Search for long-lived particles using displaced vertices with low-momentum tracks in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 100 fb$^{-1}$ of 13 TeV proton-proton collision data from the CMS experiment, this study presents a search for long-lived particles via displaced vertices with low-momentum tracks, setting the most stringent limits to date on top squark and wino-like neutralino masses in specific supersymmetric coannihilation scenarios.

The Gist

The Big Picture: Hunting for "Ghostly" Particles

Imagine the Large Hadron Collider (LHC) at CERN as a giant, high-speed car crash zone. Scientists smash protons together at incredible speeds to see what tiny pieces fly out. Usually, these pieces (particles) zip through the detectors instantly, like a bullet passing through a wall.

However, some theories suggest that certain new, mysterious particles might be "ghostly." Instead of disappearing instantly, they might travel a short distance—like a few centimeters—before they finally pop and decay into other things. These are called Long-Lived Particles (LLPs).

This paper describes a new search by the CMS experiment (one of the giant detectors at the LHC) specifically looking for these "ghosts" that travel a short distance and then leave behind a trail of low-energy debris.

The Specific Target: The "Compressed" Scenario

The scientists are looking for a very specific, tricky situation called a "compressed spectrum."

• The Analogy: Imagine two runners, a heavy one (the new particle) and a light one (the invisible dark matter particle). Usually, if the heavy runner drops something, it falls with a big thud. But in this scenario, the heavy runner is only slightly heavier than the light one (less than 25 GeV difference).
• The Result: Because they are so close in weight, the heavy runner doesn't have much energy to give away when it decays. The "debris" it leaves behind moves very slowly (low momentum).
• The Problem: Previous searches were like using a net with large holes; they missed these slow-moving, low-energy particles because they were designed to catch fast, high-energy ones. This new search uses a "fine-mesh net" to catch these slow, low-momentum tracks.

The Detective Work: How They Found Them

The search looks for a very specific signature in the data, which the paper calls a "displaced vertex."

1. The Setup: The collision happens, and a heavy particle is created.
2. The Journey: Instead of decaying immediately at the crash site, this particle travels a few millimeters or centimeters away.
3. The Explosion: It decays into a few charged particles (tracks) and an invisible particle (dark matter candidate).
4. The Clues:
   • The Displaced Vertex: The charged tracks don't start at the center of the crash; they start a few steps away. It's like finding footprints that start in the middle of a room, not at the door.
   • The Recoil: To balance the energy, there is usually a "kick" from the initial crash (an Initial State Radiation jet) that pushes the heavy particle away.
   • Missing Energy: The invisible particle flies off undetected, creating a gap in the energy balance (Missing Transverse Momentum).

The Strategy: A New Way to Count

The paper introduces a clever statistical method to guess how many "background" events (false alarms) there are, without relying on computer simulations that might be wrong.

• The Analogy: Imagine you are trying to count how many people are wearing red hats in a stadium, but you can't see them all. Instead of guessing, you count how many people are wearing blue hats in a section you can see clearly. Then, you use a "transfer factor" (a known ratio) to estimate how many red hats are in the whole stadium.
• In the Paper: They divide the data into different "planes" based on how many good tracks they see. They count the easy-to-see events (control regions) and use mathematical ratios to predict how many hard-to-see events (signal regions) should exist if there were no new physics. They then compare this prediction to what they actually see.

The Results: What Did They Find?

After analyzing data from 2017 and 2018 (100 "inverse femtobarns" of data, which is a huge amount of collisions):

1. No Ghosts Found: The number of events they saw matched the prediction for normal background noise perfectly. There was no "smoking gun" evidence of these new long-lived particles.
2. Setting Limits: Even though they didn't find the particles, they successfully ruled out where they could be hiding.
   • They excluded the possibility of Top Squarks (a type of supersymmetric particle) having masses between 400 and 1100 GeV.
   • They excluded Wino-like Neutralinos (another type) with masses between 220 and 550 GeV.
3. The Achievement: This is the most sensitive search to date for these specific "compressed" scenarios. It sets the strictest rules yet for where these particles cannot exist.

Summary

Think of this paper as the most thorough "ghost hunt" yet in a specific, difficult corner of the universe. The hunters used a new, finer net to catch slow-moving, low-energy particles that previous nets missed. They didn't find any ghosts, but they successfully proved that if these ghosts exist, they aren't hiding in the specific mass ranges they just searched. This narrows down the map for future explorers.

Technical Summary

Technical Summary: Search for Long-Lived Particles Using Displaced Vertices with Low-Momentum Tracks

Problem and Motivation
Many theories beyond the Standard Model (SM) predict the existence of long-lived particles (LLPs) with mean proper lifetimes exceeding $\sim 0.1$ ps. In specific supersymmetric (SUSY) scenarios, such as the top squark ($\tilde{t}$) next-to-lightest supersymmetric particle (NLSP) and the bino-wino NLSP models, the mass difference ($\Delta m$) between the NLSP and the lightest SUSY particle (LSP) can be small (less than 25 GeV). In these "compressed spectrum" scenarios, the decay products of the LLP are soft, resulting in low-momentum tracks. Previous searches by the ATLAS and CMS collaborations using displaced vertices suffered from reduced sensitivity in these specific mass-splitting regions due to event and vertex selection criteria that were not optimized for low-momentum tracks. This analysis aims to address this gap by targeting LLPs decaying with $\Delta m$ in the range of 12–25 GeV, utilizing well-measured low-momentum tracks to enhance sensitivity.

Methodology
The search utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV during 2017 and 2018, corresponding to an integrated luminosity of 100 fb$^{-1}$. The analysis focuses on final states containing a displaced vertex, large missing transverse momentum ($p^{\text{miss}}_T$), and a jet from initial-state radiation (ISR).

• Signal Models: Two benchmark SUSY coannihilation scenarios are considered:
  1. $\tilde{t}$ NLSP Model: A long-lived top squark decaying via four-body or two-body channels to a bino-like neutralino LSP.
  2. Bino-Wino NLSP Model: A nearly mass-degenerate wino-like neutralino ($\tilde{\chi}^0_2$) and chargino ($\tilde{\chi}^\pm_1$), where the $\tilde{\chi}^0_2$ is long-lived and decays via an off-shell $Z$ boson.
• Detector and Reconstruction: The analysis leverages the upgraded CMS tracker from 2017–2018, which offers improved performance for low-momentum tracks ($1 < p_T < 10$ GeV). Displaced vertices are reconstructed using a customized inclusive vertex finder (IVF) based on the adaptive vertex fitter. The IVF parameters were tuned to accommodate tracks with large angular separations, enhancing efficiency for LLP decays with large opening angles.
• Event Selection: Events are required to pass a trigger with $p^{\text{miss}}_T > 120$ GeV and have offline $p^{\text{miss}}_T > 400$ GeV, along with at least one ISR jet ($p_T > 100$ GeV). Lepton and photon vetoes are applied to reduce background.
• Background Estimation: A novel, data-driven background estimation method is employed using transfer factors. Events are categorized into "planes" based on the number of "good tracks" (tracks satisfying strict quality and isolation criteria) associated with a displaced vertex (0, 1, 2, or $\ge 3$ tracks). Control regions (CRs) with low $p^{\text{miss}}_T$ are used to derive transfer factors that predict the background yield in signal regions (SRs) with higher $p^{\text{miss}}_T$ and varying track multiplicities. This approach avoids reliance on simulation for background modeling.
• Systematic Uncertainties: Major uncertainties include track/vertex reconstruction efficiency (10–11%), derived from $K^0_S \to \pi^-\pi^+$ decays, and background estimation statistical uncertainties (<2%).

Key Contributions

• Optimization for Compressed Spectra: The analysis specifically targets the low-momentum track regime ($p_T < 10$ GeV) and small mass splittings ($\Delta m < 25$ GeV), a region previously less explored by displaced vertex searches.
• Custom Vertex Reconstruction: The tuning of the IVF algorithm to accept large angular separations between tracks significantly improves reconstruction efficiency for LLPs with long decay lengths and specific kinematic configurations.
• Data-Driven Background Estimation: The implementation of a transfer factor method based on track multiplicity and $p^{\text{miss}}_T$ allows for robust background prediction across multiple signal regions without relying on simulated background samples for the final yield.
• Material Map Veto: A data-derived material map is used to veto vertices originating from nuclear interactions within the tracker material, reducing background while maintaining signal efficiency.

Results
The analysis observed no significant deviation from the background-only hypothesis across the search regions, with a combined $p$-value of 0.5. Consequently, 95% confidence level (CL) upper limits on the production cross-section were set for the benchmark models.

• $\tilde{t}$ NLSP Model: Top squarks with masses less than 400–1100 GeV are excluded, depending on the mass difference ($\Delta m$) and the branching fraction of the four-body decay.
• Bino-Wino NLSP Model: Wino-like neutralinos with masses less than 220–550 GeV are excluded, depending on $\Delta m$ and the proper decay length ($c\tau$).
• The sensitivity is optimal for $c\tau$ values around 10 mm and improves with increasing $\Delta m$.

Significance
This work represents the first search at the LHC to demonstrate sensitivity to long-lived particles in compressed-spectrum scenarios using displaced-vertex signatures with low-momentum tracks. By setting the most stringent limits to date for the $\tilde{t}$ and bino-wino NLSP signal models, the analysis effectively probes previously inaccessible regions of the SUSY parameter space. The results constrain specific coannihilation scenarios where the mass difference between the NLSP and LSP is less than 25 GeV, providing critical constraints for theoretical models predicting such compressed spectra.