Search for direct pair production of top squarks in $pp$ collisions at $\sqrt{s}= 13$ TeV and $13.6$ TeV in events with two oppositely charged leptons using the ATLAS detector

Using the full Run 2 and early Run 3 datasets from the ATLAS detector, this study searches for direct top squark pair production in events with two oppositely charged leptons, $b$-jets, and missing transverse momentum, finding no significant excess over Standard Model predictions and setting improved 95% confidence level mass limits of up to 1060 GeV for top squarks and 560 GeV for neutralinos.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful smashing machine. It takes two tiny particles (protons) and smashes them together at nearly the speed of light, creating a chaotic explosion of energy. Usually, this explosion produces particles we know and understand, like the building blocks of the universe (Standard Model).

But physicists suspect there are invisible "ghosts" hiding in the debris—particles from a theory called Supersymmetry (SUSY). One of the most important ghosts they are looking for is the Top Squark (or stop). Think of the Top Squark as the "shadow twin" of the heaviest known particle, the Top Quark. If these twins exist, they could explain why the universe has mass and why gravity is so weak compared to other forces.

This paper is the report card from the ATLAS experiment, a giant detector that acts like a 360-degree security camera around the smash zone. Here is what they did, explained simply:

1. The Hunt: Catching the Ghosts

The scientists are looking for a very specific scenario:

• The Setup: Two Top Squarks are created in the crash.
• The Decay: They immediately fall apart (decay) into a regular Top Quark and a Neutralino.
• The Ghost: The Neutralino is the "Lightest Supersymmetric Particle" (LSP). It is invisible to our detectors, like a ghost that walks right through walls. Because it disappears, it carries away energy, leaving a "missing" gap in the energy balance of the crash.
• The Clues: Since the Top Quarks also break apart, they leave behind a trail of debris: two charged particles (like electrons or muons, which are like heavy cousins of electrons) and jets (sprays of particles from heavy quarks).

So, the team is looking for a crash that leaves behind: Two charged particles + some heavy debris + a big "missing energy" hole.

2. The Challenge: Finding a Needle in a Haystack

The problem is that the Standard Model (the known physics) produces similar-looking debris all the time. It's like trying to find a specific rare coin in a pile of billions of ordinary coins. The "background noise" from normal particle crashes is overwhelming.

To solve this, the ATLAS team didn't just use a magnifying glass; they built a super-smart AI detective.

3. The New Tool: The AI Detective

In this paper, the scientists used Machine Learning (specifically Neural Networks) to act as a filter.

• Training: They fed the AI millions of simulated crashes. Some were the "normal" background noise, and some were the "signal" (the Top Squark ghosts).
• The Lesson: The AI learned to spot subtle patterns that human eyes would miss. It looked at the angles, speeds, and energy levels of the particles to decide: "Is this a boring normal crash, or is this the rare ghost we are looking for?"
• The Result: This AI is much better at distinguishing the signal from the noise than previous methods, allowing them to look deeper into the data than ever before.

4. The Data: A Massive Library

They didn't just look at one day of data. They combined:

• The Run 2 Collection (2015–2018): 140 units of data (femtobarns).
• The Run 3 Collection (2022–2023): 53 units of data.
  This is like reading every book in a massive library to find a single sentence written in invisible ink.

5. The Verdict: No Ghosts Found (Yet)

After running their AI detective over all this data, the result was: No significant excess.

• The number of "ghost" events they saw matched exactly what the Standard Model predicted for normal background noise.
• There were no mysterious spikes that would prove the Top Squark exists.

6. The Silver Lining: Pushing the Boundary

Even though they didn't find the Top Squark, this is a huge success.

• Ruling Out Possibilities: Because they didn't find it, they can now say with 95% confidence: "If Top Squarks exist, they must be heavier than 1,060 GeV."
• The Analogy: Imagine you are looking for a specific type of fish in a lake. You don't find it. But by using better nets (the AI) and checking more water (more data), you can now say, "We are sure this fish isn't in the shallow water or the middle depths. If it's there, it must be hiding in the very deepest, darkest trenches."
• Improvement: They pushed the "depth limit" (mass limit) by about 10% compared to previous searches. They also proved that the AI approach works incredibly well, even for heavy particles.

Summary

The ATLAS collaboration used a massive dataset and a new, smart AI system to hunt for the "shadow twin" of the Top Quark. They didn't find the twin, but they successfully ruled out the possibility of it being "light." They have effectively told the universe: "If you are hiding these particles, they are heavier and harder to find than we thought." This narrows the search for the next big discovery in physics.

Technical Summary

1. Problem and Physics Motivation

The paper addresses the search for Supersymmetry (SUSY), specifically focusing on the direct pair production of top squarks ($\tilde{t}_1$), the scalar superpartners of the top quark.

• Theoretical Context: In the Minimal Supersymmetric Standard Model (MSSM), top squarks are theoretically motivated to cancel the large quadratically divergent loop corrections to the Higgs boson mass, solving the hierarchy problem.
• Decay Channel: The analysis targets the decay chain $\tilde{t}_1 \to t \tilde{\chi}^0_1$, where the top squark decays into an on-shell top quark ($t$) and the lightest neutralino ($\tilde{\chi}^0_1$), which is assumed to be the stable Lightest Supersymmetric Particle (LSP) and a dark matter candidate.
• Final State: The top quarks decay further ($t \to Wb$), and the $W$ bosons decay leptonically. The signature is a final state containing:
  • Two oppositely charged leptons ($e$ or $\mu$).
  • $b$-jets (from the top decays).
  • Large missing transverse momentum ($E_T^{miss}$) from the undetected neutralinos.
• Challenge: This channel is sensitive to models with massive neutralinos but suffers from significant Standard Model (SM) backgrounds, primarily $t\bar{t}$ and $t\bar{t}Z$ production.

2. Methodology

Data and Simulation

• Datasets: The analysis combines the full LHC Run 2 dataset (2015–2018, $\sqrt{s}=13$ TeV, 140 fb$^{-1}$) and the early LHC Run 3 dataset (2022–2023, $\sqrt{s}=13.6$ TeV, 53 fb$^{-1}$).
• Event Selection:
  • Triggers: Single-electron or single-muon triggers with $p_T$ thresholds ranging from 20–26 GeV.
  • Preselection: Events must contain two opposite-sign leptons ($p_T > 27$ GeV for leading, $>20$ GeV for subleading), at least two jets (one $b$-tagged), and $m_{\ell\ell} > 20$ GeV to reject low-mass resonances.
  • Kinematic Cuts: A preselection on the stransverse mass ($m_{T2}^{\ell\ell}$) is applied to restrict the phase space to the signal region, with thresholds varying by mass-splitting category (80–100 GeV).

Machine Learning Strategy

A novel aspect of this analysis is the use of six Neural Networks (NNs) to enhance signal discrimination:

• Categorization: Signal models are grouped into three categories based on the mass splitting $\Delta m(\tilde{t}_1, \tilde{\chi}^0_1)$: Low (200–300 GeV), Medium (300–500 GeV), and High ($\ge$600 GeV).
• Network Architecture: Two NNs are trained for each category (one for events with exactly one $b$-jet, one for $\ge$ two $b$-jets).
• Inputs: The NNs utilize kinematic variables ($p_T, \eta, \phi$) of leptons and jets, $b$-tagging scores, $E_T^{miss}$ and its significance, angular separations ($\Delta\phi$), transverse masses ($m_T$), and the variable $p_T^{\ell\ell, \text{boost}}$.
• Training: The networks are trained using Keras/TensorFlow on simulated samples of the dominant backgrounds ($t\bar{t}$, $t\bar{t}Z$) and signal models. The output is a signal score (0 to 1).

Background Estimation

• Data-Driven Normalization: The dominant backgrounds ($t\bar{t}$ and $t\bar{t}Z$) are normalized using a simultaneous profile likelihood fit in dedicated Control Regions (CRs).
  • $t\bar{t}$ CRs: Defined by lower NN signal scores and specific $b$-jet multiplicities.
  • $t\bar{t}Z$ CR: A unique three-lepton final state is used to isolate $t\bar{t}Z$ events with invisible $Z$ decays, utilizing a corrected $E_T^{miss}$ variable ($E_T^{miss, \text{corr}}$).
• Validation: Validation Regions (VRs) disjoint from CRs and Signal Regions (SRs) are used to verify the background modeling.
• Systematic Uncertainties: Major uncertainties include Jet Energy Scale/Resolution (JES/JER), $b$-tagging efficiency, theoretical modeling (ISR/FSR), and luminosity (0.83% for Run 2, 2% for Run 3).

Signal Regions (SRs)

Signal regions are defined by applying a high threshold on the NN signal score (e.g., $>0.93$ for Low-$\Delta m$ with 1 $b$-jet) in addition to the preselection. The analysis uses a "best-expected" approach, selecting the category (Low/Medium/High) that offers the highest sensitivity for each specific mass point.

3. Key Contributions

1. Run 3 Integration: This is one of the first ATLAS analyses to incorporate Run 3 data (13.6 TeV), demonstrating the detector's performance at higher pile-up and center-of-mass energies.
2. Machine Learning Enhancement: The implementation of category-specific Neural Networks significantly improves the separation between the complex $t\bar{t}$ background and the SUSY signal across a wide kinematic phase space.
3. Improved Sensitivity: The combination of increased luminosity, Run 3 data, and ML techniques yields a ~50% improvement in expected sensitivity for a benchmark point (1 TeV $\tilde{t}_1$, 400 GeV $\tilde{\chi}^0_1$) compared to previous Run 2-only analyses.
4. Comprehensive Background Control: The use of a dedicated three-lepton control region for $t\bar{t}Z$ and a robust simultaneous fit across Run 2 and Run 3 datasets provides precise background constraints.

4. Results

• Observation: No significant excess of events over the Standard Model prediction was observed in any Signal Region. The data is consistent with SM expectations within uncertainties.
• Exclusion Limits (95% CL):
  • Massless Neutralino: Top squark masses up to 1060 GeV are excluded. This represents an improvement of approximately 100 GeV (or ~10%) over previous ATLAS results in the same channel.
  • Massive Neutralino: For a top squark mass of 900 GeV, neutralino masses up to 560 GeV are excluded.
• Model-Independent Limits: Upper limits on the visible cross-section ($\sigma_{vis}$) were set for various discovery SRs, providing constraints applicable to generic new physics models.

5. Significance

This analysis represents a significant step forward in the search for natural SUSY. By extending the mass reach to 1.06 TeV, it places stringent constraints on the parameter space where top squarks could naturally solve the hierarchy problem. The successful integration of Run 3 data and advanced machine learning techniques demonstrates the ATLAS detector's capability to probe higher mass scales and more complex kinematic scenarios as the LHC enters the high-luminosity era. The results effectively rule out the simplest scenarios of light top squarks decaying directly to on-shell tops and light neutralinos, pushing the boundary of SUSY searches into the multi-TeV regime.