Search for Higgsinos in final states with low-momentum lepton-track pairs at 13 TeV

The CMS collaboration presents a search for nearly mass-degenerate Higgsinos using 137 fb$^{-1}$ of 13 TeV proton-proton collision data, employing final states with low-momentum lepton-track pairs to probe mass differences as small as 1.5 GeV and exclude Higgsino masses up to 115 GeV.

The Gist

The Big Picture: Hunting for "Invisible" Dark Matter

Imagine the universe is filled with a mysterious, invisible substance called Dark Matter. Scientists think this stuff makes up most of the universe's mass, but we can't see it, touch it, or smell it. It only interacts with normal matter through gravity.

One popular theory suggests that Dark Matter is made of particles called Higgsinos. Think of Higgsinos as "ghostly twins." They are very heavy, but they are almost identical in weight to their slightly heavier "siblings." Because they are so similar in weight, when a heavy one decays (breaks apart), it doesn't release a big explosion of energy. Instead, it releases a tiny, almost invisible whisper of energy.

The Problem: The "Whisper" is Too Quiet

For years, the Large Hadron Collider (LHC) at CERN has been smashing protons together to create these particles. However, previous searches were like trying to hear a whisper in a hurricane.

• The Hurricane: The background noise of the collider (other particles flying around).
• The Whisper: The tiny energy released by the Higgsino decay.

Previous experiments set the "volume threshold" too high. If the energy was too low (like a soft whisper), the detectors ignored it, thinking it was just background noise. This left a "blind spot" in the search: if the Higgsinos were very close in mass to each other, the scientists couldn't see them.

The New Strategy: Listening for the "Ghostly Footsteps"

This paper describes a new, clever way to listen for those whispers. The CMS team (the scientists at the experiment) decided to lower their volume threshold and look for very specific, subtle clues.

They focused on two main scenarios:

1. The Double-Step: Two very low-energy muons (a type of particle) appearing together.
2. The One-Step-and-a-Trace: One low-energy muon (or electron) and one "track" that looks like a particle but wasn't fully identified by the main detector.

The Analogy:
Imagine you are looking for a thief in a crowded mall.

• Old Method: You only looked for thieves carrying big, obvious bags. If they carried a small, hidden item, you missed them.
• New Method: You realize the thief might be carrying a tiny, almost invisible item. So, you start looking for two things:
  1. Two people walking very slowly together (the two low-energy particles).
  2. One person walking slowly, plus a faint footprint on the floor that suggests someone else was there, even if you can't see them (the "exclusive track").

How They Did It: The "Smart Filter"

The data from the collider is massive. To find the needle in the haystack, the scientists used Machine Learning (specifically, something called Boosted Decision Trees).

Think of this as a super-smart bouncer at a club.

• The bouncer has a list of rules.
• Most events (background noise) look like rowdy partygoers.
• The signal (Higgsinos) looks like quiet, specific guests.
• The bouncer learns to ignore the rowdy crowd and only let in the quiet guests who match a very specific profile (low energy, specific angles, missing energy).

They also used a trick to recover "lost" particles. Sometimes, a particle is there, but the detector gets confused and doesn't label it as a "muon." Instead of throwing that data away, they looked for the "track" the particle left behind and treated it as a "ghost muon." This helped them catch about 50% of the events they would have otherwise missed.

The Results: What Did They Find?

After analyzing data from 2016, 2017, and 2018 (a huge amount of information), here is what they found:

1. No Ghosts Found Yet: They did not find any Higgsinos. The data matched the "Standard Model" (the current best theory of how the universe works) perfectly. There was no evidence of new physics in this specific area.
2. Setting the Boundaries: Even though they didn't find the particles, they did something very important: they ruled out a specific range of possibilities.
   • They proved that if Higgsinos exist, they cannot be lighter than 115 GeV (a unit of mass) if the mass difference between them is very small.
   • They probed mass differences as small as 1.5 GeV.

The Analogy:
Imagine you are searching for a specific type of fish in a lake. You didn't catch the fish, but you used a very fine net to check the bottom of the lake. You can now confidently say, "If that fish exists, it is not in the bottom 10 feet of this lake." You have narrowed down the search area for future scientists.

Why This Matters

This search is crucial because of a concept called "Naturalness."

• The Problem: The universe seems "fine-tuned." The math suggests that for the universe to be stable, these Higgsino particles should be light enough to be found by now.
• The Tension: If they are too heavy, the math gets "ugly" and requires a lot of fine-tuning (like balancing a pencil on its tip).
• The Result: By pushing the search into this "compressed" region (where particles are very close in mass), this paper closes the door on the most "natural" versions of the theory. If Higgsinos exist, they are either heavier than we thought or behave in a way we haven't imagined yet.

Summary

The CMS team built a super-sensitive net to catch "ghostly" particles that are almost identical in weight. They looked for tiny whispers of energy that previous experiments ignored. They didn't find the particles, but they successfully proved that the particles aren't hiding in the specific low-mass, low-energy zone they just searched. This forces physicists to rethink where to look next.

Technical Summary

Technical Summary: Search for Higgsinos in Final States with Low-Momentum Lepton-Track Pairs at 13 TeV

Problem and Motivation
This paper addresses the search for Higgsinos, a class of supersymmetric (SUSY) particles that serve as viable dark matter candidates and offer solutions to the hierarchy problems in the Standard Model (SM). Specifically, the analysis targets scenarios with "compressed" mass spectra, where the mass difference ($\Delta m$) between the produced charginos ($\tilde{\chi}^{\pm}_1$) and neutralinos ($\tilde{\chi}^0_1, \tilde{\chi}^0_2$) is small (on the order of 1–10 GeV). In such scenarios, the decay products (leptons) possess very low transverse momentum ($p_T$) and small opening angles, rendering them difficult to reconstruct with standard trigger and identification thresholds used in previous LHC searches. Previous analyses by ATLAS and CMS have excluded Higgsino masses up to 205 GeV for mass splittings of $\Delta m \approx 7.5$ GeV, but sensitivity drops significantly for $\Delta m < 3$ GeV due to kinematic and isolation requirements (e.g., $p_T > 3.5$ GeV, $\Delta R > 0.3$). This work aims to probe the previously unexplored region of parameter space where mass splittings are below 3 GeV, extending down to 1.5 GeV.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 137 fb$^{-1}$ from the 2016, 2017, and 2018 data-taking periods. The signal model assumes four nearly mass-degenerate Higgsino eigenstates: two neutralinos ($\tilde{\chi}^0_1, \tilde{\chi}^0_2$) and two charginos ($\tilde{\chi}^{\pm}_1$), with $\Delta m^0 = m(\tilde{\chi}^0_2) - m(\tilde{\chi}^0_1)$ and $\Delta m^{\pm} = m(\tilde{\chi}^{\pm}_1) - m(\tilde{\chi}^0_1) = \Delta m^0/2$.

The search focuses on the decay $\tilde{\chi}^0_2 \to \ell\ell\tilde{\chi}^0_1$ (where $\ell$ is a muon or electron) via a virtual $Z$ boson, accompanied by large missing transverse momentum ($p_T^{\text{miss}}$) from the two undetected lightest supersymmetric particles (LSPs). To recover events with soft leptons, the analysis employs three distinct event categories:

1. Dimuon: Events with two reconstructed and identified muons, where at least one muon has $p_T < 3$ GeV or the pair has $\Delta R(\mu_1, \mu_2) < 0.3$.
2. Muon + Exclusive Track: One reconstructed muon and one isolated track not matched to any identified lepton.
3. Electron + Exclusive Track: One reconstructed electron and one isolated exclusive track.

Key technical innovations include:

• Relaxed Kinematic Thresholds: Muons are selected with $p_T$ between 2 and 15 GeV, and electrons between 5 and 15 GeV, significantly lower than standard selections.
• Exclusive Track Recovery: An "exclusive track" is defined as a track with $p_T > 1.9$ GeV, high isolation, and no geometric match to a reconstructed lepton. Dedicated Boosted Decision Tree (BDT) classifiers ("track-picking BDTs") are trained to identify which track in an event corresponds to the lepton from the neutralino decay, recovering up to 50% of lost leptons.
• Multivariate Analysis: Event-level BDTs are constructed to distinguish signal from background. Input variables include the invariant mass of the lepton pair ($m_{\ell\ell}$), $p_T$ of leptons, hard $p_T^{\text{miss}}$, and angular separations. The dimuon BDT utilizes 200 decision trees trained on signal simulations with mass splittings ranging from 0.3 to 4.6 GeV.
• Background Estimation:
  • Jetty Background: Dominated by non-prompt leptons from jet activity. Estimated using an isolation sideband control region (CR) where the jet-based isolation criterion is inverted. A transfer factor ($c_{\text{TF}}$) derived from a BDT sideband CR normalizes the prediction to the signal region (SR).
  • $Z/\gamma^* \to \tau\tau$: Estimated using simulated samples corrected by data-driven normalization factors derived in a ditau-enriched CR.
  • Exclusive Track Background: Estimated using a same-charge CR, assuming kinematic similarity between same-charge and opposite-charge backgrounds.

Systematic uncertainties, including those from jet energy scale, ISR modeling, lepton efficiency, and luminosity, are incorporated into a maximum likelihood fit using log-normal nuisance parameters.

Key Contributions and Results
The analysis defines mutually exclusive signal regions based on BDT output scores. No significant deviation from the Standard Model expectation is observed in the data. The background model provides a good description of the data across all categories. A small excess is noted in the most sensitive SR of the dimuon category (Phase 1 data), corresponding to a local significance of 2.2 standard deviations, which is not considered evidence for new physics.

Using the $CL_s$ method, the paper sets 95% confidence level (CL) exclusion limits on the Higgsino production cross-section in the plane of $\Delta m^{\pm}$ versus $m(\tilde{\chi}^{\pm}_1)$.

• Mass Sensitivity: The search probes mass differences $\Delta m^0$ down to 1.5 GeV (assuming a chargino mass of 100 GeV).
• Exclusion Limits: The maximum excluded Higgsino mass is 115 GeV, corresponding to a $\Delta m^0$ of 3.5 GeV. The sensitivity peaks around $\Delta m^{\pm} \approx 2$ GeV, where the analysis probes chargino masses up to approximately 145 GeV (expected) and 115 GeV (observed).
• Comparison: The observed limit is slightly weaker than the expected limit due to a small excess in the Phase 1 data, but the analysis successfully extends the reach into the highly compressed regime previously inaccessible to standard soft-lepton searches.

Significance
The paper claims to establish sensitivity to a previously unexplored region of the Higgsino parameter space, specifically targeting the "natural" subspace with large $\tan \beta$ and highly compressed spectra. By utilizing low-momentum lepton-track pairs and relaxed identification criteria, this analysis bridges the sensitivity gap between searches for disappearing tracks (for very small $\Delta m$) and standard soft-lepton searches (for larger $\Delta m$). The results place stringent constraints on natural supersymmetry and other models predicting electroweak multiplet dark matter, demonstrating that compressed Higgsino scenarios with mass splittings as low as 1.5 GeV can be effectively probed at the LHC.