The work, by Renjie Wang of the Institute of High Energy Physics in Beijing, focuses on the scotogenic model, one of the most elegant extensions of the Standard Model. In this framework, neutrinos acquire their tiny masses radiatively — through quantum loops rather than direct couplings — thanks to a hidden sector of new particles protected by an exact symmetry. That same symmetry also supplies a natural dark matter candidate, making the model unusually economical: one structural addition explains neutrino mass and dark matter at once.

The key insight is a numerical coincidence with profound experimental consequences. To reproduce the observed sub-electronvolt neutrino masses, the Yukawa couplings linking the hidden sector to ordinary leptons must be extraordinarily small, of order one thousandth. Such feeble interactions make the heavy neutral fermion known as N2 exceptionally long-lived: rather than decaying promptly, it survives for tens to hundreds of millimetres, travelling a macroscopic distance through the detector before it decays. Measuring that flight path would, in effect, be measuring the very coupling that generates neutrino mass.

Wang’s study explores a particularly challenging corner of the model’s parameter space, called the compressed-spectrum regime, in which a charged scalar particle and N2 are separated by only about 200 MeV — roughly the mass of a proton. In this regime, a second, even tinier Yukawa entry, of order one millionth, renders the charged scalar long-lived as well. The result is a nested cascade unique in collider physics: the charged scalar crosses the inner tracker as a high-momentum track that abruptly disappears when it decays into N2 plus a lepton too soft to be detected, and then the neutral N2 continues invisibly for another macroscopic distance before decaying into a pair of electrons or muons at a displaced vertex.

This nested disappearing-track-plus-displaced-vertex topology offers two decisive experimental handles. The first is spatial: because N2 is emitted at the endpoint of the vanishing track, the vector connecting that endpoint to the displaced vertex must align with the original track direction to within a few milliradians. No known Standard Model process produces a high-momentum charged track that disappears and is then followed, in the same flight direction, by a displaced dilepton vertex. The second handle is temporal: the two slow, sequential flights accumulate a combined time-of-flight delay of roughly 200 to 800 picoseconds, resolvable by the CMS MIP Timing Detector, a precision timing layer planned for the High-Luminosity LHC upgrade.

Together, these requirements suppress the expected Standard Model background to between one hundred-thousandth and one thousandth of an event over the full High-Luminosity LHC dataset of 3000 inverse femtobarns. Crucially, the discovery reach is robust: even if the background were underestimated by four orders of magnitude and reached ten events, a five-sigma discovery would still require only about twenty signal events. At the study’s benchmark point — an N2 mass of 150 GeV with proper decay lengths of 300 and 189 millimetres for the charged scalar and N2 respectively — the analysis yields roughly 1212 signal events, an overwhelming margin.

The analysis was performed with a deliberately conservative, reconstruction-level strategy. Every observable entering the selection, from the timing reference to the displaced-vertex position, is built from quantities a real detector would measure, with only one truth-level input: the requirement that the vanishing track traverse all four barrel pixel layers, decaying at a radius between 160 and 300 millimetres. Two complementary Level-1 trigger paths — one based on an energetic initial-state radiation jet plus missing energy, the other on a displaced muon — ensure the rare events can be recorded at all, since no hard charged object appears at the primary collision point.

Scanning a grid of 56 benchmark points across the two-dimensional plane of the two decay lengths, the study finds that all 40 points with measurable disappearing tracks exceed both the five-sigma discovery threshold and the 95 percent confidence exclusion limit, with peak sensitivity of about 1635 signal events at decay lengths of 150 and 60 millimetres. The remaining 16 points, where the charged scalar decays too early to leave a reconstructable track stub, fall into a blind zone that only a dedicated displaced-vertex search could address. No existing ATLAS or CMS analysis simultaneously targets this correlated cascade: standalone disappearing-track searches assume the downstream particle is effectively stable, while standalone displaced-vertex searches impose no upstream track requirement.

The deeper significance lies in what the measurement would reveal. Because the N2 decay length is controlled by the same Yukawa couplings that generate sub-electronvolt neutrino masses, the covered region probes couplings between roughly six ten-thousandths and four thousandths — precisely the range associated with the neutrino mass scale. Mapping the nested cascade would therefore turn the High-Luminosity LHC into a direct collider probe of the interaction responsible for neutrino mass, complementing neutrino oscillation experiments and cosmological observations.

Challenges remain before the strategy can be implemented in practice. The dominant residual background arises from pileup combinatorics at the HL-LHC’s expected 200 simultaneous collisions per bunch crossing, and a definitive estimate will require data-driven control regions or full pileup-overlay simulation with four-dimensional tracking. Tau-lepton decay channels of N2, which would demand more complex vertex reconstruction, are deferred to future work. Nevertheless, the study provides a concrete roadmap for adding the scotogenic nested cascade to the Run 4 search programme — and a vivid reminder that the next neutrino-mass clue may not come from a deep underground detector, but from a track that vanishes in the dark of the CMS pixel barrel.

Subject of Research: A collider search strategy for long-lived particles in the scotogenic neutrino mass model at the High-Luminosity LHC

Article Title: Nested disappearing-track plus displaced-vertex topology at the HL-LHC: a dual long-lived-particle signature of the scotogenic model

Article References: Wang, R. (2026). Nested disappearing-track plus displaced-vertex topology at the HL-LHC: a dual long-lived-particle signature of the scotogenic model. The European Physical Journal C, 86(10), Article 1187. https://doi.org/10.1140/epjc/s10052-026-16416-2

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16416-2

Keywords: scotogenic model, neutrino mass, long-lived particles, disappearing track, displaced vertex, HL-LHC, CMS MIP Timing Detector, dark matter, Yukawa coupling, particle physics, beyond the Standard Model, Nested

The target of the proposed search is the minimal scotogenic model, an elegant extension of the Standard Model first proposed by Ernest Ma in 2006. In this framework, neutrino masses and the dark matter particle are linked in a single loop of quantum processes. The model adds a set of particles that are odd under a symmetry called Z2, including an inert scalar doublet and heavy right-handed neutrinos. When the lightest of these new fermions plays the role of dark matter, the observed abundance of dark matter in the universe, corresponding to a relic density of about 0.12 in standard cosmological units, can be naturally explained if it co-annihilates with a charged partner scalar whose mass lies only a few gigaelectronvolts above its own.

That compressed mass regime is precisely where the LHC struggles most. When the charged inert scalar and the dark matter fermion are separated by only about 2 GeV, the scalar decays into a dark matter particle plus a single very soft charged lepton, typically carrying a transverse momentum near 2 GeV. This sits right at the edge of standard track reconstruction, which at CMS requires transverse momenta of roughly 2 GeV or more. In the detector’s 3.8 tesla magnetic field, such a low-momentum lepton curves with a gyration radius of about 1.8 meters, exceeding the tracker’s radius and degrading conventional reconstruction. Meanwhile, the charged parent itself travels visibly through the inner detector as a heavy particle before abruptly vanishing, leaving what physicists call a disappearing track: a stub of hits that terminates with no matching continuation.

Existing searches were not built for this topology. ATLAS’s displaced-lepton searches typically demand lepton momenta above 30 to 60 GeV, a factor of fifteen or more beyond what this signal produces. Displaced-vertex searches require two or more tracks at a common vertex, impossible when the decay yields only one soft charged particle. Disappearing-track and soft-track analyses retain only partial, unoptimized acceptance. Wang’s simplified truth-level estimates quantify this gap dramatically: for a benchmark with a 200 GeV charged scalar and a 2 GeV mass splitting, the ATLAS disappearing-track search would retain roughly 8.5 percent of the signal, the CMS version about 3.3 percent, and a soft displaced-track search a vanishing 0.01 percent, while displaced-vertex searches capture none at all.

The proposed remedy adds time as an independent observable, capitalizing on a unique capability of the HL-LHC era. Both CMS and ATLAS are installing precision timing layers, the CMS MIP Timing Detector in the barrel and the ATLAS High-Granularity Timing Detector in the endcaps, each offering about 30 picoseconds of timing resolution for minimum-ionizing particles. These devices were primarily conceived to disentangle the roughly 200 simultaneous proton-proton collisions expected per bunch crossing. But the study shows they can do far more. The 2 GeV mass splitting makes the charged scalar long-lived: with a Yukawa coupling of roughly nine parts in ten million, its decay length reaches about 300 millimeters, corresponding to a lifetime of one nanosecond. The parent travels macroscopic distances, between roughly 100 and 1000 millimeters, before decaying.

That journey creates a measurable delay. Because the parent scalar moves at only about 35 percent of the speed of light, the decay products arrive at the timing layer tens to hundreds of picoseconds late relative to a prompt particle born at the collision point. For the 200 GeV benchmark, the expected delay is about 700 picoseconds, once a small helical path-length correction in the magnetic field is included, more than twenty times the detector’s timing resolution. By contrast, every prompt Standard Model background, from W boson decays to b-hadron semileptonic decays, produces arrival delays below about 0.2 picoseconds, a separation of more than three orders of magnitude. The signal and background thus occupy cleanly distinct regions of a two-dimensional map of momentum versus timing delay.

The proposed signal region, labeled SR-4DT, combines six requirements: missing transverse energy above 105 GeV at trigger level and 150 GeV in the final selection, a leading jet above 100 GeV from initial-state radiation, a delayed timing hit in the MTD barrel with a delay exceeding 200 picoseconds, a mandatory low-momentum disappearing-track stub between 0.7 GeV and 300 millimeters transverse displacement that points to the timing hit, a veto on any prompt lepton above 25 GeV, and compatibility with the hard-scatter primary vertex. Crucially, the analysis never demands full lepton reconstruction, sidestepping the tracking threshold that cripples conventional approaches. The stub-hit pointing requirement, with an angular window of 0.1 in radius, suppresses accidental coincidences by roughly a factor of a thousand or more.

The simulated performance is remarkable. Across 4.2 million simulated prompt Standard Model background events, spanning W plus jet, Z plus jet and top pair production at a combined equivalent luminosity of 20.6 inverse femtobarns, not a single event survived the SR-4DT selection. Signal efficiencies range from 12 to 36 percent across the probed mass range, with 14 percent at the 200 GeV benchmark, translating to roughly 2,331 signal events at the full 3,000 inverse femtobarns of the HL-LHC program, fifty-four times above even the conservative exclusion threshold. Under deliberately conservative background assumptions derived from the finite simulated sample, the projected 95 percent confidence-level exclusion reaches charged scalar masses of about 670 GeV at a decay length of 300 millimeters; in the optimistic zero-background limit, the reach extends to roughly 1,100 GeV. The sensitivity holds across the full lifetime scan from 10 to 3,000 millimeters, with the yield peaking near 300 millimeters where both the timing delay and the stub reconstruction are optimal.

Wang is careful about the study’s limits. The simulation uses Delphes-level fast detector response with a parametrized timing layer, and instrumental and combinatorial backgrounds, including fake stubs, random timing hits, hadronic interactions in detector material and beam-induced background, were not modeled and would require full detector simulation to quantify. Physics arguments suggest each category is strongly suppressed, but the definitive residual background remains an open question for the experimental collaborations. Pile-up contamination is controlled by the mandatory stub-to-hit association, since out-of-time pile-up vertices will rarely point to a legitimate disappearing-track stub tied to the hard-scatter primary vertex.

If confirmed experimentally, the strategy would open a discovery window onto exactly the co-annihilation corridor that cosmology favors and collider searches have historically missed. The same small Yukawa coupling that renders the charged scalar long-lived automatically evades constraints from lepton-flavor-violating muon decays and direct-detection experiments, where the scotogenic candidate’s spin-independent cross section is loop-suppressed and consistent with the latest LUX-ZEPLIN limits. With the HL-LHC’s timing detectors coming online, dark matter may soon be caught not by where it goes, but by when it arrives.

The timing-based strategy also connects to a broader effort across collider physics to exploit temporal information in event reconstruction. Timing layers like the CMS MIP Timing Detector use silicon sensors with internal gain to timestamp minimum-ionizing particles, and their performance has been validated with test-beam measurements. What the new study illustrates is that such instrumentation, designed with pile-up separation in mind, can be repurposed as a discovery tool for long-lived particles whose macroscopic lifetimes imprint a characteristic time-of-flight signature.

From a theoretical standpoint, the compressed co-annihilation corridor occupies a special place in thermal dark matter calculations. When the mass gap between a particle and its charged companion shrinks to a few gigaelectronvolts, Boltzmann suppression of the heavier species weakens, and co-annihilation processes efficiently deplete the relic abundance without requiring large annihilation cross sections for the dark matter particle itself. This same kinematic compression, however, suppresses the visible energy release in collider decays, creating the tension between cosmological viability and experimental accessibility that motivates the timing approach.

The framework may generalize beyond the scotogenic model. Compressed spectra with macroscopic decay lengths and soft visible daughters arise in supersymmetric wino and higgsino scenarios, in simplified dark matter models, and in other radiative neutrino-mass constructions. A timing-assisted search requiring only a disappearing-track stub and a delayed hit is largely model-independent, depending mainly on the parent lifetime and the presence of a timing-visible charged daughter.

Verification will require the experimental collaborations to confront full detector simulation, including the combinatorial and instrumental backgrounds absent from this fast-simulation study. If the projected zero-background regime survives that scrutiny, the HL-LHC could deliver sensitivity to a class of dark matter models whose thermal production history makes them cosmologically favored yet collider-hidden.

Subject of Research: Timing-assisted collider search for ultra-compressed scotogenic dark matter at the High-Luminosity LHC

Article Title: Probing ultra-compressed scotogenic dark matter at the HL-LHC via 4D spacetime tracking

Article References: Wang, R. (2026). Probing ultra-compressed scotogenic dark matter at the HL-LHC via 4D spacetime tracking. The European Physical Journal C, 86(9), Article 1062. https://doi.org/10.1140/epjc/s10052-026-16304-9

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16304-9

Keywords: dark matter, scotogenic model, HL-LHC, disappearing tracks, precision timing, long-lived particles, neutrino masses, co-annihilation, CMS MTD, ATLAS HGTD, particle physics, displaced leptons