Search for electroweakinos in compressed-spectrum scenarios with low-momentum isolated tracks in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of 13 TeV proton-proton collision data, the CMS collaboration performed a search for nearly mass-degenerate higgsino-like electroweakinos via low-momentum isolated tracks and missing transverse momentum, finding no significant excess and setting stringent exclusion limits on chargino masses up to 185 GeV for mass splittings between 0.28 and 1.15 GeV.

The Gist

The Big Picture: Hunting for "Ghostly Twins"

Imagine you are a detective looking for a very specific type of criminal. This criminal is a "ghost" that never leaves a fingerprint, but it does leave a tiny, almost invisible footprint.

In the world of particle physics, scientists at CERN (the European Organization for Nuclear Research) are looking for evidence of Supersymmetry (SUSY). Think of SUSY as a "shadow world" where every known particle has a heavier, invisible twin. One specific type of these twins is called a higgsino.

The problem? These higgsinos are very shy. If they exist, they might be so similar in weight to their partners that they barely move when they decay (break apart). This makes them incredibly hard to spot, like trying to find a whisper in a hurricane.

The Specific Mystery: The "Compressed" Scenario

This paper focuses on a tricky situation called a "compressed spectrum."

• The Analogy: Imagine a heavy bowling ball (the heavy particle) rolling down a hill. Usually, when it breaks, it shoots out a tennis ball (a new particle) with a lot of speed. You can easily see the tennis ball flying away.
• The Twist: In this specific scenario, the bowling ball and the tennis ball are almost the exact same weight. When the bowling ball breaks, the tennis ball doesn't fly away; it just barely rolls forward. It moves so slowly (it has "low momentum") that it looks like it's just floating there.

Because these particles are so heavy and move so slowly, they don't leave the detector quickly. Instead, they travel a tiny distance (up to about 1 centimeter) before turning into a single, slow-moving pion (a type of particle). This creates a "soft, isolated track"—a faint, short line in the detector that doesn't connect to the main crash site.

The Challenge: Finding a Needle in a Haystack

The scientists are looking for these faint, slow tracks in a massive pile of data.

• The Haystack: The Large Hadron Collider (LHC) smashes protons together billions of times. Most of these crashes create a chaotic mess of particles (background noise).
• The Needle: The signal they want is a single, slow track that appears slightly away from the center of the crash, accompanied by a lot of "missing energy" (because the ghostly particles escape the detector without being seen).

The difficulty is that the background noise is huge. There are many fake tracks caused by the detector getting confused or by other common particle interactions. Distinguishing the real "ghost" signal from the noise is like trying to hear a specific person whispering in a stadium full of cheering fans.

The Solution: A Smart AI Detective

To solve this, the CMS team didn't just use simple rules (like "if the track is this long, count it"). Instead, they built a Neural Network (a type of artificial intelligence).

• How it works: Imagine training a dog to find a specific scent. You show the dog thousands of examples of the "ghost" scent (simulated signal) and thousands of examples of "noise" (background).
• The Training: The AI was fed data on the tracks: how fast they were moving, exactly where they started, and how far they drifted from the center. It learned to spot the subtle patterns that human eyes or simple math would miss.
• The Result: The AI acts as a filter, sorting the millions of tracks and saying, "This one looks like a ghost," or "This one is just noise."

The Investigation: What Did They Find?

The team analyzed data from 138 trillion proton collisions (138 fb⁻¹) recorded between 2016 and 2018. They used their AI to scan for the specific "slow track" signature.

The Verdict:

• No Ghosts Found: After looking at all the data, they found zero evidence of these higgsino twins. The number of events they saw matched exactly what the Standard Model (our current best theory of physics) predicts for normal background noise.
• Ruling Out Possibilities: Even though they didn't find the particles, they learned something important. They can now say with 95% confidence that if these higgsinos do exist, they cannot be as light as 185 GeV (a unit of mass) if the mass difference between them is small.

The Conclusion: Closing the Window

Think of this search as closing a door on a specific room in a house.

• Before this paper, scientists didn't know if these "compressed" higgsinos were hiding in that room.
• After this paper, they can say, "We have looked everywhere in that room, and the higgsinos are not there (at least not with the mass and speed we tested)."

This puts strict limits on "Natural Supersymmetry." It tells theorists that if these particles exist, they must be heavier or behave differently than the specific "compressed" models this paper tested. The search continues, but this specific hiding spot has been thoroughly checked and found empty.

Technical Summary

1. Problem Statement and Physics Motivation

The search targets compressed-spectrum supersymmetry (SUSY), specifically scenarios involving higgsino-like electroweakinos. In these models, the lightest neutralino ($\tilde{\chi}^0_1$) is the Lightest Supersymmetric Particle (LSP) and a dark matter candidate. The next-to-lightest supersymmetric particles (NLSPs)—the lightest chargino ($\tilde{\chi}^\pm_1$) and the second neutralino ($\tilde{\chi}^0_2$)—are nearly mass-degenerate with the LSP.

• The Challenge: When the mass splitting ($\Delta m^\pm = m(\tilde{\chi}^\pm_1) - m(\tilde{\chi}^0_1)$) is small (specifically 0.3–1 GeV), the decay $\tilde{\chi}^\pm_1 \to \tilde{\chi}^0_1 \pi^\pm$ produces a very low-momentum (soft) pion.
• Detection Difficulty:
  • If $\Delta m^\pm \lesssim 0.3$ GeV, the chargino is long-lived enough to produce a "disappearing track" signature.
  • If $\Delta m^\pm \gtrsim 1$ GeV, the pion is energetic enough to be easily reconstructed as a standard track.
  • The "Gap": In the intermediate range (0.3–1 GeV), the pion has a transverse momentum ($p_T$) typically below 1 GeV and a displacement of up to ~1 cm from the primary vertex (PV). These tracks are often lost due to standard reconstruction thresholds or confused with background from pileup and underlying events.

2. Methodology

Data and Selection

• Dataset: 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the CMS detector (2016–2018).
• Trigger: Events are selected with a missing transverse momentum ($p_T^{miss}$) threshold of $>120$ GeV.
• Offline Selection:
  • $p_T^{miss} > 300$ GeV and $H_T^{miss} > 300$ GeV (scalar sum of jet $p_T$).
  • At least one isolated track with $p_T < 20$ GeV and $|\eta| < 2.4$.
  • Veto on isolated electrons, muons, photons, and hadronic $\tau$ leptons.
  • Veto on $b$-tagged jets and events with $\ge 5$ jets.
  • Requirements on the angular separation ($\Delta\phi$) between $p_T^{miss}$ and jets to reject QCD multijet backgrounds.

Background Estimation

The dominant backgrounds are:

1. $Z \to \nu\nu$ + jets: Genuine $p_T^{miss}$ from neutrinos.
2. $W \to \ell\nu$: Where the lepton is lost or fails identification.
3. QCD Multijets: Mismeasured $p_T^{miss}$ and fake tracks.
4. Secondary Tracks: Tracks from pileup, underlying events, or decays of particles produced at the primary vertex (PV-associated).

Background yields are estimated using simulation corrected by data-driven methods:

• Normalization: Scale factors derived from control regions (CR) using $Z \to \mu\mu$ events (for $Z \to \nu\nu$) and inclusive track $z$-displacement ($d_z$) distributions (for PV-associated and spurious tracks).
• Refinement: A multivariate regression based on the Fast Perfekt methodology is used to correct mismodeling in the simulation of track kinematics and impact parameters, ensuring the simulated distributions match data in the control regions.

Machine Learning Strategy

A parameterized feedforward Neural Network (NN) is the core of the analysis to distinguish signal tracks from background.

• Architecture: Three hidden layers with 256 units each, using LeakyReLU activations.
• Inputs: 37 observables including track kinematics ($p_T$, $\eta$), helix fit quality, impact parameter significance ($IP_{xy}$) relative to the PV and pileup vertices, and event-level $p_T^{miss}$.
• Parameterization: The network is trained with the input mass difference ($\Delta m^\pm_{in}$) as a parameter (0.3, 0.6, and 1.0 GeV) to capture correlations across the signal phase space.
• Output: The NN classifies tracks into five categories: Signal, $\tau$-decay tracks, other secondary tracks, prompt PV tracks, and spurious tracks.
• Signal Regions (SRs): Events are categorized based on the NN score ($\tilde{P}$) for the signal class. Three distinct SRs are defined corresponding to the input $\Delta m^\pm_{in}$ values, each further binned by the score to maximize sensitivity.

3. Key Contributions

1. Novel Search Channel: This is one of the first searches specifically targeting the difficult 0.3–1 GeV mass splitting regime using low-momentum isolated tracks with a dedicated NN approach. Previous searches focused on either disappearing tracks ($\Delta m < 0.3$ GeV) or soft leptons ($\Delta m > 1$ GeV).
2. Advanced Background Modeling: The use of a parameterized NN allows for a unified treatment of signal and background across different mass splittings, significantly improving sensitivity compared to traditional cut-based analyses.
3. Data-Driven Refinement: The implementation of the Fast Perfekt regression technique to correct simulation mismodeling of soft track properties (impact parameters and $p_T$) ensures robust background estimation in a region dominated by reconstruction inefficiencies.

4. Results

• Observation: No significant excess of events was observed above the Standard Model expectation in any of the 12 Signal Regions. The data is consistent with the background-only hypothesis.
• Exclusion Limits (95% Confidence Level):
  • Mass Splitting: The higgsino model is excluded for mass splittings in the range 0.28–1.15 GeV.
  • Chargino Mass:
    • For a mass splitting of 0.55 GeV, chargino masses up to 185 GeV are excluded.
    • For a chargino mass of 100 GeV, mass splittings between 0.28 and 1.15 GeV are excluded.
• Comparison: These limits are the most stringent to date for this specific compressed-spectrum regime, effectively closing a significant gap in the search for natural higgsino dark matter.

5. Significance

This analysis addresses a critical "blind spot" in the search for natural supersymmetry. Naturalness arguments suggest that higgsinos should be light (near the electroweak scale, $\sim 100$ GeV) to avoid fine-tuning. However, if the mass splitting is small, the resulting soft pions are difficult to detect.

By successfully reconstructing and identifying these soft, potentially displaced tracks using a sophisticated machine learning approach, this result:

• Constrains Natural SUSY: It places severe constraints on the parameter space for natural higgsino scenarios, pushing the lower bound on the chargino mass significantly higher than previous limits in this specific kinematic regime.
• Demonstrates Methodology: It validates the use of parameterized neural networks and advanced track reconstruction techniques for probing low-momentum signatures, a strategy that will be essential for future high-luminosity LHC runs and future colliders.
• Dark Matter Implications: It narrows the viable window for higgsino dark matter, suggesting that if higgsinos exist, they must either be heavier than 185 GeV (increasing fine-tuning) or have mass splittings outside the 0.28–1.15 GeV range.