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 scotogenic model, originally proposed by Ernest Ma in 2006, achieves two goals at once. It generates neutrino masses radiatively, meaning they arise only through quantum loop corrections rather than at tree level, and it supplies a stable dark matter candidate in the same stroke. In its canonical form, the model extends the Standard Model with a second Higgs doublet, usually called eta, and singlet fermions known as right-handed neutrinos. A discrete Z2 symmetry is imposed by hand, forbidding the terms that would otherwise allow neutrino masses at tree level and ensuring the lightest eta component cannot decay, making it a viable dark matter particle. The trouble is that this Z2 symmetry is essentially ad hoc, inserted into the theory without any deeper justification.

Takaaki Nomura of Sichuan University and Oleg Popov of Shenzhen MSU-BIT University have now shown that this ad hoc ingredient can be replaced by something far more fundamental. In a paper published in The European Physical Journal C, they constructed scotogenic models based on non-invertible Z_M symmetries, sometimes called no-group symmetries. Unlike ordinary symmetries, which form groups in which every operation can be undone by an inverse, non-invertible symmetries obey fusion rules in which combining two operations yields a sum of possibilities rather than a single unique result. These exotic structures have surged to prominence in theoretical physics in recent years, appearing naturally in string theory constructions and in the study of generalized symmetries.

The technical machinery behind the new work is subtle but conceptually clean. Instead of assigning ordinary group representations to particles, the authors assign conjugacy classes, denoted [g^k], to each field in the theory. The product of two classes follows the rule [g^k][g^k’] = [g^(k+k’)] + [g^(M-k+k’)], and a term in the Lagrangian is allowed only if the product of the classes of its fields contains the trivial class [g^0]. This selection rule, rooted in constructions from type IIB string theory with magnetized extra dimensions, replaces the familiar group-action invariants of conventional flavor model building. Remarkably, such symmetries can be broken by radiative corrections even when they are exact at tree level, a feature that connects naturally to the radiative character of the scotogenic mechanism itself.

The authors systematically searched for the minimal choice of M and the minimal assignment of classes that could distinguish the three generations of leptons, generate neutrino masses exclusively at one loop, stabilize dark matter, and leave the Standard Model Higgs trivial so that the quark sector remains untouched. The counting is tight: at least three classes are needed to tell the three lepton generations apart, which rules out M below 4, and separating the singlet neutrinos from the Standard Model leptons requires M of at least 8. Smaller choices fail because they inevitably leave dangerous operators, such as the coupling that would let the inert Higgs doublet decay, unfrozen.

Viable models emerge for M equal to 8, 10, and 11. In the M=8 benchmark, the Standard Model leptons carry classes [g^0], [g^4], and [g^2], while two generations of singlet fermions carry [g^3] and [g^1]. This assignment produces a sparse Yukawa coupling matrix connecting the leptons to the singlet fermions through the inert doublet, and it forbids the term that would spoil dark matter stability. An elegant bonus emerges here: the viable models accidentally possess an exact Z2 symmetry at the renormalizable level, with the singlet fermions and the inert doublet each flipping sign, precisely mirroring the symmetry of the original scotogenic model. This accidental Z2 is protected against radiative breaking, so dark matter stability is guaranteed with no new fields beyond the canonical setup.

The payoff for this symmetry engineering is predictivity. Because the class assignments force a specific sparse pattern of Yukawa couplings, the resulting neutrino mass matrix has a one-zero texture, meaning exactly one of its nine entries vanishes. The location of that zero depends on which classes are assigned to which leptons, and each texture imposes analytic relations among the neutrino mixing angles, masses, and CP-violating phases. The authors performed a detailed numerical scan for two benchmark models, fitting the oscillation data from the NuFit 6.0 global analysis and computing a chi-squared measure of the fit quality. In the minimal M=8 benchmark, with only two singlet fermions, the neutrino mass matrix has rank two and only the inverted mass hierarchy can be fitted, with strikingly narrow predictions: the Dirac CP phase is pinned near plus or minus 90 degrees and the Majorana phase alpha_21 near plus or minus 20 degrees.

The richer M=11 benchmark, with three singlet fermions, accommodates both the normal and inverted hierarchies and yields broader but still structured predictions. For the normal hierarchy, the Dirac CP phase can take any value while the Majorana phase alpha_21 prefers the range from 50 to 180 degrees. For the inverted hierarchy, the Dirac phase again clusters around plus or minus 90 degrees. The model also makes concrete statements about observables at the frontier of experiment. The effective mass for neutrinoless double beta decay, which governs whether experiments like KamLAND-Zen can see this hypothetical process, falls in a range where the inverted hierarchy case could be tested in the near future, while normal hierarchy points sit below current bounds. Cosmological limits on the sum of neutrino masses from Planck and the DESI baryon acoustic oscillation measurements further constrain the allowed parameter space.

Charged lepton flavor violation provides another sharp test. The same loop diagrams that generate neutrino masses induce processes such as muon decay to an electron and a photon, muon-to-electron conversion in nuclei, and three-body lepton decays, all of which are bounded by experiments including MEG, Belle II, and earlier searches. The strongest constraint comes from the limit on muon to electron gamma decay, currently about 3.1 times 10 to the minus 13 in branching ratio. Intriguingly, the class assignments dictate which flavor-violating channels are allowed at all: a vanishing (12) element of the neutrino mass matrix permits tau to electron gamma and tau to muon gamma but forbids muon to electron gamma at one loop, while other textures flip the pattern. The authors also checked that quantum corrections do not regenerate the forbidden zero entries, showing that the induced contributions are suppressed by a factor of order 10 to the minus 8 and can be safely neglected.

The broader significance of the work lies in what it demonstrates about the toolkit of modern flavor physics. Discrete flavor symmetries have long been the orthodox route to explaining lepton mixing, modular symmetries have flourished over the past decade, and non-holomorphic modular approaches have offered a more minimal variant. Non-invertible symmetries now join this lineage, and the new study shows they can do real work: replacing an ad hoc stabilizing symmetry with one whose origins trace back to string theory, while simultaneously imposing texture zeros that sharpen the model’s predictions for CP phases, neutrinoless double beta decay, and collider signatures of the inert doublet. As experiments close in on the neutrino mass ordering, the CP phases, and rare lepton decays, models of this kind offer something increasingly precious in beyond-Standard-Model physics: concrete, falsifiable targets.

Subject of Research: A scotogenic model of radiative neutrino masses and dark matter based on non-invertible Z_M symmetries

Article Title: Scotogenic model with non-invertible symmetry

Article References: Nomura, T., & Popov, O. (2026). Scotogenic model with non-invertible symmetry. The European Physical Journal C, 86(9), Article 1070. https://doi.org/10.1140/epjc/s10052-026-16287-7

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16287-7

Keywords: scotogenic model, non-invertible symmetry, neutrino masses, dark matter, flavor symmetry, radiative mass generation, CP violation, neutrinoless double beta decay, charged lepton flavor violation, beyond the Standard Model, string theory, Z_M symmetry

The starting point is a set of facts the standard model simply cannot accommodate. Neutrino oscillation experiments have established beyond doubt that neutrinos have nonzero mass, something the standard model forbids. Observations of the abundances of light elements forged in the Big Bang, together with measurements of the cosmic microwave background, show that the early universe contained slightly more baryons than antibaryons, another phenomenon the standard model cannot produce. And a wealth of astrophysical and cosmological evidence points to dark matter, an invisible substance that outweighs ordinary matter roughly five to one, for which the standard model offers no candidate at all. Extending the model with right-handed neutrinos that carry Majorana masses has long been known to address the first two problems: the seesaw mechanism explains why observed neutrinos are so light, and leptogenesis, the out-of-equilibrium decay of heavy right-handed neutrinos, can seed the baryon asymmetry, provided those masses exceed roughly a billion giga-electronvolts.

What makes the new work striking is the claim that all three problems can be solved at the relatively low energy scale of a few tera-electronvolts, within the original scotogenic model and without adding any new interactions. The scotogenic model, introduced by Ernest Ma in 2006, extends the standard model with three right-handed neutrinos and an extra inert doublet scalar, both assigned odd parity under an imposed Z2 symmetry while all ordinary particles carry even parity. Because the inert doublet acquires no vacuum expectation value, neutrino masses vanish at tree level. Instead, they arise radiatively through a one-loop diagram in which the right-handed neutrinos couple to leptons and the inert scalar, with the small parameter lambda-5 in the scalar potential controlling the resulting tiny masses. The same Z2 symmetry renders the lightest odd particle absolutely stable, a built-in dark matter candidate.

Previous attempts to make the lightest right-handed neutrino the dark matter in this framework ran into two serious obstacles. First, if the dark matter particle annihilates efficiently enough to leave the correct relic abundance in the standard freezeout scenario, its neutrino Yukawa couplings must be of order one, and such large couplings induce lepton-flavor-violating processes such as the decay of a muon into an electron and a photon at levels already excluded by experiment. Second, generating sufficient lepton number asymmetry from right-handed neutrinos with masses of only a few tera-electronvolts is notoriously difficult, because the CP asymmetry in their decays is typically too small at that scale. Many authors have therefore extended the model with extra interactions, such as a new gauge symmetry, to circumvent these problems.

Suematsu’s solution exploits a detailed feature of the neutrino mass matrix that emerges when the diagonalization condition makes the mass eigenvalues expressible directly in terms of the Yukawa couplings. In the concrete example analyzed, the Yukawa texture yields the tribimaximal mixing pattern, with one neutrino mass eigenvalue exactly zero, and the charged-lepton sector supplies the small corrections needed to match oscillation data. Crucially, the CP asymmetry required for leptogenesis is proportional to the imaginary part of a combination of Yukawa couplings, which vanishes if those couplings are real. The analysis shows that complex Yukawa couplings, or the special case with a zero mass eigenvalue combined with Majorana phases in the right-handed neutrino masses, allow a nonzero asymmetry. A numerical benchmark with the two heavier right-handed neutrinos and the neutral component of the inert doublet all near three tera-electronvolts reproduces the measured mass-squared differences of neutrino oscillations while keeping lepton-flavor-violating decays safely below current bounds.

The dark matter abundance is handled through a mechanism quite different from the usual freezeout. Because the lightest right-handed neutrino’s Yukawa coupling is extremely small, it never reaches thermal equilibrium; instead it is produced by the gradual, so-called freeze-in process, mainly through the decay of the next-lightest inert scalar component, which itself is kept in equilibrium by standard model interactions and coannihilation. Solving the coupled Boltzmann equations for the number densities shows that the final dark matter abundance can be tuned to the observed value, corresponding to a density parameter of about 0.12, by choosing the small Yukawa coupling appropriately for dark matter masses ranging from a few giga-electronvolts up to the tera-electronvolt scale, and even down to the kilo-electronvolt range. When the dark matter mass approaches that of its decaying mother particle, the scalar quartic couplings lambda-3 and lambda-4, which control the coannihilation rate, become essential dials, and the analysis finds that a dark matter mass of at least about 8.5 giga-electronvolts is needed in the simplest case.

The leptogenesis side relies on an elegant trick: a strict near-degeneracy between the second-heaviest right-handed neutrino and the neutral inert scalar, with their masses differing by a fraction of order one hundred-thousandth or less. This degeneracy suppresses the decay width of the heavier neutrino through phase-space factors, delaying its decay until it falls far out of thermal equilibrium, exactly the condition leptogenesis requires. Meanwhile, a tiny mass splitting with the heaviest right-handed neutrino, of order one part in a billion, resonantly enhances the CP asymmetry through the self-energy diagram, boosting it to the level of ten to the minus seven needed to generate the observed lepton asymmetry of order ten to the minus ten. Quantum corrections to the right-handed neutrino masses, calculated at two loops, turn out to be far too small to spoil this delicate degeneracy, so no extra symmetry is needed to protect it.

The full numerical treatment, tracking the number densities of the decaying neutrino, the lepton asymmetry, the inert scalar and the dark matter candidate simultaneously, confirms that the scenario holds together. The late-time decay of the second-heaviest neutrino injects additional inert scalars into the plasma, which eventually decay into dark matter and modify the final abundance, so the couplings must be retuned compared with the simplified analysis. The study shows this retuning works across the mass range: for dark matter at 150 giga-electronvolts or 1.5 giga-electronvolts, a suitably small Yukawa coupling delivers the right abundance, while for dark matter near the tera-electronvolt scale the quartic couplings must be adjusted so that the combined abundance of the scalar and the dark matter particle converges to the required value. Notably, because the dark matter is the right-handed neutrino itself, direct detection experiments impose no constraint on the scalar quartics, a sharp contrast with the case where the inert scalar is the dark matter.

The scenario also carries testable consequences. The charged and neutral components of the inert doublet, with masses near three tera-electronvolts, could be produced at future colliders, where processes yielding multiple leptons plus missing transverse energy, displaced vertices from long-lived charged scalars, or deviations in the Higgs decays to two photons and to a photon plus a Z boson could distinguish this model from the ordinary inert doublet model. Predictions for the effective masses governing neutrinoless double beta decay and beta decay come out far below present experimental sensitivity, and the induced lepton-flavor-violating branching ratios and the electron electric dipole moment are similarly tiny, making them difficult but not impossible targets for next-generation searches. If the picture is right, the three great mysteries left unsolved by the standard model would trace back to a single family of particles, with the universe’s missing mass and its matter-antimatter imbalance written into the same small set of couplings, and the decisive evidence waiting in the debris of high-energy collisions rather than in a deep underground detector.

Subject of Research: Right-handed neutrino dark matter and leptogenesis in the scotogenic model

Article Title: Right-handed neutrino dark matter consistent with the generation of baryon number asymmetry

Article References: Suematsu, D. (2026). Right-handed neutrino dark matter consistent with the generation of baryon number asymmetry. The European Physical Journal C, 86(10), Article 1143. https://doi.org/10.1140/epjc/s10052-026-16425-1

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16425-1

Keywords: dark matter, right-handed neutrinos, scotogenic model, leptogenesis, baryon asymmetry, neutrino masses, seesaw mechanism, freeze-in, inert doublet, Z2 symmetry, CP asymmetry, particle physics

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