LLP Triggers in Collider Experiments

• Long-Lived Particle (LLP) triggers are dedicated selection systems designed to record events with displaced, non-standard detector signatures in high-energy collisions.
• They employ advanced techniques such as extended track reconstruction, calorimeter timing, and machine learning to overcome challenges like low visible energy and high pile-up.
• LLP triggers enhance the experimental reach for beyond Standard Model physics, including dark matter and exotic Higgs decays, by significantly improving signal efficiency across diverse decay topologies.

Long-Lived Particle (LLP) triggers are specialized online selection algorithms and hardware systems designed to record events containing particles with macroscopic lifetimes (typically $c\tau$ from $\sim$mm to tens of meters) at collider experiments such as the LHC. Unlike prompt-object triggers that rely on high-energy, promptly produced tracks, leptons, jets, or missing energy, LLP triggers are tailored for signatures featuring spatial and/or temporal displacement from the interaction point, non-standard detector patterns, and low visible energy. A robust LLP trigger program is foundational for exploring physics beyond the Standard Model—including dark matter, baryogenesis, exotic Higgs decays, and neutral naturalness—and is critical for covering large regions of parameter space inaccessible to standard triggers (Stolarski, 2017).

1. Fundamental Challenges and Motivating LLP Signatures

Long-lived particles manifest through diverse detector signatures, including displaced vertices, trackless jets, anomalous calorimeter energy deposition, slow-moving or fractionally charged particles (“FCP”), low-momentum soft-unclustered energy patterns (“SUEP”), and delayed photons or jets. These effects arise in models with mediators that couple via the Higgs or other portals, compressed spectra, dark showers, and freeze-in dark matter scenarios (Stolarski, 2017, Alimena et al., 2021). The key experimental difficulties are:

• Low visible energy: Many LLP decay products have $p_T$ below online thresholds.
• Displacement: Tracks or vertices are far from the beam axis; large $d_0$ or decay radius $r$.
• Non-pointing/delayed signatures: Arrival times shifted by $\mathcal{O}(1$–$10)$ ns; atypical shower profiles in calorimetry.
• Tracklessness: Neutral LLPs decaying in calorimeters or muon systems produce jets with few or no associated tracks.
• Pile-up suppression: LLP triggers must be robust against backgrounds from multiple collisions per bunch crossing ($\langle\mu\rangle \gtrsim$100–200 at HL-LHC).

Without dedicated triggers exploiting these features, a substantial fraction of LLP events remains unrecorded, even at high-integrated luminosity.

2. Hardware and Software Architectures for LLP Triggering

Current LHC detectors employ multi-tiered trigger systems:

• Level-1 (L1): Hardware (FPGA/ASIC) processors reduce 40 MHz collision rates to $\sim$100 kHz using calorimeter sums, muon primitives, and, increasingly, prompt tracking. Upgrades for LLP sensitivity include:
  • Track triggers: Reconstruction of tracks with expanded $d_0$ reach (up to several cm) (Gershtein, 2017, Mårtensson et al., 2019, Pica, 2024).
  • Calorimeter timing/depth: Per-tower time-stamps and depth measurements identify delayed or displaced jets/photons (Bhattacherjee et al., 2021, Collaboration, 24 Jan 2026).
  • Muon system enhancements: Removal of beam-pointing constraints (beam-unconstrained track finding), regionally clustered RoIs, and local shower identification in CSC/DT (Collaboration, 24 Jan 2026).
  • Graph-based inference: Tools such as LLPNet employ graph autoencoders for anomaly detection on L1 tracks (Bhattacherjee et al., 2023).
• High-Level Trigger (HLT): Software running on CPU/GPU farms further refines object reconstruction, applies regional displaced tracking, calorimeter shower-shape analysis, and sophisticated multivariate (BDT, DNN) classifiers for LLP identification (Collaboration, 24 Jan 2026, Alimena et al., 2021, Pica, 2024).
• Triggerless architectures (LHCb Run 3): Full software-based event reconstruction at 30–40 MHz enables LLP identification at the first trigger level (GPU-based HLT1), facilitating early selection on displaced vertices, especially for $K^0_S$, $\Lambda$, and other hadrons (Pica, 2024).

3. Algorithmic Techniques and Selection Variables

LLP triggers rely on distinct sets of algorithmic discriminants:

• Displacement observables: Transverse impact parameter ($d_0$), longitudinal displacement ($z_0$), and vertex positions are used to flag tracks inconsistent with prompt production. Efficient LLP selection requires extending $d_0$ acceptance up to tens of cm (Gershtein, 2017, Petrillo et al., 2022).
• Calorimeter and timing variables: Delayed jets/photons are identified by timing residuals $\Delta t = T_{\rm raw} - T_{\rm exp}$, computed per ECAL/HCAL tower and aggregated at jet level (mean, RMS, or “Max5” hardest-tower average). Depth segmentation further distinguishes late/deep energy deposits (Bhattacherjee et al., 2021, Collaboration, 24 Jan 2026).
• Tracklessness and isolation: “Trackless-jet” triggers require jets with minimal associated tracks; “calorimeter-ratio” triggers exploit anomalously low $f_{\rm EM}$ in jets (far below nominal prompt jets) (Collaboration, 2013).
• Muon-system triggers: Clustering of multiple muon RoIs in spatial proximity tags hadronic decays in the MS; local showers are counted via hits per chamber (Collaboration, 2013, Collaboration, 24 Jan 2026).
• Pattern recognition and ML: Associative memory banks and Hough transforms efficiently reconstruct displaced tracks; recent work introduces anomaly-detection DNNs compatible with FPGA inference budgets (Mårtensson et al., 2019, Bhattacherjee et al., 2023).
• Hybrid triggers: Combining calorimeter timing cuts with displaced track tags recovers efficiency for short-lived LLPs otherwise missed by timing-only triggers (Bhattacherjee et al., 2021).

LVL trigger definitions, variable thresholds, and background rejection rates are carefully tuned to manage bandwidth in high pile-up, ensuring $\mathcal{O}(10$--$100)$ kHz rates without excessive prompt contamination.

4. Efficiency, Rates, and Performance Studies

Comprehensive LLP trigger development quantifies efficiency versus lifetime ($c\tau$), mass, and production topology:

• Standard prompt-object triggers sharply lose efficiency for increasing $d_0$, low $p_T$, or large displacement—often $\leq 1\%$ (even at $c\tau \sim$ few cm, $m_{\rm LLP} < 50$ GeV) (Stolarski, 2017, Alimena et al., 2021).
• Dedicated displaced-track and jet triggers can recover up to $10$–$80\%$ efficiency for relevant benchmark points (Gershtein, 2017, Bhattacherjee et al., 2021, Bhattacherjee et al., 2023, Collaboration, 24 Jan 2026). For instance, LLPNet achieves $33$–$80\%$ (at $c\tau=5$ cm, $m_X=10$–$50$ GeV) at a 30 kHz L1 background rate (Bhattacherjee et al., 2023).
• Calorimeter-timing triggers: With optimized timing variables and $p_T$ cuts, signal efficiency approaches $80\%$ for pair-produced heavy LLPs ($M_X=500$ GeV, $c\tau=100$ cm) with background rates held near $30$ kHz (Bhattacherjee et al., 2021).
• Heavy-ion collisions: Looser L1 thresholds ($p_T^\mu \sim 3$ GeV) substantially increase acceptance (by up to $10\times$) for low-$p_T$ LLP decays (Drewes et al., 2018, Drewes et al., 2019, Faham et al., 2022).
• LHCb first-level triggers: New HLT1 lines targeting $K^0_S$ decays have demonstrated efficiency gains of up to $2.6\times$ for $D^0 \to K^0_S K^0_S$ with only $\sim 40$ kHz added rate at 30 MHz input (Pica, 2024).

Typical trigger rates, prescales, and cut values are provided in algorithm-specific tables within cited papers (Collaboration, 2013, Collaboration, 24 Jan 2026). Background rejection factors for QCD, cosmic rays, and punch-through are $>10^3$ for key displaced and timing triggers (e.g., muon system showers, delayed jets) (Collaboration, 2013, Collaboration, 24 Jan 2026).

5. Complementary Trigger Streams and Dataset Strategies

LLP sensitivity is maximized by exploiting complementary data-taking and trigger streams beyond standard physics runs:

• Scouting and parking: Reduced event content or delayed reconstruction allows lower HLT thresholds (single/dimuon $p_T$ as low as $3$ GeV), comparable or superior reach to standard $pp$ data especially for soft displaced signatures (Faham et al., 2022).
• Heavy-ion / low-pileup runs: Negligible pile-up and lower rate environments support very loose thresholds, making these optimal for LLPs produced with low $p_T$ (Drewes et al., 2018, Drewes et al., 2019, Faham et al., 2022).
• No-BPTX (out-of-time triggers): Special triggers flag events in empty bunch crossings to record stopped-particle decays (Collaboration, 24 Jan 2026).

Hybrid triggers combining selections across these streams are recommended to maximize statistical yield and lifetime coverage.

6. Optimization, Calibration, and Machine Learning Integration

LLP trigger performance is highly sensitive to hardware resource allocation, latency constraints, pile-up tolerance, and real-time calibration:

• Resource management: FPGAs/ASICs must balance logic, RAM (for associative memory or accumulator banks), serial I/O, and power usage. L1 hardware algorithms such as Hough transforms or graph neural networks must fit in $\mathcal{O}(1$–$4)$ μs latency (Mårtensson et al., 2019, Bhattacherjee et al., 2023, Collaboration, 24 Jan 2026).
• Timing calibration: Precise alignment of per-cell or per-tower timing is critical for minimizing prompt penalty and maximizing LLP acceptance; out-of-time backgrounds (satellite bunches, beam-halo, cosmics) require dedicated sampling (Alimena et al., 2021, Collaboration, 24 Jan 2026).
• Machine learning deployments: FPGA/ASIC-compatible BDTs or DNNs (e.g., ParticleNet, DeepJet) are used for real-time classification. Quantized weights ($8$–$4$ bit) and simplified architectures ensure sub-μs inference (Bhattacherjee et al., 2023, Collaboration, 24 Jan 2026).
• Pile-up adaptation: Trigger menu thresholds and isolation variables must scale upward with instantaneous luminosity; advanced pile-up mitigation includes tower zero-suppression, regional time-matching, and ML-based pile-up ID (Bhattacherjee et al., 2020).
• Downstream FPGA tracking (LHCb): Offloading resource-intensive tracking for downstream decays to a RETINA FPGA board reduces GPU bottlenecks and promises further rate sustainability (Pica, 2024).

7. Experimental Impact, Physics Reach, and Future Directions

The implementation and expansion of dedicated LLP trigger programs have directly extended experimental coverage:

• Run-3 CMS: LLP triggers on displaced jets, muons, ECAL-delayed photons, and HCAL depth/timing have improved signal efficiency by factors up to $8$–$17$ relative to Run 2 for key benchmarks, enabling sensitivity to $c\tau$ up to $100$ m for masses down to few GeV (Collaboration, 24 Jan 2026).
• ATLAS: Trackless-jet, Calorimeter-Ratio, and Muon-RoI-Cluster triggers collectively yield acceptance up to $2$–$10\%$ for multi-meter decays; efficiency plateaus at $40\%$ in the MS for select lifetimes (Collaboration, 2013).
• HL-LHC/HLT upgrades: Prospective deployments of hardware track triggers, MIP timing layers, and real-time ML inference at L1 will further recover $10$–$50\%$ efficiency for broad LLP scenarios without swamping bandwidth (Gershtein, 2017, Petrillo et al., 2022, Mårtensson et al., 2019, Bhattacherjee et al., 2023).
• LHCb: GPU-based first-level reconstruction enables LLP-dedicated trigger lines capable of $2.6$–$8.5\times$ efficiency gains; downstream extension is immediately feasible with minimal rate cost (Pica, 2024).

Open R&D areas include pile-up resilience via deep learning, regional 4D vertexing, non-standard background calibration, high-bandwidth track timing, and FPGA-based pattern recognition for downstream tracking.

In summary, a comprehensive set of hardware, software, and hybrid trigger strategies is essential for high-efficiency detection of LLPs across diverse lifetimes, mass ranges, and decay topologies. The ongoing evolution of these triggers, algorithms, and data-taking modes will substantially enhance the sensitivity of LHC experiments to hidden-sector and other BSM targets through Run 3 and the HL-LHC era (Stolarski, 2017, Collaboration, 2013, Collaboration, 24 Jan 2026, Alimena et al., 2021).