Searching for long-lived particles with the ILD experiment

This paper presents a full simulation study of the International Large Detector's (ILD) capabilities for searching for long-lived particles at future $e^+e^-$ colliders, demonstrating its potential to detect displaced vertices and kinked tracks across various challenging final states and establish exclusion limits for both model-independent scenarios and Higgs boson decays.

The Gist

Imagine the universe is a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. Usually, when these particles crash into each other, they break apart instantly, like a firecracker popping the moment it's lit. But what if some particles are like slow-burning fuses? They travel a visible distance—maybe a few centimeters or even several meters—before they finally "pop" and turn into other things. Scientists call these Long-Lived Particles (LLPs).

This paper is a "dress rehearsal" for a future race track called the International Linear Collider (ILC). The authors are testing a specific detector design called the ILD (International Large Detector) to see if it's good enough to catch these slow-burning fuses before they disappear.

Here is a breakdown of their findings using everyday analogies:

1. The Detector: A Giant, High-Resolution Camera

The ILD is described as a "multipurpose detector," but think of it as a massive, 3D camera with incredibly fine film.

• The Gas Chamber: The heart of this camera is a giant gas-filled box (a Time Projection Chamber). Unlike regular cameras that take a single snapshot, this one tracks a particle's path like a trail of breadcrumbs. It can spot over 200 points along a single particle's journey.
• Why it matters: Most detectors might miss a particle that wanders off the main path. This detector is so sensitive it can see a particle that starts its journey far away from the center of the crash, or one that takes a weird, "kinked" turn.

2. The Challenge: Finding a Needle in a Haystack

The main problem isn't just finding the particles; it's distinguishing them from the "noise."

• The Haystack (Background): In a particle collider, there are millions of tiny, low-energy collisions happening constantly (like static on a radio or dust motes dancing in a sunbeam). These are called "beam-induced interactions."
• The Needle (The Signal): The scientists are looking for specific, rare events where a particle travels a bit, stops, and then creates a new cluster of particles (a "displaced vertex") or suddenly changes direction (a "kinked track").
• The Analogy: Imagine trying to spot a specific, slow-moving snail in a stadium full of people running around. The snail might start walking from the stands (not the field) and leave a trail. The detector needs to ignore the thousands of runners (background noise) to focus only on that one snail.

3. The Two Main Searches

The team tested two different ways these "slow fuses" might behave:

A. The "Ghost" Particles (Neutral LLPs)
These are invisible particles that fly out of the crash and then suddenly decay into visible ones.

• The Scenario: Imagine a heavy, invisible ball rolling away, then suddenly breaking into two smaller, visible balls.
• The Difficulty: Sometimes these invisible balls are so heavy and the visible pieces so light that they move very slowly and don't go far. This makes them look just like the "dust motes" (background noise).
• The Result: The team created special filters (mathematical rules) to ignore the noise. They found that the ILD could detect these events even if they happen very rarely (as low as 1 in 100 trillion collisions).

B. The "Kinked" Particles (Charged LLPs)
These are particles that carry an electric charge and leave a visible trail, but then suddenly change direction or split.

• The Scenario: Imagine a car driving straight, then suddenly swerving sharply or splitting into two cars.
• The Result: The detector is excellent at spotting these "kinks." They found they could detect these events even if the particle traveled up to 10 meters before changing course, with a sensitivity so high they could spot a signal if it happened only once in 10 quadrillion attempts.

4. The "Higgs" Connection

The paper also looked at a specific, famous particle called the Higgs boson.

• The Theory: Some theories suggest the Higgs boson might sometimes decay into these "slow fuse" particles instead of the usual ones.
• The Test: The researchers simulated a scenario where the Higgs decays into a "dark" particle that flies away and then pops.
• The Outcome: The ILD could potentially see this happening much better than current detectors (like those at the Large Hadron Collider) if the particle lives for a long time. This would be a major discovery, proving there is "new physics" beyond what we currently know.

Summary

In simple terms, this paper says: "We built a virtual simulation of a super-sensitive camera (the ILD) for a future particle accelerator. We tested it against the 'noise' of the machine and found it is incredibly good at spotting 'slow-burning' particles that travel strange paths or appear far from the crash site. If these particles exist, this detector is ready to find them."

They didn't find the particles yet (because the machine doesn't exist yet), but they proved the design of the machine is up to the task.

Technical Summary

Technical Summary: Searching for Long-Lived Particles with the ILD Experiment

Problem Statement
While the existence of physics Beyond the Standard Model (BSM) is widely anticipated, the specific manifestation of new phenomena remains unclear. Many theoretical models predict the existence of long-lived particles (LLPs) that travel macroscopic distances (from millimeters to meters) before decaying. These signatures pose significant detection challenges, particularly in environments with high background rates. Future $e^+e^-$ colliders, specifically Higgs factories, offer a unique environment for such searches due to their clean experimental conditions and, in some operational modes, trigger-less capabilities. This study addresses the prospects for detecting both neutral and charged LLPs using the International Large Detector (ILD) at a future International Linear Collider (ILC) operating at a center-of-mass energy of $\sqrt{s} = 250$ GeV.

Methodology
The analysis employs a full Geant4 simulation of the ILD detector, focusing on its unique capabilities as a general-purpose detector optimized for particle-flow reconstruction. Key to the study is the ILD's large Time Projection Chamber (TPC), which provides almost continuous tracking (detecting over 200 points per trajectory) and particle identification via $dE/dx$ measurements.

The reconstruction chain utilizes specific processors:

• Clupatra: Finds tracks within the TPC.
• FullLDCTracking: Matches TPC segments with vertex and silicon detector segments for global refitting.
• V0Finder and KinkFinder: Specialized tools to identify displaced vertices (V0s) and kinked tracks, respectively, allowing for the selection of candidates not matching Standard Model (SM) particles.

The study adopts a model-independent approach, selecting benchmarks based on experimental signatures and kinematic properties rather than specific BSM parameter spaces. Two primary classes of neutral LLP scenarios are analyzed:

1. Heavy Scalar LLPs: Decaying into SM gauge bosons and Dark Matter (DM), characterized by small mass differences ($\Delta m$) between the LLP and DM, resulting in non-pointing, low-$p_T$ final states.
2. Light Pseudoscalar LLPs: Produced in association with a photon, characterized by high boost and collimated decay products.

A dedicated vertex-finding algorithm is used, restricting the search to decays within the TPC volume for neutral LLPs. Backgrounds are rigorously modeled, including:

• Soft, low-$p_T$ beam-induced interactions (overlay): A significant background source due to high rates.
• Hard, high-$p_T$ SM processes: Including hadronic jets and di-lepton events.

Two selection strategies are evaluated: a standard model-independent selection and a "tight" selection incorporating additional kinematic cuts. For charged LLPs, the analysis focuses on "kinked track" signatures using a similar model-independent framework but extends the search to the entire detector volume.

Key Contributions and Results
The study presents expected exclusion limits for a range of LLP lifetimes and masses:

• Neutral LLPs:

  • The ILD is projected to probe production cross-sections down to the femtobarn (fb) level for most scenarios using standard selection.
  • The tight selection improves sensitivity by approximately one order of magnitude.
  • Challenging benchmarks, specifically heavy scalar production with $\Delta m = 1$ GeV and light pseudoscalar production with $m = 0.3$ GeV, are accessible down to cross-sections of $\sim 10$ fb using standard selection.
  • Figure 2 illustrates 95% C.L. upper limits on cross-sections for scalar pair-production and light pseudoscalar production across decay lengths ($c\tau$) ranging from $10^1$ to $10^7$ mm.

• Exotic Higgs Decays:

  • Sensitivity is enhanced by optimizing for specific BSM scenarios, specifically Higgsstrahlung production ($e^+e^- \to ZH$) with the $Z$ boson decaying to neutrinos.
  • The signature requires at least one displaced vertex with no other activity in the detector.
  • By requiring no high-$p_T$ prompt tracks and applying cuts on the total $p_T$ of vertex tracks, the reach improves by two orders of magnitude compared to the general model-independent analysis.
  • The results suggest the ILD could surpass current LHC limits on Higgs branching ratios to dark scalars in the long-lifetime regime during the first stage of ILC running.

• Charged LLPs:

  • The analysis targets pair-produced long-lived dark fermions decaying into DM and SM leptons.
  • Using the kinked track signature, cross-sections below 1 fb are probed for decay lengths between 100 mm and 10 m.
  • The strongest limits reach down to $\sim 0.1$ fb.
  • The results show weak dependence on the mass difference between the LLP and DM.

Significance and Claims
The paper asserts that the ILD, leveraging its gaseous TPC and continuous tracking capabilities, offers excellent prospects for LLP searches that are difficult to achieve in other collider environments. The study demonstrates that the detector can effectively distinguish LLP signatures from both beam-induced backgrounds and high-$p_T$ SM processes.

The authors claim that the ILD can provide competitive or superior sensitivity to current LHC limits, particularly for exotic Higgs decays involving long-lived particles. The work validates the utility of the ILD reconstruction tools (V0Finder, KinkFinder) and the model-independent benchmarking strategy for testing detector capabilities against challenging final states involving soft, displaced tracks and highly boosted, collinear tracks. The findings are presented as a full simulation study within the framework of the ILD Concept Group, intended to guide future search strategies at the ILC.