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Enabling searches for long-lived particles at a future 10 TeV Muon Collider

This paper demonstrates that relaxing strict hit-timing requirements in the detector design of a future 10 TeV Muon Collider can recover sensitivity to long-lived charged particles, such as staus in a Gauge Mediated Supersymmetry Breaking model, which would otherwise be missed due to beam-induced backgrounds.

Original authors: Mira Littmann, Mark Larson, Kate Wandrisco, Benjamin Rosser, Tate Flicker, Kane Huang, Leo Rozanov, Karri Folan Di Petrillo

Published 2026-09-17

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CC BY 4.0

Original authors: Mira Littmann, Mark Larson, Kate Wandrisco, Benjamin Rosser, Tate Flicker, Kane Huang, Leo Rozanov, Karri Folan Di Petrillo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is filled with particles that behave in ways we do not yet understand. While the standard model of physics successfully describes the known building blocks of matter, it leaves many questions unanswered, such as the nature of dark matter or why the universe is made of matter rather than antimatter. To find the answers, scientists build massive machines called colliders, which smash particles together at incredible speeds to recreate the conditions of the early universe. For decades, the most powerful machines have used protons, but these create a chaotic environment full of debris that makes it hard to spot rare, new phenomena. A new generation of machines is being planned to collide muons, which are heavier cousins of the electron. These muon colliders promise a cleaner environment and much higher energy, potentially reaching ten trillion electron volts. However, muons are unstable and decay into other particles as they travel. This decay creates a constant shower of background noise inside the detector, a problem that threatens to drown out the very signals scientists hope to find.

The challenge is particularly acute when looking for long-lived particles. These are hypothetical new particles that do not vanish immediately after a collision but instead travel a measurable distance before decaying. Because they move slower than light, they arrive at the detector's sensors slightly later than the ordinary particles produced in the crash. In the past, researchers designed their detectors to ignore any signal that arrived even a tiny fraction of a second late, assuming that such delays were just noise from the muon decay. This strategy worked well for finding standard particles, but it meant that any slow-moving, long-lived new particle would be automatically discarded as garbage. A team of researchers at the University of Chicago set out to see if this strict approach was throwing away the most exciting discoveries. They asked a simple question: could they relax the timing rules just enough to catch these slow travelers without letting the background noise overwhelm the data?

To answer this, the team created a detailed computer simulation of a future ten-trillion-electron-volt muon collider. They modeled a specific type of new physics where a heavy, stable particle called a stau is produced. In their scenario, these staus would move slowly through the detector, leaving a trail of hits that arrive later than expected. They also simulated the intense background noise caused by decaying muons, which creates billions of low-energy particles hitting the detector every time the beams cross. The researchers then tested three different ways of filtering the data. The first was the standard, strict method that rejects any hit arriving outside a very narrow time window. The second was a moderate relaxation of these rules, and the third was a loose window that allowed for much larger delays. They ran their simulation to see how many of the slow staus could be found and how much background noise would slip through with each method.

The results showed that the strict, standard method was indeed too cautious. When they applied the tight timing rules, the detector failed to see almost any of the heavy, slow-moving staus because their delayed hits fell outside the allowed window. The researchers found that by loosening the timing criteria, they could recover the ability to detect these particles, even those with masses close to the maximum energy the collider could produce. However, loosening the rules also let in more background noise. The simulation showed that the number of false signals increased significantly, but the team discovered that this noise could be managed. By combining the looser timing with other checks, such as looking at the quality of the track the particle left and its speed, they could filter out the vast majority of the background.

The key to making this work was a multi-step selection process. First, the researchers required that a particle leave a clear, continuous path through the detector, which helped eliminate random noise. Next, they looked at the speed of the particle. The background noise tended to mimic the speed of light, while the new, heavy particles moved noticeably slower. By selecting only the slowest tracks, they could separate the signal from the noise. Finally, they examined the combined mass of the two particles produced in the collision. The background noise created random combinations that appeared to have very low mass, whereas the signal particles would have a mass close to the energy of the collision. When they applied all these filters together, the simulation showed that the background noise could be reduced to nearly zero, while still keeping a large fraction of the potential new particles.

This approach suggests that a muon collider could be a powerful tool for finding long-lived particles, provided the detectors are designed to be flexible. The study demonstrated that it is possible to keep the detector clean enough to work while still being sensitive to the slow, heavy particles that other methods would miss. The researchers found that with the right combination of timing and track analysis, they could potentially discover particles with masses up to four and a half trillion electron volts. This would cover a vast range of new physics that is currently out of reach. The work highlights that the design of future experiments must balance the need to reject noise with the need to catch rare, slow-moving signals. If the timing windows are too tight, the most interesting discoveries might be lost in the silence. If they are too loose, the data becomes unreadable. The study shows that there is a middle ground where both can be achieved, opening a new path to exploring the unknown.

Technical Summary: Enabling searches for long-lived particles at a future 10 TeV Muon Collider

Problem Statement
Muon colliders offer a unique path to the energy frontier by combining the clean environment of lepton collisions with the high center-of-mass energies of hadron colliders. However, the decay of muons near the interaction point generates significant beam-induced backgrounds (BIB), consisting of $\mathcal{O}(10^8)$ low-energy neutrons, photons, and electrons per bunch crossing. These particles do not point back to the interaction region and arrive out-of-time relative to collision products.

Current detector designs rely on stringent hit-timing windows (typically $-3\sigma_t < t_{corr} < +5\sigma_t$ ) to reject BIB and reduce detector occupancy to manageable levels for reconstruction. While effective for prompt Standard Model (SM) particles, these tight timing criteria inherently reject delayed hits from slowly moving, long-lived particles (LLPs). This creates a trade-off: strict timing suppresses background but eliminates sensitivity to heavy, meta-stable charged particles that traverse the tracker with $\beta = v/c < 1$ .

Methodology
The authors investigate the capability of detecting meta-stable charged particles at a 10 TeV muon collider using a simplified Gauge Mediated Supersymmetry Breaking (GMSB) model as a benchmark. In this scenario, staus ( $\tilde{\tau}$ ) are pair-produced and decay to a tau and a nearly massless gravitino ( $\tilde{\tau} \to \tau \tilde{G}$ ). The study varies stau masses from 1 to 4.5 TeV and lifetimes from 0.1 ns to 30 ns (including a stable benchmark).

The analysis utilizes the MuColl v1 detector geometry simulated within the DD4hep framework, featuring a 3.57 T magnetic field and a silicon tracker with 30 ps (Vertex) and 60 ps (Inner/Outer) time resolution. Signal and BIB events are simulated using MadGraph5 aMC@NLO, Pythia8, FLUKA, and GEANT4, with hits overlaid and digitized using a key4hep-based framework.

The core of the methodology involves relaxing the hit-timing criteria to capture delayed signals. Three timing windows are defined:

Nominal: Standard tight window optimized for SM particles.
Medium: A midpoint between Nominal and Loose.
Loose: Defined to capture $>90\%$ of hits from a 4 TeV stau in the outermost tracker layers.

Track reconstruction is performed using ACTS (v32.1.0). The study evaluates reconstruction efficiency, track purity, and kinematic resolution under these varying timing windows, with 10% of the expected BIB per bunch crossing overlaid on signal events. Backgrounds are estimated from random BIB hit combinations and SM muons ( $\mu^+\mu^- \to \mu^+\mu^-$ ).

Key Contributions and Results

Impact of Timing on Occupancy and Efficiency:
- Loosening timing windows increases BIB occupancy significantly (e.g., Loose windows increase occupancy by 73% in the Vertex Detector, 105% in the Inner Tracker, and 144% in the Outer Tracker relative to Nominal).
- However, Nominal and Medium windows result in near-zero reconstruction efficiency for staus with masses $>2.5$ TeV in the Inner and Outer Trackers because delayed hits fall outside the acceptance.
- The Loose timing window recovers $\sim70\%$ track reconstruction efficiency for staus traversing the full barrel, even for masses up to 4 TeV. Crucially, despite higher occupancy, the Loose window maintains track purity above 95% and improves momentum and velocity resolution (reaching $\sim1\%$ ) by retaining more signal hits and extending the lever arm.
Background Suppression Strategies:
- Track-Level Selections: Requirements on hit timing consistency ( $wRMS < 1.4$ ), geometric acceptance ( $|\eta| \le 0.8$ ), and hit multiplicity (e.g., $\ge3$ Vertex, $\ge2$ Inner, $\ge2$ Outer hits) strongly suppress BIB tracks.
- Event-Level Selections: The analysis requires two high- $p_T$ tracks with mass-dependent cuts on $p_T$ , $\beta$ , and reconstructed mass ( $m_{reco}$ ).
- ABCD Method: A per-track ABCD estimate is used to extrapolate BIB rejection from a small sample of 10 fully simulated BIB events to the full dataset. This predicts that the number of events with two fake BIB tracks passing all selections is negligible (far less than one event) across all timing windows and mass hypotheses.
- Ditrack Invariant Mass: The invariant mass of the leading and subleading tracks provides strong discrimination, with signal concentrated near $\sqrt{s} = 10$ TeV and BIB concentrated at lower masses.
Projected Sensitivity:
- Assuming a zero-background scenario (justified by the ABCD estimate and the absence of surviving SM muon events in high-statistics samples), the study projects 95% confidence-level exclusion limits for an integrated luminosity of $10 \text{ ab}^{-1}$ .
- Nominal and Medium windows lose sensitivity at high stau masses due to reconstruction inefficiency.
- Loose windows maintain sensitivity across the entire mass range (up to 4.5 TeV) for stau lifetimes $\gtrsim 3$ ns. The Loose configuration excludes a substantially larger region of the mass-lifetime parameter space compared to tighter windows.

Significance and Claims
The paper argues that maximizing discovery potential for long-lived particles at a muon collider requires a departure from the strictly optimized timing windows used for prompt SM physics. The authors demonstrate that:

Looser timing criteria are essential to recover sensitivity to heavy, slowly moving charged particles that would otherwise be rejected as out-of-time noise.
Backgrounds can be managed not by tightening timing (which kills the signal), but by leveraging kinematic selections (mass, $\beta$ , $p_T$ ) and track quality metrics that effectively distinguish signal from the remaining BIB.
Detector performance is robust: Even with increased BIB occupancy from loose timing, track reconstruction algorithms (ACTS) can maintain high purity and resolution, provided that hit-based matching and quality cuts are applied.

The study concludes that while current designs prioritize BIB rejection for prompt particles, future 10 TeV muon collider experiments must incorporate flexible or "loose" timing acceptance strategies to ensure they do not miss potential discoveries of heavy meta-stable charged particles. The authors note that further improvements in track reconstruction algorithms (e.g., 4D timing-aware reconstruction) and sensor-level BIB rejection (e.g., smart pixels) will be critical to fully exploit this potential.

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