Searches for massive, long-lived particles in events with displaced vertices with ATLAS

This paper presents two ATLAS searches for massive, long-lived particles decaying into displaced vertices using Run 2 missing transverse energy and Run 3 muon triggers, introducing novel reconstruction and trigger techniques to set limits on various Beyond the Standard Model scenarios including Higgs Portal, SUSY, and axino models.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Scientists smash protons together at nearly the speed of light to see what tiny pieces fly out. Usually, they are looking for particles that pop into existence and vanish instantly—like a firework that explodes the moment it's lit. These are called "prompt" particles.

But what if there are particles that don't vanish immediately? What if they are like ghosts that drift through the detector for a while before finally disappearing? These are called Long-Lived Particles (LLPs).

This paper is a report from the ATLAS experiment at the LHC, detailing two new "ghost hunts" designed to catch these elusive travelers.

The Problem: The "Ghost" is Hard to See

Standard detectors are built to catch things that happen right where the crash occurs. If a particle travels a few centimeters or even a few meters before decaying (exploding into other particles), it creates a "Displaced Vertex" (DV). It's like finding a bullet hole in a wall that is far away from the shooter.

The challenge is that the computer algorithms used to reconstruct these events are usually tuned to look for things happening right at the center. If the "ghost" decays into heavy, messy particles that don't line up perfectly, the standard software might miss it entirely, thinking it's just background noise.

Hunt #1: The "Fuzzy" Net (Run 2 Data)

The first search looked at events where energy seemed to vanish (Missing Transverse Energy). Think of this as looking for a crime scene where the thief ran away with the loot, leaving a hole in the budget.

The Innovation:
In the past, the computer required all the debris from a decay to point back to one single, perfect dot. But sometimes, a long-lived particle decays into heavy quarks, which themselves are slightly long-lived. It's like a Russian nesting doll: the outer doll opens, revealing a second doll that opens a few inches away.

• Old Way: The computer demanded all the pieces point to the exact same spot. If they didn't, it threw the data away.
• New "Fuzzy" Way: The scientists introduced a "Fuzzy Vertex" algorithm. Instead of demanding a perfect dot, they allowed the computer to look for a "fuzzy cloud" or a small volume where the pieces roughly converge.

The Result:
By loosening the rules, they didn't lose any real signals; they actually caught more. They set strict limits on several theoretical models (like "Higgs Portal" or "SUSY"), essentially saying, "If these ghost particles exist, they must be heavier or live longer than we previously thought."

Hunt #2: The "Displaced" Trigger (Run 3 Data)

The second search is even newer, using data from 2022–2024. This time, they were looking for events triggered by muons (heavy cousins of electrons).

The Innovation:
Usually, the detector's "trigger" (the gatekeeper that decides which collisions to save for later) only looks for muons that appear right at the center. If a muon appears far away, the gatekeeper often ignores it, thinking it's a mistake.

• The Fix: They built a new "Displaced Muon Trigger." Imagine a security guard who usually only checks people walking through the front door. This new guard is trained to also check people who sneak in through the back door or appear in the hallway.
• The Benefit: This allowed them to catch muons that traveled a bit before appearing, specifically those with lower energy that the old system would have missed.

The Result:
They looked for signs of "R-parity Violating SUSY" (a specific type of supersymmetry theory). They found no ghosts, but they set new, tighter limits on where these particles could be hiding.

The Big Picture: Why Does This Matter?

Think of the Standard Model (our current understanding of physics) as a map of a known city. We know where the streets are, but we suspect there are secret tunnels and underground bunkers we haven't found yet.

• Long-Lived Particles are the keys to those secret tunnels.
• Displaced Vertices are the footprints left behind when someone walks through those tunnels.
• The "Fuzzy" algorithm and "Displaced Trigger" are new, more sensitive flashlights and footprints scanners.

Even though they didn't find the ghosts this time, they proved that their new tools work. They have successfully mapped out the "no-ghost zones" more precisely than ever before. As the LHC enters its "High Luminosity" phase (shooting even more particles), these new tools will be ready to catch whatever strange, long-lived particles might be hiding in the shadows of the universe.

Technical Summary

1. Problem Statement

The Standard Model (SM) fails to explain several major cosmological and theoretical issues, suggesting the existence of Beyond the Standard Model (BSM) particles. While most collider searches focus on "prompt" decays (where particles decay within $\tau \lesssim 0.0033$ ns or $c\tau \lesssim 1$ mm), many well-motivated BSM theories predict Long-Lived Particles (LLPs). These particles travel a measurable distance through the detector before decaying.

Standard reconstruction algorithms are optimized for prompt tracks and often fail to reconstruct LLPs, particularly in complex scenarios where:

• The LLP decays into heavy quarks (e.g., $b$-quarks) that are themselves slightly long-lived, creating "fuzzy" vertices where decay products do not converge to a single point.
• The decay products include muons with large displacement, which are difficult to trigger on using standard muon spectrometer triggers.

The paper addresses the challenge of detecting these Displaced Vertices (DVs) in high-pileup environments by introducing novel reconstruction and triggering strategies.

2. Methodology

The paper presents two distinct analyses utilizing data from Run 2 (2016–2018, 137 fb$^{-1}$) and Run 3 (2022–2024, 164 fb$^{-1}$) of the LHC.

A. Run 2 Analysis: DVs in MET-Triggered Events

• Trigger Strategy: Events are selected based on Missing Transverse Energy ($MET \ge 150$ GeV).
• Novel Reconstruction (Fuzzy Vertexing):
  • Standard Vertexing: Requires all tracks to point back to an exact single point. This fails when an LLP decays into heavy quarks that travel a short distance before decaying again, creating multiple sub-vertices.
  • Fuzzy Vertexing: A new algorithm relaxes the requirement for a single point, allowing the vertex to be reconstructed as a "fuzzy volume." This significantly improves efficiency for LLPs decaying into heavy quarks.
• Signal Regions (SRs):
  • 1SDV: $\ge 1$ Standard DV.
  • 1FDV: $\ge 1$ Fuzzy DV.
  • 2FDV: $\ge 2$ Fuzzy DVs (exploiting the rarity of background events with multiple DVs to relax track/mass requirements).
• Selection Cuts: DVs must have $|DV_{rxy}|, |DV_z| \le 300$ mm, be outside detector material, and have a transverse distance $> 4$ mm from the primary vertex.
• Background Estimation: Uses a photon-triggered control region to estimate the fraction of events with DVs based on track/jet activity, assuming DVs are uncorrelated with photons.

B. Run 3 Analysis: DVs in Muon-Triggered Events

• Trigger Strategy: Introduces a new displaced muon trigger utilizing Large-Radius Tracking (LRT) at the trigger level. This complements standard muon spectrometer triggers.
• Performance: The new trigger significantly increases efficiency for highly displaced muons ($|d_0| > 2$ mm) and allows for the detection of lower transverse momentum ($p_T$) muons compared to previous methods.
• Signal Regions:
  • "Near" SR: $1 \text{ mm} \le |d_0| \le 4 \text{ mm}$, $m_{DV} \ge 40$ GeV.
  • "Far" SR: $|d_0| \ge 4 \text{ mm}$, $m_{DV} \ge 20$ GeV.
• Background Estimation: Uses an ABCD method based on the independence of muon background sources (heavy flavor, cosmic rays, fakes) and DV activity. Validation regions are created by inverting DV requirements.
• Vetos: Strict vetoes are applied to remove heavy-flavor, cosmic ray, and fake muon backgrounds.

3. Key Contributions

1. Fuzzy Vertexing Algorithm: The first implementation of a "fuzzy" vertex reconstruction in ATLAS. This allows for the effective reconstruction of LLPs decaying into heavy quarks where sub-vertices prevent standard track convergence, drastically improving signal efficiency for specific BSM scenarios.
2. Displaced Muon Trigger: The first use of an LRT-based displaced muon trigger in ATLAS. This enables the collection of data with high efficiency for muons originating from displaced vertices, a capability previously limited by standard trigger constraints.
3. Multi-Region Strategy: The introduction of signal regions requiring multiple DVs (2FDV) to suppress backgrounds more effectively, allowing for relaxed kinematic cuts and sensitivity to lighter LLPs.
4. Run 3 Data: The first ATLAS LLP results utilizing 2024 data (Run 3), demonstrating the viability of new trigger strategies in the high-luminosity era.

4. Results

• Observations: No significant excess of events over the Standard Model background was observed in either analysis.
• Run 2 (MET) Limits:
  • Gluino R-hadrons: Exclusion limits improved by 200–300 GeV in peak regions compared to previous partial Run 2 searches.
  • Wino-Bino Co-annihilation: Limits included in official SUSY summary plots.
  • Higgs Portal: High sensitivity at high lifetimes; the search effectively probes scenarios where one LLP decays outside the detector (appearing as MET).
  • DFSZ Axino: First explicit exclusion limits set for this scenario and the axion itself.
• Run 3 (Muon) Limits:
  • RPV Supersymmetry: Limits were set on R-parity violating (RPV) models involving Higgsino and Stop pair production.
  • Couplings: Constraints were placed on three specific RPV couplings ($\lambda'_{211}$, $\lambda''_{323}$, $\lambda'_{233}$).
  • Improvements: The $\lambda'_{211}$ limits improved upon Run 1 results; $\lambda''_{323}$ limits are complementary to CMS hadronic searches; $\lambda'_{233}$ limits improved upon previous ATLAS Run 2 muon searches.

5. Significance

This work represents a critical evolution in the search for Long-Lived Particles at the LHC. By moving beyond "prompt" decay assumptions, the ATLAS Collaboration has:

• Expanded Sensitivity: The fuzzy vertexing and displaced muon triggers open up parameter spaces for BSM models (SUSY, Axions, Higgs Portals) that were previously inaccessible or poorly constrained.
• Validated New Techniques: The successful deployment of LRT at the trigger level and fuzzy reconstruction algorithms proves that the detector and software can adapt to exotic signatures in real-time.
• Future Readiness: These methodologies are essential for the upcoming High-Luminosity LHC (HL-LHC) phase, where the ability to trigger on and reconstruct complex, displaced signatures will be paramount for discovering new physics.