vs. The Light: The muons are heavy and strong. The electrons they spit out are much lighter and weaker.
2. The Bend: When the muon beam hits a curved section of the track with a strong magnetic field, the heavy muons stay on their main path. But the lighter electrons, being weaker, get pushed off course much more easily.
3. The "Pre-Septum" Magnet: The authors realized that the magnets already built into the curve of the track act like a natural "deflector." They push the unwanted electrons sideways, away from the main muon beam, without needing any extra, expensive machinery.

The Analogy: Imagine a river (the muon beam) flowing through a curved canal. The main current stays in the middle. But if you throw some light leaves (the electrons) into the river, the curve of the canal naturally pushes the leaves to the side bank, while the heavy rocks (muons) keep going straight. The authors are saying, "Let's build a net on that side bank to catch the leaves!"

They calculated that this "side-catch" works incredibly well, deflecting the electrons by a significant amount (0.1 to 10 milliradians), which is huge for particle physics. This means we can easily separate the "trash" electrons from the "gold" muon beam.

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Two Different Tools for Two Different Jobs

The paper looks at two different future muon collider designs, which produce these "harvested" electrons in very different ways. The authors propose using each design for a specific type of treasure hunt.

1. The µTRISTAN Design: The "Steady Stream"

• The Beam: This design produces a continuous, steady stream of electrons (like a garden hose running constantly).
• The Hunt: Missing Energy (Dark Matter).
• The Analogy: Imagine you are shooting a steady stream of water at a target. You measure exactly how much water hits the target. If you see a "hole" in the spray where water should be but isn't, you know something invisible (like a ghost or a dark matter particle) stole that water and ran away.
• Why it works here: Because the beam is continuous, you can track every single electron. If one disappears into a dark matter particle, you know exactly when and where it happened. This design is perfect for finding Dark Matter that interacts very weakly with normal matter.

2. The IMCC Design: The "Bursty Fireworks"

• The Beam: This design produces bunches of electrons (like a firework exploding in a burst, then a pause, then another burst). It has a huge number of particles in each burst.
• The Hunt: Visible Decay (New Light Particles).
• The Analogy: Imagine you are shooting a massive burst of marbles at a wall. Some marbles might hit a hidden, invisible spring (a new particle) that launches them into the air. If that spring is unstable, it might pop and release two bright sparks (photons) that you can see.
• Why it works here: Because the bursts are so intense, you can look for those bright sparks (photons) appearing in the empty space after the wall. This design is perfect for finding Axion-like particles or light scalars that decay into light.

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Why This Matters

Currently, we are building massive machines (like the Large Hadron Collider) to smash things together to find new physics. But this paper suggests a "side hustle."

By simply harvesting the particles that muon colliders already produce as waste, we can run two experiments at the same time:

1. The main experiment smashing muons to find heavy particles.
2. A side experiment using the "waste" electrons to hunt for light, invisible particles (Dark Matter) or new forces.

The Bottom Line:
This paper is like finding out that your car's exhaust pipe is actually a secret fuel line. It shows that future muon colliders don't just have to be one big machine; they can be two-for-one deals. We can use the "waste" to explore a completely different part of the universe, potentially finding Dark Matter or new forces that other experiments might miss. It turns a radiation problem into a physics solution.

Technical Summary

Here is a detailed technical summary of the paper "Muon collider experiments as electron/positron beam sources: case studies of new light-particle searches" by Yasuhito Sakaki and Daiki Ueda.

1. Problem Statement

Muon colliders are proposed as next-generation high-energy facilities (center-of-mass energies of 1–10 TeV) capable of probing heavy new physics and precision electroweak/Higgs sectors. However, a significant challenge in their design is the radiation background caused by the natural decay of muons ($\mu \to e \nu \bar{\nu}$). These decays produce high-energy electrons/positrons and neutrinos, which can damage detectors, quench magnets, and cause long-term radiation damage.

While current designs focus on shielding against these decay products, the authors identify an underutilized opportunity: extracting these decay electrons and positrons as a usable beam. Unlike conventional accelerator beams, these decay products possess unique properties:

• High Energy: They carry TeV-scale energies (inheriting momentum from TeV-scale muons).
• Continuous Structure: Unlike bunched muon beams, the decay products can form a quasi-continuous beam due to the uniform decay probability along the ring.
• Purity: They are essentially free of hadronic contamination.

The core problem addressed is the feasibility of extracting and transporting these high-energy, continuous electron/positron beams from the curved sections of a muon collider ring to perform fixed-target experiments for new light particle searches, which are difficult to conduct at the main interaction point (IP).

2. Methodology

The authors employ a multi-step methodology combining beam dynamics simulation with phenomenological physics analysis:

• Simulation Tool: They use the PHITS (Particle and Heavy Ion Transport code System) Monte Carlo simulation tool to model particle transport.
• Benchmark Scenarios: The analysis is based on parameters from two distinct future muon collider proposals:
  1. IMCC (International Muon Collider Collaboration): Features high-energy stages (1.5–5 TeV) with large bunch populations but lower repetition rates.
  2. $\mu$TRISTAN: Features a 1 TeV muon beam with a very high repetition rate (50 Hz) and smaller bunch populations.
• Beam Extraction Mechanism:
  • The study analyzes the curved sections of the collider ring where bending magnets (dipoles) are installed.
  • Since decay electrons have lower momentum than their parent muons, they experience larger bending radii in the same magnetic field.
  • The authors propose using the ring's existing bending magnets (or equivalent fields) as a "pre-septum magnet" to naturally deflect electrons away from the muon reference orbit, potentially eliminating the need for an additional kicker magnet.
  • They calculate the spatial ($x, y$), angular ($\theta$), and energy ($r = p/p_\mu$) distributions of the extracted electrons at the downstream edge of an extraction region ($L_{ext}$).
• Physics Sensitivity Studies:
  • $\mu$TRISTAN (Missing Energy/Momentum): Simulates a LDMX-like setup using the continuous beam to search for sub-GeV Dark Matter (DM) via dark photon mediators.
  • IMCC (Visible Decay): Simulates a beam-dump setup using the bunched, high-intensity beam to search for Axion-Like Particles (ALPs) and light scalars decaying into photons.

3. Key Contributions

A. Feasibility of Beam Extraction

• Deflection Capability: The simulations demonstrate that the bending magnets in the collider ring can achieve deflection angles of 0.1–10 mrad for electrons carrying large energy fractions ($r \simeq 0.6–1.0$). This is significantly larger than the $\sim 0.27$ mrad deflection typical of LHC extraction systems, suggesting the extraction scheme is practically feasible.
• Independence from Extraction Length: A crucial theoretical finding is that the total number of extractable electrons ($N_e$) is independent of the extraction length ($L_{ext}$). This is due to the cancellation between the decay probability (proportional to $L_{ext}$) and the phase-space acceptance of the transport line (which decreases as $L_{ext}$ increases).
• Flux Estimates: The study estimates that $10^{14}$to$10^{15}$ electrons can be extracted per year of operation, depending on the collider design.

B. Complementary Search Strategies

The authors propose two distinct strategies tailored to the specific beam properties of the two collider designs:

1. $\mu$TRISTAN for Missing Momentum:
   • Beam Property: High repetition rate ($\sim$MHz) but low particles per bunch ($\sim$1–10). This mimics a continuous beam.
   • Strategy: A fixed-target experiment with a thin target and a recoil tracker (LDMX style).
   • Target: Sub-GeV Dark Matter produced via dark photon bremsstrahlung ($e N \to e X N$).
2. IMCC for Visible Decays:
   • Beam Property: High energy (up to 4 TeV) and high intensity per bunch ($\sim$1000 electrons/bunch).
   • Strategy: A thick target beam-dump experiment with a decay volume and electromagnetic calorimeter.
   • Target: Axion-Like Particles (ALPs) and light scalars produced via Primakoff processes and decaying into photon pairs ($a/\phi \to \gamma\gamma$).

4. Key Results

• Extraction Efficiency: The study confirms that deflections of 0.1–10 mrad are achievable even for high-energy electrons ($r \approx 0.8$), allowing for a compact separation from the muon beam without excessive drift lengths.
• Dark Matter Sensitivity ($\mu$TRISTAN):
  • Assuming $N_e = 4 \times 10^{14}$ and $E_{beam} = 800$ GeV, the setup can probe Dark Matter masses in the MeV–GeV range.
  • The sensitivity extends to thermal relic targets for scalar, Majorana, and pseudo-Dirac DM, covering parameter space beyond current limits (BaBar, NA64, LDMX Phase 1).
  • Backgrounds (neutrino trident production, Møller scattering + CCQE) are calculated to be negligible ($\sim 10^{-16}$ to $10^{-22}$ probability per event).
• ALP/Scalar Sensitivity (IMCC):
  • Assuming $N_e = 10^{15}$ and $E_{beam} = 4$ TeV, the setup probes ALP and scalar couplings to photons.
  • The high energy allows access to shorter lifetimes (higher masses) than current experiments like SHiP or FASER.
  • Backgrounds from charged pions and neutrons are suppressed to negligible levels ($\sim 0.008$ expected background events) using tracking detectors, sweep magnets, and kinematic cuts.

5. Significance

• Dual-Purpose Facility: The paper demonstrates that a muon collider can serve a dual purpose: a high-energy collider for heavy new physics at the main IP, and a high-intensity, high-energy fixed-target facility for light new physics using extracted beams.
• Cost-Effective Physics: By utilizing the decay products (which are otherwise a radiation hazard) as a physics resource, the facility gains significant discovery potential without requiring a separate dedicated accelerator.
• Complementarity: The proposed strategies cover different regions of the new physics parameter space (MeV-GeV DM vs. ALPs/Scalars) and utilize different detection techniques (missing momentum vs. visible decay), providing a comprehensive search program.
• Technical Validation: The work provides a quantitative basis for the "pre-septum" extraction concept, showing that existing collider magnet designs can naturally facilitate beam extraction, potentially simplifying the engineering requirements for future muon collider facilities.

In conclusion, the authors establish that extracting electron/positron beams from muon colliders is not only theoretically sound but also offers a powerful, complementary avenue for discovering light dark sector particles, significantly broadening the physics reach of future muon collider projects.