Boosting long lived particles searches at $μ$TRISTAN

This paper demonstrates that the proposed $\mu$TRISTAN experiment, utilizing its asymmetric energy collisions to produce boosted Higgs bosons, can surpass High Luminosity LHC sensitivity in constraining long-lived particle decays with large proper decay lengths via a far detector, though it offers no improvement over existing LHC far detector proposals.

The Gist

The Big Picture: Hunting Ghosts in a Tunnel

Imagine the universe is full of "ghosts"—particles that are very light, very shy, and don't interact much with normal matter. Physicists call these Long-Lived Particles (LLPs). They are like shy ghosts that are born in a collision, travel a long distance without hitting anything, and then suddenly "poof" into visible particles (like light or electrons) far away from where they started.

The Standard Model of physics (our current rulebook) has holes in it, and these ghosts might be the missing pieces. The big question is: Where do we look for them?

This paper proposes a new hunting ground: a proposed experiment called µTRISTAN.

The Hunting Ground: A High-Speed Train vs. A Stroller

Usually, particle colliders smash two beams of particles together head-on, like two trains hitting each other at full speed. The debris flies out in all directions (360 degrees).

µTRISTAN is different. It's an "asymmetric" collider. Imagine one beam is a super-fast bullet train (muons at 1 or 3 TeV) and the other is a slow-moving stroller (electrons at 30 or 50 GeV).

When the bullet train hits the stroller, the crash doesn't happen in the middle. Because the train is so much faster and heavier, the debris from the crash gets kicked forward in the direction the train was going. It's like if you threw a tennis ball at a speeding semi-truck; the ball doesn't bounce back at you; it gets launched forward at high speed.

In physics terms, the particles produced are "boosted." Instead of flying everywhere, they are concentrated in a tight, narrow cone pointing straight down the track.

The Strategy: The Far-Field Detector

Because these "ghosts" (LLPs) are boosted, they travel in a very straight line, like a laser beam, far down the tunnel.

The authors suggest building a Far Detector (a giant sensor box) about 100 to 150 meters down the track, right in the path of this "laser beam" of particles.

• The Advantage: Since the ghosts are all running in the same direction, this detector can catch a huge percentage of them, even though it's small compared to the whole universe. It's like setting up a net at the end of a hallway where everyone is running; you catch almost everyone, even if the net is small.
• The Goal: They want to see if the Higgs boson (a famous particle) is secretly decaying into these ghosts. If the Higgs turns into two ghosts, and those ghosts travel 100 meters before turning back into normal matter inside the detector, we've found new physics!

The Results: Good News and Bad News

The authors ran simulations to see how well this plan works compared to other ideas.

1. The Good News (Beating the Current Giants):
The current giant collider, the LHC (Large Hadron Collider), has main detectors (ATLAS and CMS) that are right next to the crash site. They are great at catching ghosts that decay quickly (within a few meters).

• µTRISTAN's Edge: Because the ghosts at µTRISTAN are boosted so hard, they travel much further before decaying. The paper shows that for ghosts that live a very long time (traveling 100+ meters), µTRISTAN could actually find them better than the LHC can, even though the LHC is much bigger. It's like a specialized fishing rod that catches the specific fish that the big net misses because they swim too far out.

2. The Bad News (The "Super-Detectors" are Coming):
There are other proposed experiments for the LHC called CODEX-b, ANUBIS, and MATHUSLA. These are also "Far Detectors" designed to catch these long-lived ghosts.

• The Reality Check: The paper concludes that while µTRISTAN is cool, these proposed LHC detectors are likely to be better. Why? Because the LHC produces way more Higgs bosons (more collisions = more ghosts). Even though µTRISTAN has a better "aim" (the boost), the LHC has a much bigger "gun." If the LHC builds these far detectors, they will set stricter limits on these ghosts than µTRISTAN ever could.

The "Neutrino Noise" Problem

There is one tricky part. The muon beam itself creates a lot of neutrinos (another type of ghost particle). These neutrinos fly straight down the track and hit the detector, creating a lot of "noise" or background static.

• The Fix: The authors suggest using timing (waiting for the exact moment the collision happens) and looking at the shape of the tracks to tell the difference between a "ghost from the Higgs" and a "ghost from the beam." It's like trying to hear a specific whisper in a noisy room; you have to know exactly when to listen and what the voice sounds like.

The Conclusion

µTRISTAN is a clever idea. By using a "fast train vs. slow stroller" collision, it creates a focused beam of particles that allows a small detector far down the line to catch long-lived ghosts that other detectors miss.

• Can it beat the LHC's main detectors? Yes, for ghosts that travel very far.
• Can it beat the LHC's future far detectors? No. The LHC is just too powerful. If the LHC builds its own specialized ghost-hunting detectors, they will likely find the answer first.

In short: µTRISTAN is a brilliant, specialized tool that proves a unique strategy works, but it might be upstaged by the bigger, more powerful tools coming to the LHC.

Technical Summary

1. Problem Statement

The search for Long-Lived Particles (LLPs) is a primary strategy for probing "dark sectors" (light, weakly coupled new physics) that explain Standard Model (SM) shortcomings like Dark Matter and neutrino masses.

• The Challenge: While LHC experiments (ATLAS, CMS) can detect LLPs with decay lengths of $O(10^{-3} - 10)$ m via displaced vertices, they lose sensitivity for particles with longer lifetimes ($O(10 - 100)$ m) because these particles decay outside the main detector volume.
• The Context: Proposed LHC far detectors (CODEX-b, ANUBIS, MATHUSLA) aim to solve this by placing large volumes far from the interaction point (IP). However, future lepton colliders like µTRISTAN (a proposed muon-electron collider) offer a unique kinematic environment due to energy asymmetry.
• The Question: Can the highly boosted nature of events in the asymmetric $\mu^+ e^-$ mode of µTRISTAN allow a far detector to intercept a significant fraction of LLP flux, potentially outperforming or complementing LHC-based searches for exotic Higgs decays ($h \to \phi\phi$)?

2. Methodology

The authors perform a phenomenological study using Monte Carlo (MC) simulations to evaluate the sensitivity of µTRISTAN to a benchmark scenario: the production of a pair of long-lived neutral scalars ($\phi$) from the decay of the SM Higgs boson ($h \to \phi\phi$).

• Collider Configuration:

  • Mode: Energy-asymmetric $\mu^+ e^-$ collisions.
  • Scenarios:
    1. Low Energy: $E_{\mu^+} = 1$ TeV, $E_{e^-} = 30$ GeV ($\sqrt{s} \approx 346$ GeV).
    2. High Energy: $E_{\mu^+} = 3$ TeV, $E_{e^-} = 50$ GeV ($\sqrt{s} \approx 775$ GeV).
  • Luminosity: Integrated luminosity of $1 \text{ ab}^{-1}$ (Low) and comparable sample (High).
  • Production Mechanism: Higgs bosons are produced primarily via Vector Boson Fusion (VBF): $\mu^+ e^- \to \bar{\nu}_\mu \nu_e h$ (WW fusion) and $\mu^+ e^- \to \mu^+ e^- h$ (ZZ fusion).
  • Polarization: Beam polarizations $(P_{\mu^+}, P_{e^-}) = (+0.8, -0.7)$ are assumed to maximize the VBF cross-section.

• Kinematic Analysis:

  • The authors simulate $10^4$ parton-level events and perform $10^6$ toy experiments to map the angular distribution of the $\phi$ particles.
  • Due to the asymmetric beam energies, the Higgs boson is highly boosted in the laboratory frame along the $\mu^+$ beam direction. Consequently, the decay products ($\phi$) are collimated into a small solid angle (polar angle $\theta_\phi \approx 5^\circ$).

• Detector Simulation:

  • A far detector is modeled as a cylinder placed along the beam line at distance $D$ from the IP.
  • Geometry Optimization:
    • Low Energy: $D=100$ m, Radius $r=10$ m, Length $L=70$ m.
    • High Energy: $D=150$ m, Radius $r=7.5$ m, Length $L=125$ m.
    • Volume is $\sim 1.5 \times$ the volume of the proposed ANUBIS detector.
  • Signal Calculation: The probability of at least one $\phi$ decaying within the detector volume is calculated using the exponential decay law, accounting for the boost factor ($\beta\gamma$) and the specific trajectory intersection.
  • Backgrounds:
    • Muons/Neutrinos: Muon-induced backgrounds are suppressed via veto systems.
    • Neutrino Flux: A significant flux of neutrinos from the decaying $\mu^+$ beam is identified as a potential background ($\sim 10^5$ events). The authors propose mitigation strategies: timing cuts (bunch structure), track vertex reconstruction, and hollow cylindrical detector designs to reject forward-going neutrinos.

3. Key Contributions

• Kinematic Advantage Quantification: The paper demonstrates that the energy asymmetry in $\mu^+ e^-$ collisions creates a "boosted" environment where the LLP flux is concentrated in a narrow cone. This allows a far detector to intercept a large fraction ($>10\%$) of the total LLP flux, compensating for the lower total Higgs production cross-section compared to the LHC.
• Sensitivity Projections: The study provides the first comprehensive sensitivity projections for µTRISTAN in the $c\tau_\phi$ (proper decay length) vs. $BR(h \to \phi\phi)$ parameter space for various decay modes ($e^+e^-, \mu^+\mu^-, \tau^+\tau^-, \pi\pi, \gamma\gamma$).
• Background Mitigation Strategy: The authors explicitly address the unique challenge of neutrino backgrounds in a muon collider environment, proposing specific detector design and analysis techniques to handle them.

4. Results

• Comparison with HL-LHC (ATLAS/CMS):
  • µTRISTAN cannot reach the lowest branching ratios ($BR < 10^{-5}$) achievable by the High-Luminosity LHC (HL-LHC) in the short-to-medium decay length regime.
  • Crucial Finding: In the large proper decay length regime ($c\tau_\phi \gtrsim 10$ m), µTRISTAN surpasses the projected reach of HL-LHC main detectors (ATLAS/CMS) for specific decay modes (e.g., $\phi \to e^+e^-, \tau^+\tau^-, \pi^0\pi^0, \gamma\gamma$ at $m_\phi = 0.5$ GeV). The boosted nature allows the far detector to catch particles that would decay too far for ATLAS/CMS to see.
• Comparison with LHC Far Detectors (CODEX-b, ANUBIS, MATHUSLA):
  • µTRISTAN is not competitive with these proposed LHC far detectors.
  • The LHC far detectors, benefiting from a much higher Higgs production cross-section ($\sim 50$ pb vs. $\sim 100$ fb at µTRISTAN) and the ability to be placed closer to the IP (especially off-axis detectors like CODEX-b), will set significantly stronger limits across the entire parameter space.
• Mass Dependence:
  • For heavier $\phi$ masses ($m_\phi > 15$ GeV), the sensitivity to the $\mu^+\mu^-$ channel diminishes at µTRISTAN compared to lighter masses.
  • Higher center-of-mass energy ($\sqrt{s}=775$ GeV) extends the reach for hadronic decays at higher masses.

5. Significance and Conclusion

• Complementarity: While µTRISTAN cannot replace the sensitivity of proposed LHC far detectors, it offers a complementary search strategy. It is particularly effective in the "large $c\tau$" regime where main LHC detectors fail, providing an independent probe of the $h \to \phi\phi$ channel.
• Feasibility: The study confirms that a dedicated far detector along the beam line is a viable and powerful tool for LLP searches at a muon-electron collider, leveraging the unique kinematic boost of the asymmetric beam.
• Limitations: The primary limitation remains the lower Higgs production rate compared to hadron colliders. Consequently, µTRISTAN's reach is capped by the projected limits of the LHC far detectors (CODEX-b, ANUBIS, MATHUSLA), which are expected to be the gold standard for LLP searches in the post-LHC era.

In summary, the paper establishes that µTRISTAN's asymmetric beam configuration creates a unique "boosted" environment that enhances the geometric acceptance for far detectors, allowing it to probe specific regions of the LLP parameter space (large decay lengths) that are inaccessible to current and future main LHC detectors, though it remains secondary to dedicated LHC far detectors in overall sensitivity.