Search for squarks and gluinos in $pp$ collisions at $\sqrt{s} = 13$ TeV and $13.6$ TeV in events with $τ$-leptons, jets and missing transverse momentum using the ATLAS detector

Using the ATLAS detector, this paper presents a search for R-parity-conserving supersymmetry in proton-proton collisions at 13 and 13.6 TeV involving tau-leptons, jets, and missing transverse momentum, which excludes gluino masses below 2.25 TeV and squark masses up to 1.7 TeV based on 140 fb⁻¹ and 51.8 fb⁻¹ of data.

The Gist

The Big Picture: Looking for "Ghost" Particles

Imagine the universe is a giant, high-speed car race. The Large Hadron Collider (LHC) is the track, and the ATLAS detector is a massive, ultra-high-speed camera system that records every crash.

Physicists know the rules of the race very well; this rulebook is called the Standard Model. It explains how particles like electrons and quarks behave. But the rulebook has holes. It doesn't explain why gravity is so weak compared to other forces, or what Dark Matter (the invisible stuff holding galaxies together) actually is.

To fix these holes, scientists have a theory called Supersymmetry (SUSY). It's like a "shadow world" theory. It suggests that for every known particle (like a quark), there is a heavier, invisible "super-partner" (like a squark or gluino). If these super-partners exist, they would be the perfect candidates for Dark Matter.

The Mission: Catching the Shadows

The problem is, we've never seen these super-partners. If they exist, they are likely very heavy and decay (break apart) instantly into other particles.

This paper describes a search for a specific "signature" of these super-partners. The scientists are looking for a crash that produces:

1. Jets: Sprays of ordinary particles (like debris from a crash).
2. Tau Leptons: A specific, heavy type of particle (think of it as a "heavy electron").
3. Missing Transverse Momentum: This is the most important clue. In a normal crash, the debris flies out in all directions, balancing perfectly. If the camera sees debris flying one way but nothing flying the other way, it means something invisible flew off the track. In this theory, that "invisible something" is the Lightest Supersymmetric Particle (LSP), which is our candidate for Dark Matter.

The Strategy: Two Different Detective Styles

The team didn't just look at the data one way. They used two different detective styles to ensure they didn't miss anything.

1. The "Cut-and-Count" Approach (The Rigid Filter)
Imagine you are looking for a specific type of fish in a pond. You set up a net with very specific holes: "Only catch fish that are bigger than 5 inches, have red fins, and are swimming left."

• How it works: The scientists set strict rules (cuts) on the data. For example, "We only look at crashes where the missing energy is huge" or "We only look at crashes where the tau particle is moving very slowly."
• Why: This is great for finding specific, predictable patterns. They created different "nets" for different scenarios: one for "compressed" models (where the super-particles are close in mass) and one for "high mass" models.

2. The Machine Learning Approach (The Smart AI)
Imagine instead of setting strict rules, you hire a super-smart AI that has studied millions of photos of normal crashes and a few photos of "shadow" crashes.

• How it works: They fed the computer millions of simulated crashes. The AI learned to spot subtle patterns that humans might miss. It didn't just look at one number; it looked at the shape of the whole event.
• The Result: The AI gives every crash a "suspicion score" from 0 to 1. If the score is high, it's likely a shadow particle. If it's low, it's just a normal crash. This method is very inclusive and catches a wider variety of potential signals.

The Data: A Massive Library

The scientists didn't just look at a few crashes. They analyzed a massive library of data:

• 140 "Petabytes" of data (collected between 2015–2018).
• 51.8 "Petabytes" of data (collected between 2022–2023).
• They looked at three different "channels" (types of crashes):
  • Exactly one tau particle and no other light particles.
  • Exactly one tau particle and at least one other light particle (electron or muon).
  • Two or more tau particles.

The Challenge: The "Fake" Clues

One of the hardest parts of this job is distinguishing a real "tau particle" from a "fake tau."

• The Analogy: Imagine you are looking for a specific type of bird. But sometimes, a cloud looks like a bird, or a piece of trash looks like a bird.
• The Solution: The scientists used a "data-driven" method. They looked at areas of the data where they knew there were no shadow particles, counted how often clouds looked like birds, and used that math to estimate how many "fake birds" were in their main search area. This allowed them to subtract the noise and see the real signal.

The Results: The Silence of the Shadows

After running the numbers, checking the AI scores, and comparing the rigid filters against the data, the result was clear: They found nothing.

• No Ghosts: There were no significant deviations from the Standard Model. The number of "missing energy" events matched exactly what the known physics predicted.
• The Exclusion: While they didn't find the particles, they did find out where they aren't.
  • They can now say with 95% confidence that Gluinos (a type of super-partner) are not lighter than 2.25 TeV (a very heavy mass).
  • They can say Squarks are not lighter than 1.7 TeV.
  • They ruled out many specific combinations of masses for the "shadow" particles.

The Conclusion

Think of this search like looking for a needle in a haystack. The scientists didn't find the needle. However, by using better magnets (newer detectors), a bigger haystack (more data), and smarter search algorithms (Machine Learning), they were able to prove that the needle is not in the bottom half of the haystack.

They have pushed the boundaries of where we know these particles cannot exist, forcing theorists to rethink where to look next. The search continues, but the "easy" places to find these particles have been ruled out.

Technical Summary

Technical Summary: Search for Squarks and Gluinos in Events with $\tau$-Leptons, Jets, and Missing Transverse Momentum

Problem and Motivation
The Standard Model (SM) of particle physics, while experimentally robust, remains an incomplete effective theory. It fails to address the hierarchy problem, the fine-tuning of the Higgs potential, and the nature of dark matter. Supersymmetry (SUSY) offers a theoretical extension that introduces a symmetry between bosons and fermions, predicting superpartners for all known particles. In many SUSY scenarios, R-parity is conserved, implying that supersymmetric particles are produced in pairs and that the lightest supersymmetric particle (LSP) is stable, serving as a viable dark matter candidate.

This paper presents a search for R-parity-conserving SUSY, specifically targeting the pair production of gluinos ($\tilde{g}$) and first- or second-generation left-handed squarks ($\tilde{q}$). The analysis focuses on decay chains where these particles cascade through intermediate states ($\tilde{\chi}^{\pm}_1$, $\tilde{\chi}^0_2$) into $\tau$-sleptons ($\tilde{\tau}$) or $\tau$-sneutrinos ($\tilde{\nu}_{\tau}$), which subsequently decay into the LSP ($\tilde{\chi}^0_1$) and a SM $\tau$-lepton or $\nu_{\tau}$. This results in final states characterized by hadronically decaying $\tau$-leptons, jets, and significant missing transverse momentum ($E^{\text{miss}}_T$). Previous searches by ATLAS (2015–2016) and CMS (2011) excluded gluino masses below 2 TeV and 1.15 TeV, respectively. This analysis aims to extend these limits using the full Run 2 dataset and early Run 3 data, leveraging improved reconstruction techniques and advanced analysis strategies.

Methodology
The analysis utilizes proton-proton collision data collected by the ATLAS detector at center-of-mass energies of $\sqrt{s} = 13$ TeV (2015–2018, 140 fb$^{-1}$) and $\sqrt{s} = 13.6$ TeV (2022–2023, 51.8 fb$^{-1}$).

• Event Selection and Channels: Events are required to pass a preselection of $E^{\text{miss}}_T > 200$ GeV, at least one hadronically decaying $\tau$-lepton, and at least two jets (one with $p_T > 120$ GeV). The search is divided into three orthogonal channels based on lepton content:

  1. 1tau0lep: Exactly one hadronic $\tau$, no electrons or muons.
  2. 1tau1lep: Exactly one hadronic $\tau$ and at least one electron or muon.
  3. 2tau: Two or more hadronic $\tau$-leptons.

• Analysis Strategies: Two independent approaches are employed and combined statistically:

  1. Machine-Learning (ML) Approach: A multi-class classification using Boosted Decision Trees (XGBoost) is trained to distinguish signal from SM backgrounds (including $W$+jets, $Z$+jets, dibosons, Top, and fake $\tau$s). The entire phase space is utilized, with Signal Regions (SRs) defined by high classifier scores (>0.75–0.8). This approach captures correlations between variables without imposing hard kinematic cuts.
  2. Cut-and-Count Approach: Traditional selection cuts are applied to define SRs optimized for specific signal topologies. This includes "Compressed" SRs (targeting low mass splittings $\Delta m$ with soft $\tau$-leptons) and "High Mass" SRs (targeting large mass splittings). Kinematic variables such as $E^{\text{miss}}_T$, $H_T$, and transverse masses ($m_T$, $m_{T2}$) are used for binning.

• Background Estimation:

  • Top and Diboson: Estimated using Monte Carlo (MC) simulations normalized to data in dedicated Control Regions (CRs).
  • Fake $\tau$s (Jets misidentified as $\tau$): Estimated using a data-driven Universal Fake Factor (UFF) approach. Fake factors are measured in dedicated regions (Multijet, $Z(\ell\ell)$, $W(\mu\nu)$) and applied to anti-identification regions in the analysis.
  • Systematic Uncertainties: A comprehensive set of uncertainties is considered, including detector calibration (jets, $\tau$s, leptons), luminosity, pile-up, theoretical modeling (PDFs, scale variations), and statistical uncertainties in data-driven methods.

• Statistical Analysis: A simultaneous likelihood fit (using HistFitter/pyhf) is performed across all CRs, Validation Regions (VRs), and SRs. Background-only fits are used to validate modeling, while model-dependent fits (CL$_s$ prescription) are used to set exclusion limits on simplified SUSY models.

Key Contributions

• Combined Run 2 and Run 3 Data: This is the first ATLAS search in this channel to combine the full Run 2 dataset with early Run 3 data at 13.6 TeV, significantly increasing statistical power.
• Dual-Strategy Approach: The simultaneous use of ML-based and cut-and-count strategies allows for optimal sensitivity across different regions of the SUSY parameter space. The ML approach excels in high-mass regions, while the cut-and-count approach, with its dedicated compressed SRs, is superior for low mass-splitting scenarios.
• Advanced Background Modeling: The implementation of the UFF method for fake $\tau$ estimation and the use of multi-class BDTs for signal/background separation represent a refinement over previous iterations.
• Comprehensive Channel Combination: The statistical combination of the 1tau0lep, 1tau1lep, and 2tau channels maximizes sensitivity to various decay topologies.

Results
No significant deviations from the SM predictions were observed in any of the signal regions. The largest local excess had a significance of less than $2\sigma$.

• Exclusion Limits:

  • Gluino Models: Gluino masses ($m_{\tilde{g}}$) up to 2.25 TeV are excluded for LSP masses ($m_{\tilde{\chi}^0_1}$) up to 1.35 TeV. In the compressed region, models with $\Delta m(\tilde{g}, \tilde{\chi}^0_1) > 150$ GeV are excluded.
  • Squark Models: Squark masses ($m_{\tilde{q}}$) up to 1.7 TeV are excluded for LSP masses up to 0.85 TeV. In the compressed region, models with $\Delta m(\tilde{q}, \tilde{\chi}^0_1) > 130$ GeV are excluded.
  • Comparison: These limits represent a significant improvement over previous searches (e.g., the 2015–2016 analysis), primarily driven by the larger dataset, improved $\tau$-lepton identification, and the inclusion of ML techniques.

• Model-Independent Limits: Upper limits on the visible cross-section ($\sigma_{\text{vis}}$) for new physics processes in specific SRs were set, ranging from 0.02 to 0.31 fb at 95% confidence level.

Significance
The paper concludes that the search places the most stringent limits to date on simplified SUSY models involving gluino or squark pair production with $\tau$-rich cascade decays. The absence of a signal constrains the parameter space for R-parity-conserving SUSY, particularly ruling out lighter gluino and squark scenarios that were previously accessible. The study demonstrates the effectiveness of combining traditional cut-based methods with machine learning and utilizing early Run 3 data to probe higher mass scales and more compressed spectra. The results are interpreted within the context of simplified models but are noted to be applicable to other SUSY frameworks (such as NUHM, mSUGRA, or GMSB) that produce similar final states.