Search for long-lived charginos and $τ$-sleptons using final states with a disappearing track in $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

Using 137 fb$^{-1}$ of 13 TeV proton-proton collision data from the ATLAS detector, this study searches for long-lived charginos and $\tau$-sleptons via disappearing tracks and sets 95% confidence level lower mass limits of up to 880 GeV for wino charginos and 320 GeV for $\tau$-sleptons, finding no significant excess over Standard Model background predictions.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Scientists at CERN's ATLAS detector are like detectives at a massive crime scene, smashing protons together at near-light speed to see what "debris" flies out. Usually, they are looking for heavy, stable particles that leave clear footprints. But in this specific paper, they are hunting for something much sneakier: ghosts that vanish mid-step.

Here is the story of their search, explained simply.

The Mystery: The "Disappearing Track"

In the world of physics, some theories suggest the existence of "Supersymmetry" (SUSY). This theory predicts that every known particle has a heavier, invisible partner.

The detectives are looking for two specific types of these partners:

1. Charginos: Heavy, charged particles.
2. Staus (𝜏-sleptons): Heavy partners of the tau lepton.

The Catch: These particles are unstable, but they don't die instantly. They live for a tiny fraction of a second (nanoseconds).

• The Analogy: Imagine a runner sprinting through a stadium. Usually, they run the whole track. But imagine a runner who trips and falls after just 10 meters, then instantly turns into a ghost and vanishes.
• The Signature: In the detector, these particles leave a short, straight line of "footprints" (hits in the silicon sensors) and then stop. The track just ends. This is called a "disappearing track."

The Challenge: Finding a Needle in a Haystack

The problem is that the detector is full of "noise."

• The Haystack: Real particles (like electrons or protons) sometimes get knocked off course by the detector's material, or random sensor glitches happen. These can look like a track that stops, even though no new physics occurred.
• The Needle: The real signal is a very specific type of short track that doesn't connect to a big energy explosion in the calorimeters (the part of the detector that stops particles).

To find the needle, the team had to get creative:

1. Looking for Shorter Tracks: Previous searches only looked for tracks that hit 4 layers of sensors. This team developed a new algorithm to find tracks that only hit 3 layers. This is like looking for a runner who only took three steps before vanishing, rather than waiting for them to take four.
2. The "Soft" Pion: When a chargino vanishes, it sometimes spits out a tiny, low-energy particle called a pion. It's so weak that standard detectors ignore it. The team used a Machine Learning AI (a "Boosted Decision Tree") to act like a super-smart bloodhound, sniffing out these faint, low-energy pions that usually get lost in the noise.

The Strategy: The "Missing Money" Trick

How do you know a ghost is there if you can't see it? You look for what's missing.

• The Setup: When these heavy particles are created, they usually recoil against a high-speed jet of ordinary matter (like a cannonball firing a bullet).
• The Clue: The heavy particle (the chargino or stau) turns into a ghost (a neutralino or gravitino) and flies away undetected. This creates a massive imbalance in momentum.
• The Analogy: Imagine two people on ice skates pushing off each other. If one person suddenly vanishes, the other person will slide backward. The detectives look for that "slide" (Missing Transverse Momentum) combined with the short, disappearing track.

The Results: No Ghosts Found (Yet)

After analyzing a massive amount of data (137 "inverse femtobarns," which is a huge number of collisions), the team looked at their four main search zones:

1. Zone 1 & 2: Tracks with 4 sensor hits.
2. Zone 3 & 4: Tracks with 3 sensor hits (the new, shorter ones), with and without the "soft pion."

The Verdict:

• No significant excess: The number of "disappearing tracks" they found matched exactly what they expected from normal background noise. They didn't find any ghosts.
• Setting Limits: Even though they didn't find new particles, they set strict boundaries. They can now say with 95% confidence:
  • If Wino-like charginos exist, they must be heavier than 880 GeV (if they live for about 1 nanosecond).
  • If Higgsino-like charginos exist, they must be heavier than 225 GeV (if they live for a very short time).
  • If Staus exist, they must be heavier than 320 GeV.

Why This Matters

Think of this like searching for a specific type of fish in an ocean.

• Before: We knew the fish might be anywhere from 10cm to 10 meters long.
• Now: We have scanned the ocean with better nets and sonar. We didn't find the fish, but we can now say, "If that fish exists, it cannot be smaller than 880cm."

This narrows the search for the next generation of physicists. It tells us that if Supersymmetry is real, these specific particles are heavier and harder to catch than we hoped. The search continues, but the "easy" spots have been checked off the list.

In summary: The ATLAS team used smarter algorithms and AI to look for particles that vanish after a few steps. They didn't find them, but they successfully pushed the "No Entry" sign further out into the universe, telling us exactly where these particles aren't.

Technical Summary

Here is a detailed technical summary of the ATLAS paper "Search for long-lived charginos and $\tilde{\tau}$-sleptons using final states with a disappearing track in $pp$ collisions at $\sqrt{s}=13$ TeV."

1. Problem and Motivation

The search targets Supersymmetry (SUSY), a theoretical framework proposing a partner for every Standard Model (SM) particle. Specifically, it investigates scenarios where the lightest supersymmetric particles (LSPs) are stable and weakly interacting, serving as Dark Matter candidates.

• The Signature: In specific SUSY models (Wino-like, Higgsino-like, and certain $\tilde{\tau}$-slepton scenarios), the next-to-lightest supersymmetric particle (NLSP) is a charged particle (chargino $\tilde{\chi}^\pm_1$ or stau $\tilde{\tau}$) that is nearly mass-degenerate with the LSP.
• The Decay: Due to the small mass splitting ($\Delta m \sim 100-300$ MeV), the charged particle has a long lifetime ($\tau \sim 0.01 - 10$ ns). It travels a short distance (millimeters to centimeters) through the inner detector before decaying into a neutral LSP (escaping detection) and a very low-momentum charged pion (or $\tau$-lepton).
• The "Disappearing Track": The charged particle leaves a track in the innermost pixel layers of the detector but decays before reaching the outer tracking layers (SCT/TRT). This results in a "disappearing track" (or tracklet) with missing transverse momentum ($E_T^{miss}$) and typically a high-$p_T$ jet from Initial State Radiation (ISR) to trigger the event.
• Challenge: Previous searches required tracks with hits in four pixel layers, limiting sensitivity to longer lifetimes. This analysis aims to probe shorter lifetimes (specifically the Higgsino region) by reconstructing tracks with only three pixel hits and identifying the low-momentum decay products.

2. Methodology

Data and Simulation

• Dataset: 137 fb$^{-1}$ of proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the ATLAS detector during LHC Run 2 (2015–2018).
• Signal Models:
  • Wino-like Charginos: Mass splitting $\sim 160$ MeV, lifetime $\sim 0.2$ ns.
  • Higgsino-like Charginos: Mass splitting $\sim 300$ MeV, lifetime $\sim 0.026-0.048$ ns.
  • $\tilde{\tau}$-sleptons: CMSSM-inspired (decay $\tilde{\tau} \to \tau \tilde{\chi}^0_1$) and GMSB-inspired (decay $\tilde{\tau} \to \tau \tilde{G}$) scenarios.
• Simulation: Signal samples generated with MadGraph5_aMC@NLO and Pythia 8. Backgrounds modeled using data-driven methods and MC (Sherpa for $V$+jets).

Event Reconstruction and Selection

• Tracklet Algorithm: A dedicated algorithm reconstructs short tracks using hits in the three innermost pixel layers (IBL, Layer 1, Layer 2).
  • 3-layer Tracklets: Target very short lifetimes (Higgsino region).
  • 4-layer Tracklets: Target longer lifetimes (Wino region).
  • Veto: Tracks extending into the SCT or TRT are vetoed to ensure the particle "disappeared."
• Low-Energy Pion Reconstruction: For chargino decays ($\tilde{\chi}^\pm_1 \to \pi^\pm \tilde{\chi}^0_1$), the pion has very low momentum ($p_T \sim 250-350$ MeV).
  • A Boosted Decision Tree (BDT) machine learning algorithm is trained to identify these "soft tracks" (reconstructed from SCT hits) associated with the tracklet, distinguishing them from random noise or fake tracks.
• Signal Regions (SRs): Four orthogonal regions are defined based on tracklet layers and pion presence:
  • SR4High / SR4Mid: Require 4-layer tracklets. Distinguished by $E_T^{miss}$ thresholds (>300 GeV vs 150–300 GeV).
  • SR3High1$\pi$: Requires 3-layer tracklet + at least one low-energy charged pion ($E_T^{miss} > 240$ GeV).
  • SR3High0$\pi$: Requires 3-layer tracklet + veto on low-energy pions ($E_T^{miss} > 280$ GeV).
• General Cuts: Zero leptons, $\ge 1$ jet ($p_T > 100$ GeV), large azimuthal separation between the jet and $E_T^{miss}$.

Background Estimation

All backgrounds are estimated using data-driven methods to minimize reliance on simulation:

1. Fake Tracklets (Dominant): Arise from random pixel hits or pile-up. Estimated using Template Regions (TRs) with inverted $E_T^{miss}$ and large impact parameter selections, corrected by Transfer Factors (TFs) derived from data.
2. Electron/Muon Backgrounds: Arise from bremsstrahlung or interactions causing standard tracks to fail reconstruction and appear as tracklets. Estimated using $Z \to ee$ and $Z \to \mu\mu$ tag-and-probe methods to derive TFs for tracklet reconstruction and calorimeter/muon spectrometer vetoes.
3. Hadronic Backgrounds: Estimated using MC simulation normalized to data in Control Regions (CRs) enriched in hadronic tracks.

3. Key Contributions

• 3-Layer Tracklet Reconstruction: First major ATLAS analysis to successfully reconstruct and utilize tracks with only three pixel hits, significantly extending sensitivity to shorter lifetimes ($\tau < 0.03$ ns).
• Soft Pion Identification: Implementation of a BDT algorithm to reconstruct the low-momentum charged pion from chargino decays, allowing for a dedicated search region (SR3High1$\pi$) that enhances signal purity for specific mass-splitting scenarios.
• Improved Background Rejection: Introduction of a "calorimeter veto" requirement (no energy deposits in the calorimeter associated with the tracklet) which accounts for two-thirds of the improvement in mass reach for wino-like scenarios.
• Comprehensive Background Modeling: A robust, purely data-driven framework for estimating fake-tracklet backgrounds, validated in multiple Validation Regions (VRs).

4. Results

• Observation: No significant excess of events over the Standard Model background was observed in any Signal Region.
  • The largest local excess was in SR4High (3 observed events vs. $0.68 \pm 0.14$expected), corresponding to a local significance of **1.9$\sigma$**.
  • The other regions showed good agreement between data and prediction.
• Exclusion Limits (95% CL):
  • Wino-like Charginos: Excluded masses up to 880 GeV (expected 1020 GeV) for lifetimes $\sim 1$ ns.
  • Higgsino-like Charginos:
    • For lifetimes $< 0.03$ ns (pure Higgsino): Excluded masses up to 225 GeV (expected 250 GeV). This is the strongest limit in this phase space to date.
    • For lifetimes $\sim 1$ ns: Excluded masses up to 720 GeV (expected 840 GeV).
  • $\tilde{\tau}$-sleptons:
    • CMSSM scenarios: Excluded masses up to 320 GeV (expected 390 GeV).
    • GMSB scenarios: Excluded masses up to 300 GeV (expected 380 GeV).
• Comparison: These results improve upon previous ATLAS Run-2 analyses by approximately 100 GeV in mass reach for SUSY particles, particularly in the challenging short-lifetime Higgsino region.

5. Significance

• Dark Matter Constraints: The results place stringent constraints on "Natural SUSY" and Anomaly-Mediated Supersymmetry Breaking (AMSB) models, which predict light Higgsinos or Winos as Dark Matter candidates.
• Phase Space Coverage: By targeting 3-layer tracklets and soft pions, the analysis covers the "blind spot" of previous searches where charginos decay too quickly to leave 4 hits. This is crucial for testing Higgsino Dark Matter scenarios where the mass splitting is driven by SM loop corrections.
• Methodological Advancement: The successful application of machine learning (BDT) for soft track reconstruction and the refined data-driven background estimation techniques set a new standard for long-lived particle searches at the LHC, paving the way for future high-luminosity runs.
• Future Outlook: While no new physics was found, the exclusion limits significantly narrow the parameter space for electroweakinos and sleptons, pushing the frontier of SUSY searches to higher masses and shorter lifetimes.