Search for long-lived particles using displaced vertices of oppositely charged leptons in 140 fb$^{-1}$ of pp collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, this study presents a search for long-lived particles decaying into displaced opposite-charge lepton pairs, setting leading upper limits on production cross-sections for benchmark $Z'$ and $R$-parity violating supersymmetric models without observing any candidate events.

The Gist

The Big Picture: Hunting for "Ghost" Particles

Imagine the Large Hadron Collider (LHC) as a giant, high-speed car crash arena. Scientists smash protons together at nearly the speed of light, hoping to recreate the conditions of the universe just after the Big Bang. Usually, when these particles crash, they break apart into other particles that fly off and hit detectors almost instantly.

But what if some of these particles are like ghosts? What if they are created in the crash, but instead of vanishing immediately, they travel a few centimeters or even meters through the detector before finally "poofing" into something we can see? These are called Long-Lived Particles (LLPs).

This paper is a report from the ATLAS team (a massive group of scientists) saying: "We looked very carefully for these ghosts in our data from 2015–2018, but we didn't find any."

The Detective Work: Looking for "Displaced Vertices"

To find these ghosts, the scientists had to look for a specific clue called a Displaced Vertex (DV).

• The Normal Scenario: Usually, when particles are created, they leave a "smoke ring" (a track) that starts right at the center of the crash (the Primary Vertex).
• The Ghost Scenario: If a long-lived particle exists, it travels away from the center, then decays. When it decays, it creates a new "smoke ring" (a pair of charged particles, like electrons or muons) that starts far away from the center.

The Analogy:
Imagine a firework display.

• Normal particles: The firework explodes right in your hand, and the sparks fly out immediately.
• Long-lived particles: The firework is launched into the air, flies for a few seconds, and then explodes in the sky. The "explosion point" (the vertex) is displaced from where you launched it.

The ATLAS detector is a giant, high-tech camera that takes pictures of these fireworks. The scientists built a special algorithm to ignore the fireworks exploding in your hand and only look for the ones exploding in the sky.

The Three Suspects (Benchmark Models)

The scientists didn't just look for any ghost; they had three specific "suspects" in mind based on theories that extend our current understanding of physics (Standard Model). They checked if these suspects could be hiding in the data:

1. The Heavy Scalar & The $Z'$ Boson: Imagine a heavy, invisible parent particle (a scalar) that splits into two long-lived "children" ($Z'$ bosons). These children fly off and eventually turn into pairs of oppositely charged particles (like an electron and a positron, or two muons).
2. The Gluino & The Neutralino: In a theory called Supersymmetry (SUSY), there are heavy particles called gluinos. When they decay, they might produce a "neutralino" (a ghostly particle) that lives for a while before turning into two charged particles and a neutrino.
3. The Electroweakino: A variation of the above, where the neutralino is produced by other heavy particles called charginos or heavier neutralinos.

The Search Strategy: How They Looked

The team analyzed 140 fb⁻¹ of data. To put that in perspective, if one "fb" is a single grain of sand, they analyzed a mountain of data.

• The Net: They set up a very specific net. They only caught events where:
  • Two charged particles (leptons) appeared.
  • They formed a clear "vertex" (a meeting point) inside the inner tracking system of the detector.
  • This meeting point was displaced (at least 2mm away from the center of the crash).
  • The particles had enough energy to be real, not just random noise.
• The Background Noise: The universe is messy. Sometimes, random tracks cross each other by accident, or cosmic rays (particles from space) hit the detector and look like a decay. The scientists used clever math to estimate how many of these "fake ghosts" they should expect.
  • Analogy: If you are looking for a specific type of bird in a forest, you have to know how many leaves look like that bird so you don't get fooled.

The Results: The Great Silence

The Verdict: They found zero events that matched their criteria.

• The Expectation: Based on their calculations of background noise (random accidents), they expected to see a tiny number of events (less than one, essentially zero).
• The Reality: They saw zero.

This is actually a good result! It means their detector works perfectly and their background calculations are accurate. However, it also means no new long-lived particles were found in this specific search.

What This Means for Physics

Since they didn't find the particles, they didn't discover a new law of physics. Instead, they did something equally important: They drew a "Do Not Enter" sign.

• Setting Limits: Because they didn't find the particles, they can say with 95% confidence: "If these ghost particles exist, they cannot be this heavy, or they cannot live this long, or they cannot be produced this often."
• Ruling Out Theories: They have now ruled out a huge chunk of the "map" where these particles might have been hiding. Specifically, they excluded:
  • Heavy scalars decaying into $Z'$ bosons with masses between 0.1 and 2.2 TeV.
  • Neutralinos (from the SUSY models) with masses up to 2.2 TeV, provided they live for a certain amount of time (from 1mm to 10,000mm of travel).

The Takeaway

Think of this paper as a very thorough search of a house for a lost cat.

• The scientists looked in every room (the inner tracker).
• They looked for the cat's specific paw prints (the displaced vertex of two leptons).
• They checked for fake paw prints made by the dog (background noise).
• Result: No cat was found.

Conclusion: The cat isn't in this house (or at least, not in the specific rooms and sizes they were looking for). This tells future cat hunters (physicists) that they need to look in different houses, or perhaps the cat is a different color than they thought. The search continues, but the "easy" hiding spots have been cleared.

Technical Summary

Technical Summary: Search for Long-Lived Particles Using Displaced Vertices of Oppositely Charged Leptons

Problem and Motivation
Long-lived particles (LLPs) are a well-motivated prediction in various extensions of the Standard Model (SM), including Hidden Valley models, split supersymmetry, $R$-parity violating (RPV) supersymmetry, and gauge-mediated SUSY breaking. These particles often possess macroscopic decay lengths due to small couplings, small mass splittings, or approximate symmetries. A neutral LLP decaying into a pair of oppositely charged leptons ($\mu^+\mu^-$, $e^+e^-$, or $e^\pm\mu^\mp$) produces a displaced vertex (DV) within the inner tracking system, a signature with minimal SM background. While previous searches by ATLAS and CMS have targeted lighter LLPs or utilized partial datasets, this analysis addresses the need for a comprehensive search using the full Run-2 dataset to probe heavier mass scales and a broader range of lifetimes, including mixed lepton flavors ($e\mu$) which had not been previously targeted in this specific context by ATLAS.

Methodology
The analysis utilizes 140 fb$^{-1}$ of proton-proton collision data collected by the ATLAS detector at $\sqrt{s} = 13$ TeV between 2015 and 2018. The search targets heavy, neutral LLPs decaying into dilepton pairs within the inner detector (ID).

• Reconstruction: To recover efficiency for tracks originating from displaced decays, the analysis employs both the Standard Track (ST) algorithm and the Large Radius Track (LRT) algorithm. The LRT algorithm relaxes requirements on transverse ($d_0$) and longitudinal ($z_0$) impact parameters (up to 300 mm and 1500 mm, respectively) and allows for more shared silicon modules. A dedicated DV reconstruction algorithm forms vertices from combinations of ST and LRT tracks, requiring no hits between the vertex and the primary vertex (PV) and at least one hit in the first pixel or SCT layer as the track emerges from the DV.
• Event Selection: Events are triggered using "MS only" muon triggers ($p_T > 60$ GeV) or photon triggers (single photon $p_T > 140$ GeV or diphoton $p_T > 50$ GeV) to avoid reliance on ID track information which is inefficient for displaced objects. Signal events require a PV with at least two tracks, a reconstructed DV with transverse displacement $R_{xy} > 2$ mm, and a DV located within $R_{xy} < 300$ mm and $|z_{DV}| < 300$ mm. The dilepton invariant mass must exceed 12 GeV. A cosmic-ray veto is applied to reject back-to-back muon pairs.
• Background Estimation: SM backgrounds from prompt decays are suppressed by kinematic and geometric requirements. The remaining backgrounds are estimated from data:
  • Cosmic Rays: Estimated using a control region with inverted cosmic veto criteria, extrapolating the $\Delta R_{cos}$ distribution.
  • Random Track Crossings: Estimated using a "toy" event mixing method where leptons from different data events are combined. No reconstructed dilepton DVs were found in $10^6$–$10^8$ toy events per channel, establishing an upper limit on the probability of random crossing.
• Benchmark Models: The results are interpreted in three models:
  1. $Z'$ Model: Pair production of a heavy scalar $S$ decaying to long-lived $Z'$ bosons, which decay to lepton pairs.
  2. Gluino Model (RPV MSSM): Pair production of gluinos ($\tilde{g}$) decaying to quarks and a long-lived neutralino ($\tilde{\chi}^0_1$), which decays via RPV couplings ($\lambda_{121}$ or $\lambda_{122}$) to $\ell^+\ell'^-\nu$.
  3. EWkino Model (RPV MSSM): Direct electroweakino production ($\tilde{\chi}^\pm_1\tilde{\chi}^0_1$, etc.) where the $\tilde{\chi}^0_1$ is the long-lived LSP.

Key Contributions

• Full Run-2 Dataset: This is the first published ATLAS analysis to use the full 140 fb$^{-1}$ of Run-2 data for a search for dilepton displaced vertices.
• Flavor Coverage: It is the only search to simultaneously include displaced vertices for dimuon, dielectron, and electron-muon pairs.
• Model Independence: The selection does not require missing transverse momentum or jets, and allows for additional tracks in the DV, maintaining sensitivity to a wide range of models.
• Reconstruction Efficiency: The inclusion of LRT tracks and modified identification criteria significantly improves reconstruction efficiency for displaced leptons compared to previous analyses relying solely on standard tracks or muon spectrometer information.

Results
No events were observed in the signal region, consistent with the background expectation. Upper limits on the production cross-sections are set at the 95% confidence level using the $CL_s$ method.

• $Z'$ Model: Limits are set for scalar masses ($m_S$) from 0.5 to 1.5 TeV and $Z'$ masses from 100 to 700 GeV. For a fixed $m_S$, lighter $Z'$ bosons are constrained to longer lifetimes, while heavier $Z'$ bosons are constrained to shorter lifetimes due to kinematic boosts.
• Gluino Model: For gluino masses ($m_{\tilde{g}}$) of 1.5 to 2.5 TeV and neutralino masses ($m_{\tilde{\chi}^0_1}$) from 0.1 to 1.7 TeV, the analysis excludes significant portions of the $\lambda_{121}$ and $\lambda_{122}$ coupling parameter space. For $m_{\tilde{g}} = 1.5$ TeV, lifetimes ($c\tau$) from 1 to 10,000 mm are excluded for most neutralino masses.
• EWkino Model: For neutralino masses from 0.1 to 1.3 TeV, the analysis excludes lifetimes from 1 mm up to several meters, depending on the mass and coupling. For $m_{\tilde{\chi}^0_1} \le 0.5$ TeV, the full range of considered lifetimes (1–10,000 mm) is excluded.

Significance
The paper claims this analysis sets leading limits on the production cross-sections for multiple models, including parameter space that has never been directly probed. Specifically, it provides the first limits on high-mass, long-lived neutralino models using gluino and electroweakino production modes with decays into lepton pairs (with the exception of gluino-produced neutralino decays into muons targeted in a previous muon-spectrometer-only search). The results complement previous searches by extending the mass reach and covering the full range of Run-2 data, offering a robust test of RPV SUSY and generic $Z'$ scenarios in the heavy LLP regime.