Search for massive, long-lived particles in events with displaced vertices and displaced muons in $pp$ collisions at $\sqrt{s}=13.6$ TeV with the ATLAS experiment

Using 164 fb$^{-1}$ of 13.6 TeV proton-proton collision data collected by the ATLAS detector from 2022 to 2024, this study searches for massive long-lived particles decaying into displaced vertices and displaced muons, finding no significant excess over the expected background and setting 95% confidence level upper limits on the production cross-sections of various $R$-parity-violating supersymmetry models.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. It fires two beams of protons (tiny subatomic particles) at each other at nearly the speed of light, creating a chaotic explosion of energy. Usually, when these particles smash together, they create new, exotic particles that vanish almost instantly—like soap bubbles popping the moment they form.

But what if some of these particles were like slow-motion ghosts? What if, instead of popping immediately, they traveled a measurable distance through the detector before decaying? These are called Long-Lived Particles (LLPs).

This paper from the ATLAS collaboration at CERN is a report on a massive "ghost hunt" conducted between 2022 and 2024. Here is the story of their search, explained in simple terms.

1. The Mystery: Why Look for Ghosts?

The Standard Model of physics is like a very successful instruction manual for how the universe works. But it has missing pages. It doesn't explain Dark Matter (the invisible stuff holding galaxies together) or why there is more matter than antimatter in the universe.

Physicists suspect that "Beyond Standard Model" physics exists. Some theories suggest that new, heavy particles exist but are "long-lived." They don't vanish instantly; they drift a bit before turning into normal particles. If we can find them, we might finally solve the mystery of Dark Matter.

2. The Trap: How They Tried to Catch the Ghosts

The ATLAS detector is a giant, 40-story-tall onion made of layers of sensors. To catch these "ghosts," the scientists set a specific trap:

• The Displaced Vertex (The Crime Scene): When a heavy, long-lived particle decays, it leaves behind a "crime scene" (a vertex) that is not at the center of the collision. It's like finding a broken vase in the middle of a room, rather than right next to the person who dropped it.
• The Displaced Muon (The Fingerprint): Muons are heavy cousins of electrons that can punch through walls. The scientists looked for muons that appeared far away from the center of the collision, carrying a "large impact parameter" (a fancy way of saying they arrived at a weird angle and distance).

They specifically looked for events where both a distant crime scene (vertex) and a distant fingerprint (muon) appeared in the same event.

3. The Challenge: The Noise Problem

The real world is messy. Most of the time, when particles collide, they create a lot of "background noise" that looks like a ghost but isn't.

• Heavy Flavor Decays: Sometimes, heavy particles (like bottom quarks) decay and create muons that look displaced.
• Cosmic Rays: High-energy particles from outer space sometimes crash into the detector from the top, looking like a displaced muon.
• Algorithmic Fakes: Sometimes the computer software gets confused and thinks a random jumble of tracks is a muon.

To solve this, the team used a clever "Data-Driven" trick. Instead of guessing how much noise there is using computer simulations, they used the data itself. They created "control zones" in their data where they knew the signal couldn't exist, measured the noise there, and mathematically projected how much noise should be in their "signal zone." It's like counting how many stray cats are in the alley behind your house to estimate how many might be in your living room.

4. The Hunt Results: The Silence

After analyzing 164 "inverse femtobarns" of data (which is a massive amount of collision data, equivalent to watching billions of particle collisions), the team looked for the "smoking gun."

• The Verdict: They found zero convincing evidence of these long-lived particles.
• The Observation: They saw 3 events in one category and 1 in another. However, their "noise calculator" predicted they should see about 1.8 and 2.9 events respectively. The numbers matched the background noise perfectly. No new physics was found.

5. The Silver Lining: Pushing the Boundaries

Even though they didn't find the ghosts, the hunt was a huge success for a different reason: They set the rules for where the ghosts aren't.

Think of it like searching for a lost key in a dark room. You don't find the key, but you shine your flashlight everywhere and say, "Okay, the key is definitely not in the corner, not under the rug, and not on the table."

By not finding the particles, the scientists have:

• Ruled out many specific theories about how Supersymmetry (a popular theory of new physics) works.
• Improved the search significantly compared to previous runs. They used new, faster triggers (like a security camera with a faster shutter speed) to catch lighter, faster-moving particles that previous searches missed.
• Extended the reach: They can now say, "If these particles exist, they must be heavier than 1.6 TeV (for some models) or have a lifetime longer than 100 nanoseconds."

The Bottom Line

This paper is a testament to the rigorous nature of science. Sometimes, the most important discovery is proving that a popular idea is wrong, or narrowing down the search space so future experiments know exactly where to look next.

The ATLAS team has cleaned up the "noise," built better traps, and told us exactly where the "long-lived ghosts" of the universe are not hiding. The search continues, but now we know the game is harder than we thought!

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics fails to explain several fundamental phenomena, including dark matter, the matter-antimatter asymmetry, and neutrino masses. These gaps motivate the search for Beyond the Standard Model (BSM) physics. A specific class of BSM theories predicts Long-Lived Particles (LLPs) that travel measurable distances before decaying, producing distinctive signatures such as Displaced Vertices (DVs).

While many BSM searches focus on promptly decaying particles, this paper targets scenarios where the Lightest Supersymmetric Particle (LSP) is unstable due to $R$-parity violation (RPV). In these models, the LSP (e.g., a higgsino or top squark) decays into SM particles with a macroscopic lifetime. The specific signature targeted is an event containing:

1. A massive displaced vertex (DV) with multiple tracks inside the ATLAS inner detector.
2. At least one muon with a large transverse impact parameter ($d_0$), indicating it originated from a displaced decay rather than the primary interaction point.

2. Methodology

Data and Detector

• Dataset: Proton-proton collision data collected by the ATLAS detector at the LHC between 2022 and 2024 (Run 3).
• Energy: Center-of-mass energy $\sqrt{s} = 13.6$ TeV.
• Integrated Luminosity: 164 fb$^{-1}$.
• Key Run 3 Upgrades: The analysis utilizes a dedicated displaced-muon trigger (introduced in Run 3) capable of reconstructing muons with transverse momentum ($p_T$) as low as 20 GeV and large impact parameters ($|d_0| > 2$ mm). This significantly improves sensitivity to lower-mass LLPs compared to previous Run 2 searches. Specialized tracking algorithms for large-impact-parameter tracks were also employed.

Event Selection

Events were selected based on the presence of:

• Signal-like Muon: A muon with $p_T > 25$ GeV, $2 \text{ mm} < |d_0| < 300$ mm, and high displacement significance ($|d_0|/\sigma_{d_0} > 150$). It must pass "Tight_VarRad" isolation, cosmic-ray, and algorithmic-fake vetoes.
• Displaced Vertex (DV): Reconstructed from at least 4 tracks with an invariant mass $m_{DV} \ge 20$ GeV (for "far" DVs) or $40$ GeV (for "near" DVs).
• Signal Regions (SRs): Two regions were defined based on the transverse distance of the DV from the primary vertex ($d_T$):
  • SR$_{far}$: $d_T \ge 4$ mm.
  • SR$_{near}$: $1 \text{ mm} < d_T < 4$ mm.
• No Association: The displaced muon is not required to be associated with the DV, preserving model independence.

Background Estimation

A fully data-driven Transfer Factor (TF) method was used to estimate backgrounds, avoiding reliance on simulation for rare background processes.

• Background Sources: Heavy-flavour decays, cosmic-ray muons, and algorithmic fakes (misreconstructed tracks).
• Method: The data was divided into exclusive regions based on whether events passed or failed specific muon vetoes and DV selection criteria.
  • Region A (Signal Region): Passes all criteria.
  • Regions B, C, D: Inverted criteria used to derive Transfer Factors ($TF = N_C / N_D$).
• Validation: The method was validated in zero-DV and material-map-vetoed regions, showing good agreement between data and prediction. A non-closure uncertainty was applied to the heavy-flavour estimate in specific validation regions.

Signal Models

The results were interpreted in the context of three RPV SUSY benchmark models:

1. Higgsino Pair Production ($L$-violating): $\tilde{\chi}^0_1 \tilde{\chi}^0_2$ or $\tilde{\chi}^\pm_1$ pairs decaying via $\lambda'_{211}$ to $\mu u \bar{d}$.
2. Higgsino Pair Production ($B$-violating): Decaying via $\lambda''_{323}$ to $t s b$ (leading to muons via top semileptonic decay).
3. Top Squark Pair Production: $\tilde{t}\bar{\tilde{t}}$ decaying via $\lambda'_{233}$ to $\mu b$.

3. Key Contributions

• First Run 3 Search: This is the first ATLAS search for LLPs using the full Run 3 dataset at 13.6 TeV, leveraging the new 13.6 TeV luminosity and upgraded trigger/reconstruction capabilities.
• Enhanced Low-$p_T$ Sensitivity: The dedicated displaced-muon trigger extends sensitivity to muons with $p_T \approx 20$ GeV, allowing the exclusion of lower-mass LLPs (down to $\sim 100$ GeV) that were previously inaccessible.
• Improved Background Estimation: The implementation of a robust, fully data-driven TF method with rigorous validation regions minimizes systematic uncertainties associated with background modeling.
• Model-Independent Limits: Provided limits on the visible cross-section for generic DV + displaced muon topologies, applicable to a wide range of BSM scenarios beyond just SUSY.

4. Results

Observation

• Observed Events: 3 events in SR$_{far}$ and 1 event in SR$_{near}$.
• Background Prediction: $1.8 \pm 1.1$ (SR$_{far}$) and $2.9 \pm 0.8$ (SR$_{near}$).
• Conclusion: The observed yields are fully consistent with the expected background. No significant excess was observed.

Limits on Visible Cross-Section

Model-independent 95% Confidence Level (CL) upper limits on the visible cross-section ($\langle \sigma A \epsilon \rangle$) were set. The most stringent limits were found in the highest reduced invariant mass bins ($m^{\text{red}}_{DV} \ge 13$ GeV for SR$_{far}$ and $\ge 15$ GeV for SR$_{near}$), reaching values of approximately 0.018 fb.

Limits on SUSY Benchmark Models

• Higgsinos ($L$-violating $\lambda'_{211}$):
  • Excluded masses up to 1600 GeV for proper lifetimes ($\tau$) of 0.1 ns.
  • Excluded masses between 100 GeV and 450 GeV for lifetimes between 1 ps and 100 ns.
  • Improvement: Cross-section limits improved by approximately two orders of magnitude compared to ATLAS Run 1 results.
• Higgsinos ($B$-violating $\lambda''_{323}$):
  • Excluded masses up to 1150 GeV for $\tau = 0.1$ ns.
  • Extended lifetime reach up to 100 ns, providing complementary coverage to CMS searches which are optimized for shorter lifetimes.
• Top Squarks ($\lambda'_{233}$):
  • Excluded masses up to 1850 GeV for $\tau = 0.1$ ns.
  • Excluded masses between 700 GeV and 1500 GeV for lifetimes between 10 ps and 5 ns.
  • Improvement: Significantly improved sensitivity for lifetimes $< 5$ ns compared to previous ATLAS Run 2 results, thanks to the new muon triggers.

5. Significance

This analysis represents a major advancement in the search for long-lived particles at the LHC. By utilizing the full Run 3 dataset and novel trigger strategies, ATLAS has:

1. Extended the mass reach for higgsinos and top squarks significantly beyond previous limits.
2. Improved sensitivity to lower-mass particles and shorter lifetimes, filling gaps in the parameter space previously unexplored.
3. Demonstrated the power of data-driven background estimation in complex displaced signature searches.
4. Provided stringent constraints on $R$-parity violating SUSY scenarios, ruling out large portions of the parameter space for higgsino and top-squark LSPs, thereby guiding future theoretical developments and experimental strategies for the High-Luminosity LHC era.