Long-Lived Particles (LLPs)

• LLPs are hypothetical particles characterized by macroscopic lifetimes that cause their decays to occur far from the initial production vertex.
• They arise in multiple beyond-Standard-Model theories, including supersymmetry, dark sectors, and neutrino mass mechanisms, addressing key open questions in physics.
• Experimental detection of LLPs relies on innovative methods like displaced vertex reconstruction and precision timing, enhancing the search for new phenomena.

Long-lived particles (LLPs) are hypothetical states characterized by macroscopic lifetimes such that their decays occur at spatial locations displaced from the production vertex or with time delays resolvable by modern detectors. LLPs are an essential feature of many extensions of the Standard Model (SM), predicted by a diverse range of theories addressing the hierarchy problem, the nature of dark matter, baryogenesis, and the origin of neutrino masses. Their discovery would signal new fundamental principles in particle physics. The phenomenology of LLPs is distinguished by the interplay of their suppressed decay widths, the unique production topologies, and the distinctive detector signatures they produce—necessitating dedicated experimental strategies.

1. Theoretical Motivation and Characteristic Lifetimes

A long-lived particle is defined by a proper lifetime τ large enough that the mean decay length in the lab frame, $d = \beta\gamma c\tau$, exceeds experimental spatial (∼100 μm) or temporal (∼100 ps) resolution (Jeanty et al., 22 Nov 2025). The mechanisms driving large τ are diverse:

• Small couplings: Decay via higher-dimensional operators or portals (e.g., Higgs portal, kinetic mixing) leads to polynomial or exponential suppression of Γ.
• Kinematic suppression: Small mass splittings (e.g., co-annihilation, inelastic dark matter) reduce phase space, further diminishing partial decay rates as $\propto(\Delta m)^n$.
• Heavy mediators: Decays proceeding through propagators of mass $M_{\rm med}\gg m_{\rm LLP}$ produce additional suppression $|\mathcal{M}| \sim g^2 / M_{\rm med}^2$.

The resulting lifetimes span a wide range: from $\sim10^{-13}$ s (prompt) to cosmologically relevant values, with experimentally accessible regions corresponding to decay lengths from microns to kilometers (Jeanty et al., 22 Nov 2025, Curtin et al., 2018).

Leading theoretical scenarios that predict LLPs include:

• Supersymmetry: Gauge-mediated SUSY breaking, split SUSY, and R-parity violating (RPV) scenarios generically produce neutralinos, gluinos, or sleptons with macroscopic cτ (Chou et al., 2016).
• Dark Sectors: Hidden Valleys with confining dynamics, twin sectors (Neutral Naturalness), or models with light dark photons or scalars can yield LLPs via portal couplings (Curtin et al., 2018, Collaboration, 30 Oct 2025).
• Neutrino Mass Mechanisms: Low-scale seesaw models introduce sterile neutrinos stabilized by small Yukawa mixing or right-handed scale (Jeanty et al., 22 Nov 2025, Beltrán et al., 2023).
• Freeze-in/Asymmetric DM and Baryogenesis: Out-of-equilibrium decays governed by small rates to dark states, natural in various baryogenesis and freeze-in dark matter frameworks (Curtin et al., 2018).
• Type-I Two-Higgs-Doublet Models and Extended Higgs Sectors: Allow for light, weakly-coupled scalars and pseudoscalars with large lifetimes (Qi et al., 17 Aug 2025).

These generic mechanisms can produce neutral, singly or doubly charged, hadronic, or leptonic LLPs, spanning vast regions of mass–lifetime parameter space (Jeanty et al., 22 Nov 2025, Qi et al., 17 Aug 2025).

2. Production Mechanisms and Detector Signatures

LLPs are produced at colliders and fixed-target experiments via several channels:

• Heavy resonance decays: Exotic Higgs decays (e.g., $h\to XX$), $Z'$ or other mediator decays, and on- or off-shell heavy parent states (Alipour-fard et al., 2018, Collaboration, 30 Oct 2025).
• Drell–Yan or QCD production: Pair or associated production in hadronic collisions, prevalent for neutralinos, gluinos, or heavy vectorlike quarks (Jackson, 2011, Bhattacherjee et al., 11 Mar 2025).
• Meson decays: Rare $B$, $D$, or $K$ decays produce light LLPs (e.g., ALPs, heavy neutral leptons), with reach at dedicated experiments like DUNE and FASER (Coloma et al., 2023, Qi et al., 17 Aug 2025).

The unique signatures of LLPs are dictated by their cτ and quantum numbers:

• Heavy stable charged particles (HSCPs): Charged LLPs traversing the entire detector, detected via anomalous $dE/dx$, time-of-flight (ToF), and high $p_T$ tracks (Jackson, 2011, Jeanty et al., 22 Nov 2025).
• Displaced vertices (DVs): Neutral LLPs decaying inside the tracker, calorimeter, or muon system, reconstructed from two (or more) tracks with large transverse impact parameters or via secondary vertices (Gonski, 2022, Alipour-fard et al., 2018).
• Delayed or non-pointing objects: Photons, jets, or leptons appearing out-of-time or failing to point back to the primary vertex, enabled by precision timing detectors (Liu et al., 2018).
• Stopped-particle decays: LLPs stopping in detector material and decaying out-of-time (Jackson, 2011).
• Emerging jets or “jet–lepton–MET” topologies: Multi-decay signatures from dark showers or multipartite LLP production (Jeanty et al., 22 Nov 2025, Collaboration, 2 Feb 2024).

These features drive the necessity for custom reconstruction techniques and trigger strategies, exploiting impact parameter, timing, energy deposition, and topological variables.

3. Experimental Methods and Analytical Techniques

Experimental discovery of LLPs faces significant challenges due to rare backgrounds and the non-standard signature morphologies:

• Tracking and vertexing: Dedicated large-radius tracking (LRT), vertex reconstruction algorithms, and impact-parameter fitting recover tracks/vertices with $|d_0|$ up to several centimeters (Gonski, 2022, Klamka, 2023).
• Calorimeter and muon system use: Precision timing (down to 30 ps), shower pointing, and calorimeter energy deposition algorithms identify delayed or non-pointing objects (Liu et al., 2018, Collaboration, 2 Feb 2024).
• Data-driven background estimation: Isolation-based ABCD methods using orthogonal triggers enable robust background determination in regions where simulation fails, especially for single-DV searches (Coccaro et al., 2016).
• Machine learning and deep learning: Deep neural network classifiers (CNNs, GNNs) operating on low-level hit or track data improve background rejection and maximize signal efficiency, achieving model-independent branching ratio sensitivity down to $10^{-6}$ for $H\to$ LLPs at lepton colliders (Zhang et al., 10 Jan 2024).
• Timing-based event selection: Precision timing allows discrimination of delayed LLP decay products from prompt SM backgrounds, with background suppression scaling exponentially with the timing cut (Liu et al., 2018).

Model-independent strategies relying on minimal assumptions about the decay topology or kinematics, as well as reinterpretation frameworks to translate between different simplified models, are critical for coverage of broad classes of LLPs (Beltrán et al., 2023).

4. Detector Infrastructure and Dedicated LLP Facilities

While ATLAS, CMS, and LHCb employ inner tracking, calorimetry, muon systems, and upgraded timing layers, principal limitations arise for decay lengths $c\tau \gg 1$–$10$ m, soft final states, or non-hadronic LLPs (Chou et al., 2016, Curtin et al., 2018). This motivates:

• Auxiliary large-volume detectors: MATHUSLA (surface, $200{\rm m}\times200{\rm m}\times20\rm m$), ANUBIS (cavern or shaft above ATLAS), CODEX-b (LHCb), and FASER (far-forward) extend sensitivity to $c\tau$ from $O(1)$ m up to the BBN limit ($10^7$ m), targeting neutral, non-interacting signatures (Collaboration, 30 Oct 2025, Chou et al., 2016, Curtin et al., 2018).
• Future lepton-collider detectors: The ILD at ILC or IDEA at FCC-ee employ low-material, high-efficiency tracking and specialized displaced-vertex algorithms, offering nearly background-free coverage of lifetimes up to the tracker/muon-system radius (Klamka, 2023, Bhattacherjee et al., 11 Mar 2025).
• Dedicated timing/trigger systems: CMS MTD, ATLAS HGTD, and future timing layers further enhance delayed signature acceptance for medium-lifetime ($c\tau \sim 0.1$–10 m) regimes (Liu et al., 2018, Gonski, 2022).

Hybrid geometries and staged deployments are being considered to maximize both geometric acceptance and cost-effectiveness, with designs informed by detailed Monte Carlo and data-driven effectiveness analyses (Collaboration, 30 Oct 2025, Bhattacherjee et al., 11 Mar 2025).

Representative Sensitivities

Detector/Experiment	Typical $c\tau$ reach	Sensitivity to BR($h\to$ LLPs)	Notes
ATLAS/CMS	0.1–10 m (main), up to few $\times$10 m (muon sys)	$10^{-3}$–$10^{-2}$	Prompt/displaced, high $p_T$
MATHUSLA	10–$10^7$ m	$10^{-6}$–$10^{-5}$	Surface, model-independent
ANUBIS	0.1–$10^3$ m	$10^{-6}$--$10^{-5}$	Cavern/shaft, complementary to others
FCC-ee (IDEA)	mm–few m (VTX, DCH)	$10^{-5}$–$10^{-4}$	Clean, low-mass, full PID
FASER/FASER 2	10–$10^3$ m	$10^{-6}$ (rare meson LLPs)	Far-forward, light/ultra-long-lived
DUNE ND-GAr	0.1–10 m	BR($M\to$ LLP) $\sim 10^{-18}$	Meson decays, low-mass, clean final

5. Parameter Space, Constraints, and Future Prospects

Current experimental searches have begun excluding broad classes of LLPs:

• HSCPs: Gluino R-hadrons excluded up to $m_{\tilde{g}}\sim2$ TeV for $c\tau \gg 10$ m; stau masses $<430$ GeV for $c\tau>10$ m (Jackson, 2011, Gonski, 2022).
• Displaced vertex/jet/photon: Exclusions at typical $\sigma\times{\rm BR}\gtrsim 0.1$–$1$ pb for $c\tau\sim1$ mm–1 m and $m\sim100$ GeV; exotic Higgs branching fractions below 1% for $c\tau\lesssim10$ m (Alipour-fard et al., 2018, Collaboration, 2 Feb 2024).
• Higgs exotic decays: HL-LHC prospects down to ${\rm BR}(h\to$ LLPs$)\sim 10^{-4}$ with advanced triggers and deep learning; FCC-ee, ILC, and CLIC projections approach ${\rm BR}<10^{-6}$ in clean final states (Zhang et al., 10 Jan 2024, Bhattacherjee et al., 11 Mar 2025).

Astrophysical and cosmological probes, including Big Bang Nucleosynthesis (BBN), supernova cooling, and CMB/structure formation, impose constraints on excessively long-lived or feebly-coupled states, bounding $c\tau\lesssim10^8$ m for electromagnetically coupled LLPs and requiring dedicated cosmological modeling in regions beyond laboratory reach (Jeanty et al., 22 Nov 2025, Chou et al., 2016).

The next generation of experiments, with enhanced tracker, timing, and vertex-finding capabilities, and the construction of auxiliary detectors, are projected to bridge the current “lifetime frontier,” completing sensitivity to proper lifetimes from ∼100 μm up to the BBN limit in a model-independent way (Chou et al., 2016, Collaboration, 30 Oct 2025). Data-driven background estimation frameworks, machine learning–augmented signal selection, and rapid recasting techniques for reinterpretation will be central to fully realizing the LLP discovery potential.

6. Impact, Model Independence, and Programmatic Directions

LLP searches probe fundamentally inaccessible regions for promptly decaying exotica, often being the only viable signatures for critical BSM scenarios such as Neutral Naturalness, low-scale leptogenesis, gauge mediation, or asymmetric dark matter (Jeanty et al., 22 Nov 2025, Curtin et al., 2018). The parameter scaling of signal yield with lifetime varies with analysis design:

• Paired-DV or double-LLP: $N_{\rm signal} \propto (c\tau)^{-2}$ for decays inside the tracker/muon system with both LLPs required to decay visibly (Coccaro et al., 2016).
• Single-DV, inclusive or timing-based: $N_{\rm signal} \propto (c\tau)^{-1}$; lifetime reach is extended at the price of slightly increased backgrounds, now controllable with model-independent techniques (Liu et al., 2018, Coccaro et al., 2016).

A comprehensive LLP program requires:

• Inclusive, minimally model-dependent searches sensitive to all possible lifetimes and decay modes (Coccaro et al., 2016).
• Transparent background estimation and validation using orthogonal trigger or object definitions (Coccaro et al., 2016, Gonski, 2022).
• Analysis strategies accounting for low-mass, soft, or low-multiplicity decay patterns—often missed by standard high-mass, high-multiplicity search pipelines (Bernreuther et al., 2020).

The ongoing development of auxiliary detectors, advanced analysis pipelines, and model-independent statistical methods ensures that the LLP sector remains at the forefront of discovery potential, offering a unique probe into otherwise unreachable BSM phenomena.