Search for Beyond the Standard Model physics with anomaly detection in multilepton final states in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Using 140 fb$^{-1}$ of ATLAS Run 2 data, this model-agnostic search for Beyond the Standard Model physics in multilepton final states employs unsupervised machine learning to identify anomalies, finding no significant excess and setting new limits on various benchmark models, including the first constraints on a flavourful vector-like lepton model.

The Gist

The Big Picture: Looking for Ghosts in a Crowded Room

Imagine the Large Hadron Collider (LHC) at CERN is a massive, high-speed dance party. Every second, billions of protons (the guests) crash into each other. Most of the time, the party follows a strict, predictable script called the Standard Model. We know exactly how the music plays, how people dance, and what snacks are served.

But physicists suspect there are "ghosts" at the party—new, exotic particles that don't follow the rules. These are the Beyond the Standard Model (BSM) particles. The problem is, we don't know what these ghosts look like, where they hide, or what they wear. If we only look for ghosts wearing red hats, we might miss the ones wearing blue hats.

This paper is about a new way to find the ghosts. Instead of looking for a specific costume, the ATLAS team set up a "smart security system" that looks for anything that feels out of place.

The Strategy: The "Outlier" Detector

Usually, scientists search for new physics by building a specific trap. "If the ghost is a vampire, it will avoid sunlight." They build a trap for vampires. But what if the ghost is a werewolf? They miss it.

In this paper, the team used a technique called Anomaly Detection (AD). Think of it like a bouncer at a club who has memorized the behavior of 140,000 regular partygoers (the Standard Model data).

• The Training: The bouncer watches thousands of videos of normal dancing. He learns the "normal" rhythm.
• The Search: When a new guest walks in, the bouncer doesn't ask, "Are you a vampire?" Instead, he asks, "Does your dancing feel weird compared to everyone else?"
• The Result: If someone is doing a backflip when everyone else is doing the cha-cha, the bouncer flags them as an anomaly.

This paper is the first time this "bouncer" technique has been used on events with four or more light particles (leptons). Usually, these searches are done with jets (sprays of particles), but looking at clean, high-energy particles like electrons and muons is like looking for a needle in a haystack where the haystack is made of gold.

The "Needle" They Were Looking For

The team focused on events with at least four light leptons (electrons or muons).

• The Analogy: Imagine the Standard Model is a factory that usually produces boxes with 2 or 3 items inside. Occasionally, due to a glitch, it produces a box with 4 items.
• The Goal: They wanted to see if the factory ever produced a box with 4 items that looked strange (e.g., the items were arranged in a weird pattern, or the box was the wrong color).
• The Models: They also tested specific "suspects" to see if their bouncer could catch them:
  • Vector-Like Leptons (VLLs): Heavy, exotic cousins of electrons.
  • Supersymmetry (SUSY): A theory suggesting every particle has a "super-partner."
  • Flavorful VLLs: A new, complex model where these heavy particles can change their "flavor" (type) when they decay.

The Investigation Process

1. The Data: They looked at 140 inverse femtobarns of data. That's a fancy way of saying they analyzed a massive amount of collision data collected between 2015 and 2018.
2. The Machine Learning: They used a type of AI called Normalizing Flows. Imagine this as a super-smart artist who draws a map of "normal" particle behavior. If a particle event falls outside the map (in the "weird" zones), it gets a high "Anomaly Score."
3. The Sorting: They split the data into different rooms based on the "topology" (how the particles are arranged).
   • Room A: 4 particles, total charge zero.
   • Room B: 4 particles, total charge positive or negative.
   • Room C: 5 or more particles.
4. The Check: They compared the real data against their "normal" map.

The Verdict: No Ghosts Found (Yet)

After running the bouncer through the entire party:

• The Result: The bouncer found no significant anomalies.
• The Translation: The data matched the Standard Model predictions perfectly. There were no "weird dancers" that stood out from the crowd.
• The Significance: While finding nothing might sound disappointing, in physics, ruling things out is a huge victory. It tells us that the "ghosts" we were looking for either don't exist, or they are hiding in a part of the party we haven't checked yet.

Why This Matters

Even though they didn't find new physics, this paper is a milestone for two reasons:

1. New Tool: It proved that Anomaly Detection works in complex, multi-particle environments. It's like proving a metal detector works not just on beaches, but also in a busy airport. This opens the door for future searches where we don't need to guess what the new physics looks like.
2. Firsts: They set the first-ever limits on a specific model called "Flavorful Vector-Like Leptons." They essentially said, "If these particles exist, they must be heavier than X, because we would have seen them by now."

The Bottom Line

The ATLAS team threw a massive net into the ocean of particle collisions, looking for anything that didn't fit the usual pattern. They didn't catch any new fish, but they proved their net is strong and smart enough to catch almost anything. This gives them confidence that if the "ghosts" of new physics are out there, their next generation of nets will find them.

In short: The party is still following the script, but the bouncers are now much smarter, and they are ready for whatever surprise guest arrives next.

Technical Summary

1. Problem Statement

The Standard Model (SM) of particle physics, while highly successful, fails to explain several fundamental phenomena, including the hierarchy of fermion masses, neutrino masses, dark matter, and the matter-antimatter asymmetry. Traditional searches for Beyond the Standard Model (BSM) physics at the Large Hadron Collider (LHC) are typically model-dependent, targeting specific signatures predicted by theoretical frameworks (e.g., Supersymmetry or Vector-Like Leptons). However, without a clear theoretical direction, these targeted searches may miss novel BSM signatures that do not fit pre-defined topologies.

This paper addresses the need for a model-agnostic search strategy. Specifically, it targets final states with at least four light leptons (electrons or muons), a channel characterized by low SM background but high sensitivity to exotic high-mass particle decays. The challenge lies in identifying rare, anomalous events within a high-dimensional feature space without assuming a specific signal model.

2. Methodology

The analysis utilizes the full Run 2 dataset of the ATLAS detector, corresponding to an integrated luminosity of 140 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV. The methodology is divided into two parallel approaches: Model-Independent and Model-Dependent searches, both utilizing Anomaly Detection (AD) techniques.

A. Event Selection and Reconstruction

• Trigger: Events are selected using single-lepton or dilepton triggers depending on the final state multiplicity.
• Objects: Light leptons ($e, \mu$) are reconstructed with strict identification and isolation criteria. Jets are reconstructed using the anti-$k_t$ algorithm ($R=0.4$) and calibrated. $b$-tagging is performed using a deep-learning neural network.
• Categories: Selected events are categorized into three orthogonal final states:
  1. $4\ell$ with total charge $Q=0$.
  2. $4\ell$ with total charge $Q=\pm 2$.
  3. $\ge 5\ell$.
• Sub-categorization: Regions are further split based on the number of $Z$-boson candidates (lepton pairs with invariant mass near 91.2 GeV), $b$-jet multiplicity, and lepton flavor composition.

B. Anomaly Detection (AD) Technique

The core innovation is the use of Unsupervised Machine Learning, specifically Normalizing Flows (RealNVP architecture), to perform outlier detection.

• Training: The flow is trained exclusively on simulated SM background events within specific search regions. It learns the probability density function $p(x)$ of the background in a high-dimensional feature space.
• Input Variables: The model uses physically motivated high-level variables, including:
  • Transverse momenta sums ($H_{T}^{lep}$, $H_{T}^{jets}$).
  • Missing transverse energy ($E_{T}^{miss}$).
  • Invariant masses of lepton pairs and systems ($m(4\ell)$, $m(Z)$, $m(\ell\ell)$).
  • Transverse masses ($m_T$).
  • A pseudo-continuous $b$-tagging score sum.
• Anomaly Score: Events are assigned a score $s(x)$ based on the log-probability density relative to the background distribution. High scores indicate events that are "out-of-distribution" (rare or anomalous).
• Binning:
  • Model-Independent: The anomaly score distribution is split into overlapping signal bins (e.g., top 0.1%, 1%, 10% of events) to scan for excesses without bias.
  • Model-Dependent: The score distribution is binned to maximize sensitivity to specific benchmark models.

C. Background Estimation

Backgrounds are estimated using Monte Carlo (MC) simulations (e.g., $ZZ$, $t\bar{t}Z$, $VVV$, $t\bar{t}$) normalized to data using a simultaneous profile likelihood fit.

• Control Regions (CRs): Five orthogonal CRs are defined to constrain background normalizations:
  • $WZ/t\bar{t}Z$ (enriched in $WZ$ and $t\bar{t}Z$).
  • Conversions (enriched in photon conversions).
  • $HFe$, $HF\mu$ (enriched in heavy-flavor non-prompt leptons).
  • $LFe$ (enriched in light-flavor non-prompt leptons).
• Systematics: Extensive systematic uncertainties are included, covering luminosity, lepton/jet reconstruction, $b$-tagging, and theoretical modeling (scale variations, PDFs, parton shower matching).

3. Key Contributions

1. First AD Search in Multilepton Final States: This is the first time anomaly detection using normalizing flows has been applied to multilepton ($\ge 4\ell$) channels at the LHC. Previous AD searches were predominantly focused on jet-heavy final states.
2. Model-Agnostic Framework: The analysis demonstrates a robust method to search for BSM physics without assuming a specific signal topology, effectively casting a "wide net" over the phase space.
3. Flavorful Vector-Like Lepton (VLL) Limits: The paper presents the first-ever exclusion limits on the "flavorful VLL" model, where VLLs decay via a new scalar $S_{ji}$ allowing for lepton-flavor-violating decays and high lepton multiplicities.
4. Dual-Strategy Analysis: The simultaneous execution of model-independent (discovery) and model-dependent (benchmark) searches allows for both broad sensitivity and specific constraints on benchmark scenarios.

4. Results

• Observation: No significant excess of events above the Standard Model expectation was observed in any of the signal regions. The data is consistent with the background-only hypothesis.
• Global Significance: The largest local excesses were found in the $Q=\pm 2$ and $0Z$ $2SFOS$ regions, corresponding to a local significance of $2\sigma$. After accounting for the "look-elsewhere effect," the global significance is 0.90$\sigma$.
• Model-Independent Limits: Exclusion limits on the visible cross-section ($\sigma_{vis}$) were set for each model-independent signal bin. The search is dominated by statistical uncertainties due to the low event yields in high-multiplicity lepton channels.
• Model-Dependent Limits (95% CL):
  • Vector-Like Leptons (VLLs):
    • $SU(2)$ Singlet VLL ($VLL^S_e$): Excluded up to 290 GeV.
    • $SU(2)$ Doublet VLL ($VLL^D_e$): Excluded up to 925 GeV.
    • $VLL^S_\mu$: Excluded up to 320 GeV.
    • $VLL^D_\mu$: Excluded up to 850 GeV.
    • Flavorful VLLs: Excluded up to 1300 GeV ($VLL^e$) and 1280 GeV ($VLL^\mu$) for a wide range of scalar masses.
  • Supersymmetry (SUSY):
    • Wino-like Charginos/Neutralinos: Excluded up to 1600 GeV.
    • Smuons: Excluded up to 495 GeV (for $\Delta m > 140$ GeV), showing improved sensitivity over previous dedicated searches in specific mass splitting regions.

5. Significance

This work represents a significant step forward in the ATLAS BSM search program by successfully integrating unsupervised machine learning into a complex, low-background multilepton channel.

• Validation of AD: It proves that normalizing flows can effectively identify anomalous kinematic regions in high-dimensional data without prior knowledge of the signal, complementing traditional cut-based and model-specific searches.
• New Physics Reach: By setting the first limits on the flavorful VLL model, the analysis opens a new window for testing BSM theories that involve lepton flavor violation and new scalars.
• Future Prospects: The model-independent results provide a benchmark for future reinterpretations. As the LHC moves to Run 3 and the High-Luminosity LHC (HL-LHC), these AD techniques will become increasingly powerful for discovering unexpected physics in the high-multiplicity lepton sector.