The authors construct a model in which a piecewise mass function describes a Schwarzschild black hole surrounded by a finite, electromagnetically inert dark-matter distribution. The dark matter is treated as an effective addition to the black hole’s mass, with separate parameters for the mass ratio ΔM/M, the shell’s inner boundary rs and its thickness Δrs. The authors state that the framework can represent dark matter bound in a galactic halo as well as locally captured objects such as brown dwarfs, stellar-mass black holes, primordial black holes and non-radiating dust.

For the non-rotating case, the analysis identifies a critical shell mass beyond which the metric develops an additional pair of horizons. With rs/M = 2 and Δrs/M = 200, the critical values are r*/M = 152 and ΔM/M = 800/9, or about 88.9. Below that threshold, the original event horizon remains in place, although the photon sphere and shadow radius can change slightly. Above it, the outermost root becomes a new event horizon enclosing the central black hole and part of the dark-matter shell, while the photon-sphere and shadow scales increase substantially.

The authors then generalize the static model to an axisymmetric rotating spacetime using the Newman–Janis Algorithm. The resulting metric returns to the Kerr solution when ΔM = 0 and to the static configuration when the spin parameter is zero. They report that the metric satisfies the Einstein field equations and derive corresponding dark-matter density and pressure profiles. The surface stress-energy at the interfaces of the piecewise mass distribution is found to vanish.

In the rotating model, the critical dark-matter mass depends on spin and shell geometry. For an extremal black hole with a/M = 1 and Δrs/M = 200, the reported threshold is ΔM/M = 88.3 at r*/M = 150.5. Models above this threshold develop an enlarged outer horizon and additional roots in the stationary-limit equation, changing the locations and number of ergosphere layers. The reported changes concern the horizon, ergosphere, critical photon-orbit and shadow scales; the study does not establish a general expansion of every physical scale in the system.

Null geodesics are used to locate the unstable circular photon orbits that define the shadow boundary. In the high-mass regime, the critical photon orbits lie outside the dark-matter shell, where the mass function is constant and the geometry has the Kerr form with a much larger total mass. At a fixed spin, rotation and frame-dragging then have less influence relative to the enlarged shadow scale. The calculated distortion parameter consequently approaches zero, producing a nearly circular shadow even at high spin. This circularization is a model prediction rather than an observed black-hole feature.

The study also estimates the high-frequency absorption cross section from the average shadow radius and uses the surface gravity of the outer horizon to calculate Hawking temperature and thermal energy emission. At fixed dark-matter mass, the model predicts a lower emission rate as spin increases. Dark-matter masses below the critical threshold have a marginal effect, whereas above the threshold the calculated Hawking temperature becomes very small and the emission rate is strongly suppressed.

The authors compare predicted shadow diameters with EHT values of dsh/M = 11 ± 1.5 for M87* and dsh/M = 9.77 ± 0.67 for Sagittarius A*. For M87*, all theoretically allowed dark-matter masses in the plotted compatible region satisfy both the 1σ and 2σ observational intervals. For Sagittarius A*, the full allowed region satisfies the 2σ interval, while a 1σ upper limit emerges and decreases as spin rises. At a/M = 0.9, the reported constraint is ΔM/M ≤ 22.3853.

Because the high-mass branch predicts a shadow diameter beyond the EHT-compatible range, the model disfavors dark-matter configurations large enough to trigger the new outer-horizon branch near the two observed black holes. Within the study’s assumptions, the dark matter must either be absent from the immediate vicinity or have a localized mass below the relevant critical value. These limits are conditional on the piecewise, electromagnetically inert shell model, its chosen shell geometry and the adopted horizon and shadow calculations, rather than being general constraints on all possible dark-matter distributions.

Subject of Research: Theoretical modeling of rotating black holes surrounded by finite dark-matter shells and their observable shadows

Article Title: Shadow of rotating black hole surrounded by dark matter

Article References: Feng, H., Cai, Z., Yang, R.-J., & Zhang, J. (2026). Shadow of rotating black hole surrounded by dark matter. The European Physical Journal C, 86(10), Article 1180. https://doi.org/10.1140/epjc/s10052-026-16437-x

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16437-x

Keywords: black holes, dark matter, black hole shadows, Kerr spacetime, Event Horizon Telescope, null geodesics, Newman–Janis Algorithm, M87*, Sagittarius A*, Hawking radiation, Shadow, rotating

The alternative model in question is holographic dark energy, an idea born from the holographic principle of quantum gravity, which suggests that the information content of a region of space is bounded by its surface area rather than its volume. In the influential formulation proposed by Miao Li in 2004, the energy density of the vacuum is set by the square of the future event horizon, the largest horizon accessible to a future observer, divided by a constant called c. That single parameter c controls everything: for values below one, the dark energy density grows with time, the universe eventually enters a phantom regime in which the expansion accelerates ever faster, and the cosmos may end in a so-called Big Rip, a finite-time catastrophe in which galaxies, stars, atoms and ultimately spacetime itself are torn apart. Measuring c precisely is therefore not academic hair-splitting; it is a probe of how the universe ends.

Unfortunately, the simplest holographic model has run into trouble with modern data. Recent analyses of DESI DR2, which maps the three-dimensional clustering of millions of galaxies through baryon acoustic oscillations, the fossil sound waves of the primordial plasma, showed that a single fixed value of c cannot simultaneously satisfy the constraints from baryon acoustic oscillations, type Ia supernovae and the cosmic microwave background, the relic radiation of the Big Bang. The dark energy community has therefore been exploring minimal extensions of the model, and one of the most natural is to let dark matter and dark energy exchange energy. Such interacting dark energy scenarios have a long pedigree, partly because a coupling between the two dark components could explain the coincidence problem, the puzzling fact that the densities of dark matter and dark energy are comparable today despite evolving so differently over cosmic history.

The new work introduces what the authors call a density-triggered interaction. In their model, the energy transfer rate Q is proportional to 3H times a coupling function xi times the product of the dark matter and dark energy densities divided by their sum, where H is the Hubble expansion rate. The crucial novelty is that the coupling is not constant: it is suppressed at early times by a switch function that depends on the scale factor, effectively staying near zero before some transition epoch and switching on afterwards. Baryons, the ordinary matter we can observe directly, are strictly conserved and take no part in the exchange. This design protects the early universe from unwanted contamination while allowing the dark sectors to talk to each other during the late, accelerating era.

Getting the cosmology right, however, demands unusual care, and here the study makes its most instructive technical point. Even if the instantaneous coupling vanishes before recombination, the epoch when the cosmic microwave background was released, the accumulated effect of the interaction does not. The authors show that the interaction rescales the pre-recombination dark matter density by a factor smaller than one, and this modified early-time density must be consistently propagated into the computed acoustic scale, the damping scale and the drag-epoch redshift, the quantities that connect a model to CMB data. Doing this properly turns out to be decisive for the final answer.

The authors confronted the model with an unusually broad data combination: measurements of the expansion rate H(z) from cosmic chronometers, passively evolving galaxies whose ages can be dated from their stellar populations; the DESI DR2 baryon acoustic oscillation measurements; three separate supernova compilations, namely Pantheon+, the Dark Energy Survey five-year sample and the Union3 collection; and compressed CMB distance priors distilled from the Planck satellite’s final release. The parameter inference was carried out with Markov chain Monte Carlo sampling, and the competing models were compared with information criteria including the Akaike and Bayesian information criteria, which penalize models for extra free parameters.

The result for the full data combination is striking: instead of a well-defined measurement of the coupling strength, the data deliver only a lower bound, xi zero greater than 0.30 at 95 per cent confidence, sliding along a degeneracy between the coupling and the present-day matter density. Within that allowed region, the best fit improves on the non-interacting holographic model by a change in chi-squared of minus 8.4, so the coupling is genuinely preferred over the simpler version of the model. Yet the coupling leaves the holographic parameter essentially untouched: c comes out at 0.652 plus or minus 0.020, compared with 0.647 plus or minus 0.018 without the interaction. Because c remains comfortably below one, the model still predicts a phantom-like dark energy and the Big Rip fate survives the interaction unscathed.

The story takes a twist when the authors also let the switch scale, at which the interaction turns on, float freely. Allowing this extra freedom improves the fit further, but only by pushing the switch to the boundary of its prior range, where more than half of the present-day dark matter has been converted from dark energy. That is a regime in which the model behaves in ways that many cosmologists would consider physically suspect, effectively manufacturing dark matter out of the vacuum energy at a prodigious rate. A preference that appears only at the edge of an allowed range, rather than at an interior best-fit point, is a classic warning sign that the improvement may reflect parameter freedom rather than genuine physics.

Even more cautionary is the methodological finding at the heart of the paper. When the CMB shift parameter, a compressed summary of the acoustic peaks, is evaluated using the present-day matter density instead of the correctly rescaled early-time density, the data appear to deliver a highly significant preference for the coupling. The authors identify this as a spurious effect: an inconsistency in how the theory is mapped onto the observable, not evidence for new physics. The lesson generalizes far beyond holographic dark energy. In an era when extensions of the standard model are routinely tested against compressed CMB summaries, any interaction that alters the early-time matter budget must be propagated consistently through every derived quantity, or the statistics will happily reward an error with a false detection.

Where does this leave the holographic idea? Within the holographic family, the density-triggered coupling is mildly favored, and the improved fit is real as far as it goes. But the bigger picture is unforgiving: every holographic model considered remains statistically disfavored relative to plain Lambda-CDM, and none of them, interacting or not, relieves the Hubble tension, the persistent disagreement between the expansion rate measured locally from supernova-calibrated distances and that inferred from the early universe. The DESI DR2 era has sharpened the questions rather than settling them, with hints of evolving dark energy tantalizing the field while the humble cosmological constant continues to defend its title. For now, the universe’s two dark components may be whispering to each other through a density-triggered channel, but the data say the conversation is quiet, the holographic endpoint of cosmic history still looms, and lambda, improbably, remains the answer to beat.

Subject of Research: Observational constraints on an interacting holographic dark energy model with a density-triggered dark matter coupling, tested against DESI DR2 BAO and complementary cosmological data.

Article Title: Density-triggered interacting holographic dark energy: joint constraints from DESI DR2 BAO and complementary cosmological probes

Article References: K.R., T., & S.K., N. (2026). Density-triggered interacting holographic dark energy: joint constraints from DESI DR2 BAO and complementary cosmological probes. Astrophysics and Space Science, 371(10), Article 122. https://doi.org/10.1007/s10509-026-04658-1

Image Credits: AI Generated

DOI: 10.1007/s10509-026-04658-1

Keywords: dark energy, holographic dark energy, DESI DR2, baryon acoustic oscillations, cosmic microwave background, type Ia supernovae, cosmic chronometers, dark matter, interacting dark energy, Lambda-CDM, Hubble tension, Big Rip

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 research, carried out by Giorgio Arcadi of the University of Messina and INFN Catania, Abdelhak Djouadi of the University of Granada, and Stefano Profumo of the University of California, Santa Cruz, focuses on a theoretical framework known as the 2HD+a model. This construction extends the Standard Model of particle physics by adding two Higgs doublets, which give rise to two neutral scalar bosons, a pair of charged Higgs particles, and two CP-odd pseudoscalar states. One of these pseudoscalars is a light singlet field that mixes with the heavier doublet component through an angle theta, and it serves as the mediator between dark matter and ordinary matter. The dark matter candidate itself is a fermionic particle coupled to the two CP-odd bosons, and the model has become the primary benchmark that the ATLAS and CMS collaborations use to guide dark matter searches at the Large Hadron Collider.

What makes this framework especially interesting is the behavior of pseudoscalar-mediated interactions at low velocities. When dark matter particles scatter off nuclei in a detector, they move slowly compared with the speed of light, and in this non-relativistic limit, interactions mediated by pseudoscalars are suppressed by the momentum transferred in the collision. At tree level, the scattering is helicity-suppressed, meaning the direct detection cross-section becomes extraordinarily small. The dominant contribution instead arises only at one-loop order, through box and triangle diagrams involving virtual Higgs bosons circulating in quantum loops. This suppression is precisely what can push viable dark matter scenarios below the neutrino fog, where conventional searches lose their clean discovery power but where the particles may still be hiding.

Crucially, the same suppression does not apply to the processes that governed dark matter production in the early Universe. Annihilation of dark matter particles in the hot primordial plasma proceeds at much higher velocities, where s-wave contributions dominate and are not suppressed by the pseudoscalar structure. This means the model can simultaneously satisfy the observed relic density of dark matter, measured precisely by the Planck satellite, while predicting scattering cross-sections far below current experimental sensitivity. The researchers performed extensive parameter scans using the micrOMEGAs package together with purpose-built codes for the loop-induced scattering cross-section, generating roughly ten thousand viable model points in their main scan and about one thousand in a subsidiary scan designed to explore fine-tuned regions of parameter space.

The team organized their analysis into three distinct regimes based on the strength of the mixing between the singlet and doublet pseudoscalar states. In the standard regime with substantial mixing, they found that a significant fraction of parameter space naturally falls inside the neutrino fog, particularly for dark matter masses above roughly one hundred gigaelectronvolts, where annihilation into pairs of Higgs bosons becomes kinematically accessible and governs the freeze-out process. Current limits from the LUX-ZEPLIN experiment and from Fermi-LAT observations of dwarf spheroidal galaxies already constrain much of this territory, but projected sensitivities of the next-generation XLZD observatory and the Cherenkov Telescope Array will probe deeper into the surviving regions.

In the regime of strongly suppressed mixing, where the mixing angle drops below one part in a thousand, the phenomenology changes dramatically. The annihilation channel into fermion pairs becomes negligible, and freeze-out proceeds almost exclusively through annihilation into pairs of Higgs bosons or into heavy CP-even states. The direct detection cross-section becomes entirely loop-induced, sinking comfortably into the neutrino fog for the smallest mixing values. Remarkably, the same suppression that hides dark matter from direct detection also extends the lifetime of the light pseudoscalar to macroscopic scales, producing displaced-vertex signatures at the Large Hadron Collider that are within the acceptance of existing ATLAS searches for long-lived particles. This creates a genuine complementarity between underground dark matter experiments and collider physics, because parameter points that are difficult to reach through conventional dark matter searches may be accessible through displaced hadronic jets at the LHC.

The most extreme case, where the mixing angle vanishes entirely, produces something qualitatively different: a two-component dark matter scenario. In this limit, the light pseudoscalar becomes a pure singlet with no direct coupling to Standard Model fermions, and if its mass falls below half the mass of the fermionic dark matter candidate, it becomes cosmologically stable and constitutes a second dark matter component alongside the fermion. The researchers solved the coupled Boltzmann equations governing the evolution of both components in the early Universe and found that the pseudoscalar component, which scatters off nucleons at tree level through exchange of the heavy CP-even Higgs boson, produces direct detection signals that are already strongly constrained by current data. Most of the viable parameter space in this two-component scenario is disfavored by existing limits alone, making it the most tightly constrained of the three regimes the team explored.

The study also identified ways to broaden the viable parameter space in both single-component and two-component scenarios by imposing specific relations among the model parameters that suppress the coupling between the 125-GeV Higgs boson and pairs of light pseudoscalars. This fine-tuning, which requires adjusting quartic couplings in the scalar potential to precisions of a few percent, opens up regions at lower dark matter masses that would otherwise be excluded. In these tuned regions, the correct relic density is achieved through p-wave suppressed annihilation processes, and the resulting parameter points populate the neutrino fog with a distinctive narrow strip in the plane of dark matter mass versus coupling strength.

Looking forward, the authors argue that their results provide strong motivation to fully exploit future ton-scale detectors such as XLZD, which will extend sensitivity by another order of magnitude beyond current liquid xenon experiments like PandaX-4T, XENONnT, and LUX-ZEPLIN. But they also emphasize that direct detection alone will not be sufficient. The complementarity between direct detection, indirect detection through gamma-ray observations, and collider searches for displaced vertices means that the Cherenkov Telescope Array, rather than the next generation of xenon experiments, may be the instrument that first probes the sub-floor parameter space identified in this work, particularly for dark matter masses in the range of one hundred to several hundred gigaelectronvolts.

The broader lesson emerging from this analysis is that the neutrino fog should not be understood as a barrier marking the end of the WIMP paradigm, but rather as a threshold beyond which the multichannel nature of dark matter phenomenology becomes essential. Neither direct detection alone, nor indirect detection alone, nor collider searches alone can fully characterize the parameter space explored here. The combination of all three approaches is necessary and, taken together, largely sufficient to probe the model across the full mass range from ten gigaelectronvolts to several teraelectronvolts. As experiments push toward the fog, the theoretical framework developed in this study offers a concrete roadmap for interpreting whatever signals, or absences of signals, the coming decade of dark matter searches may reveal.

Subject of Research: Dark matter phenomenology of the 2HD+a model and its detectability below the neutrino fog

Article Title: Charting dark matter down to the neutrino floor/fog in the 2HD+a scenario

Article References: Arcadi, G., Djouadi, A., & Profumo, S. (2026). Charting dark matter down to the neutrino floor/fog in the 2HD+a scenario. Frontiers in Physics, 14, Article 1920686. https://doi.org/10.3389/fphy.2026.1920686

Image Credits: AI Generated

DOI: 10.3389/fphy.2026.1920686

Keywords: dark matter, WIMP, neutrino fog, 2HD+a model, direct detection, indirect detection, LHC, pseudoscalar mediator, Higgs physics, XLZD, Cherenkov Telescope Array, relic density

The Large-Sized Telescopes, or LSTs, do not observe gamma rays directly. Instead, they are built to catch the fleeting blue flash of Cherenkov light, the ephemeral glow emitted when a very high-energy gamma ray strikes Earth’s atmosphere and triggers a cascade of relativistic particles traveling faster than light moves through air. Each telescope’s 23-meter-diameter reflector funnels this nanosecond-scale flash onto an ultra-fast camera, allowing astronomers to reconstruct the direction and energy of the original gamma ray. The LSTs are the most sensitive instruments in the world for observing gamma rays at energies between approximately 20 gigaelectronvolts and several teraelectronvolts, a range that covers the transition between what space-based gamma-ray telescopes can see and what ground-based instruments excel at detecting.

That exceptional sensitivity at the lowest gamma-ray energies is what sets the LSTs apart. As very high-energy gamma rays travel across the Universe, they are progressively absorbed by the diffuse fog of optical and infrared photons that fills intergalactic space, the so-called extragalactic background light. The farther away a source lies, the more its gamma rays are attenuated before they reach Earth. The LSTs’ low energy threshold allows scientists to compensate for this absorption by detecting the faintest, lowest-energy gamma rays that still manage to survive the journey, opening a window onto sources at cosmological distances and letting researchers look further back into cosmic history than any previous ground-based gamma-ray facility.

The sub-array’s design also makes it uniquely suited to studying transient phenomena. Many of the most dramatic gamma-ray sources, including gamma-ray bursts, novae, and flaring active galactic nuclei, evolve on timescales of minutes or seconds. The LSTs’ sensitivity to short variability, combined with the statistical power gained from observing the same gamma-ray shower simultaneously from multiple telescopes, gives astronomers the temporal and spectral resolution needed to dissect these rapidly changing events with unprecedented accuracy.

The inauguration crowns a productive history for the project’s prototype. Even during its commissioning phase, the first Large-Sized Telescope, LST-1, has delivered groundbreaking scientific results since 2020. Its observations have included detailed studies of pulsars, the rapidly rotating stellar corpses whose beams of radiation sweep across Earth like cosmic lighthouses, as well as investigations of active galactic nuclei at cosmological distances and rapid follow-up observations of transient phenomena such as novae and gamma-ray bursts. These early results validated the telescope’s novel design and demonstrated that the instrument could achieve the lowest energy threshold ever reached by a ground-based gamma-ray observatory.

With LST-2, LST-3, and LST-4 now joining their pioneer sibling, the four telescopes will operate as a true array. When a gamma-ray shower strikes the atmosphere, each telescope records the Cherenkov flash from a slightly different vantage point. Combining these multiple perspectives substantially improves the array’s sensitivity, sharpens its angular resolution, and refines its energy reconstruction, opening a new level of precision in the study of the gamma-ray Universe. Stereoscopic observation also suppresses the background of cosmic-ray events that mimic gamma rays, a critical advantage when hunting for the faintest and most distant sources.

Professor Masahiro Teshima, Principal Investigator of the LST Collaboration and Spokesperson of the CTAO Consortium, emphasized the scientific promise of the completed sub-array. According to Teshima, the completion of the LST sub-array is the culmination of more than fifteen years of international collaboration and technological innovation, and the telescopes will allow scientists to explore some of the most extreme environments in the Universe, including supermassive black holes, neutron stars, the possible origins of cosmic rays, and the nature of dark matter. These targets represent some of the most fundamental open questions in modern astrophysics and particle physics, and the LSTs are designed to attack them from the low-energy frontier of the gamma-ray spectrum.

One of the most ambitious goals of the new sub-array is to reach back to the early Universe. The LSTs will provide a unique opportunity to probe the cosmos at an epoch roughly 12 billion years ago, when the Universe was less than two billion years old. Their sensitivity to the lowest-energy gamma rays will enable the detection and study of bright very high-energy gamma-ray bursts at high redshift, potentially extending gamma-ray observations to sources at redshifts of around z of approximately 4. Because gamma-ray bursts are among the most energetic explosions since the Big Bang, catching their high-energy emission from such vast distances would give cosmologists a new probe of star formation, black hole growth, and the physical conditions prevailing in the young Universe.

The LST sub-array is a key component of the broader Cherenkov Telescope Array Observatory, which will ultimately deploy more than 60 telescopes of three types across two hemispheres. In addition to the Large-Sized Telescopes, the observatory will operate Medium-Sized Telescopes and Small-Sized Telescopes, each optimized for a different portion of the enormous energy range from 20 GeV to 300 TeV. CTAO-North, at the Roque de los Muchachos Observatory on La Palma in Spain, and CTAO-South, at the Paranal Observatory in Chile’s Atacama Desert, together will give the observatory full-sky coverage. Over the coming years, the LSTs will undergo commissioning and integration into CTAO operations alongside the other telescopes planned for both arrays, addressing fundamental questions in astrophysics, particle physics, and cosmology, from the origin of cosmic rays to searches for deviations from Einstein’s theory of relativity.

The project’s scale extends beyond its optics. The CTAO is a Big Data undertaking that will generate hundreds of petabytes of data each year, roughly 12 petabytes after compression, and it is committed to operating as the first gamma-ray observatory of its kind to function as an open, proposal-driven facility providing public access to its high-level science data and software products. The LST project itself was made possible by a strong international partnership involving institutions from Brazil, Bulgaria, the Czech Republic, Croatia, France, Germany, Italy, Japan, Poland, Spain, and Switzerland, while the CTAO ERIC, the organization in charge of construction and operation, includes members from across Europe along with the European Southern Observatory, with further countries engaged as Strategic Partners or Third Parties. As the four gleaming reflectors on La Palma begin their coordinated watch on the night sky, astronomers anticipate a decade in which the most violent, distant, and enigmatic events in the cosmos will be observed with a clarity never before achievable from the ground.

Subject of Research: Inauguration of the Large-Sized Telescope sub-array at the Cherenkov Telescope Array Observatory's northern site for very high-energy gamma-ray astronomy

Article Title: A new era in exploring the extreme universe: The large-sized telescope sub-array is inaugurated on CTAO-north

Article References: A new era in exploring the extreme universe: The large-sized telescope sub-array is inaugurated on CTAO-north. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: CTAO, Large-Sized Telescope, gamma-ray astronomy, Cherenkov light, La Palma, Roque de los Muchachos Observatory, gamma-ray bursts, active galactic nuclei, dark matter, cosmic rays, high-energy astrophysics, early Universe

The framework, developed by Gustav Stålhammar of St. Erik Eye Hospital and the Karolinska Institutet in Stockholm, rests on one deceptively simple hypothesis. Ordinary matter is modeled as a collection of localized emitters, each radiating waves of an additional scalar field with random, mutually uncorrelated phases. In neutral matter, a bound atom acts as one emitter; in fully ionized plasma, each free charged particle counts as an independent source. No individual emitter is observable, and the frequencies involved are arbitrary. What matters is only the statistics of the summed field, which by the central limit theorem behaves as a Gaussian random field regardless of the underlying spectrum.

When the waves from roughly 10^57 emitters in a star like the Sun are added together at any point in space and the intensity of the total field is averaged over time, three kinds of terms appear, and each maps onto one aspect of gravitation. The first is the set of self-terms: each wave multiplied by itself, always positive, adding incoherently like the masses of the sources. The framework identifies ordinary Newtonian gravity with this stationary part, taking Newton’s constant from measurement and leaving the tensor sector of gravity exactly that of general relativity. The hypothesized waves are not gravitational waves; they belong to an additional scalar degree of freedom of the kind long studied in scalar-tensor theories.

The second and third sectors arise from the cross-terms in the double sum. Waves arriving from all matter within the causal horizon combine into a fluctuating background whose variance sets a characteristic acceleration scale. Using the cosmic mean baryon density multiplied by the Hubble length, and a geometric factor of 3 over 8π, the framework derives an acceleration scale g_w of about 7.9 × 10^-11 meters per second squared, fixed entirely by measured cosmological parameters rather than fitted. This is tantalizingly close to the acceleration scale near cH_0, the speed of light times the Hubble constant, at which galaxy dynamics are known to depart from Newtonian expectations, a coincidence that modified Newtonian dynamics, or MOND, has long treated as fundamental but never explained.

The crucial new ingredient is the interference between the locally generated field and this cosmic background. The signed average of the cross-term is zero, so nothing would happen if the medium responded to the instantaneous signed product. The framework’s central assumption, labeled A2, is that the material medium responds instead to the product of the two components’ envelope amplitudes, their absolute magnitudes, independent of phase. Under this rectified response, the mean of the product for two independent Gaussian envelopes is exactly π/2 times the product of their standard deviations, a result verified by Monte Carlo simulation to within 0.12 percent. The result is an additional attractive acceleration proportional to the geometric mean of the Newtonian acceleration and the cosmic scale, directed along the local field, precisely the square-root behavior that characterizes dark-matter phenomenology in the weak-field regime.

Three phenomenological functions modulate this term. A screening factor suppresses the effect where a system’s own column density exceeds the cosmic source column, which is what keeps the Solar System clean. A transport saturation factor describes how the rectified response accumulates over a density-dependent length anchored at the local Galactic disk value. And an ionized-gas enhancement reflects the emitter-counting rule: ionization multiplies the number of independent emitters per unit mass, so plasma environments should feel a stronger effect. Three constants are fixed in advance from cosmology and local Galactic measurements; only one coefficient, the plasma coefficient γ_p, is calibrated on data, using the X-COP sample of twelve massive clusters, and then frozen for every other test.

The performance on galaxy rotation curves is the headline result. Applied with no galaxy-fitted parameters whatsoever to 3,187 weak-field points in 175 galaxies from the SPARC database, the framework achieves a root-mean-square error of 0.228 dex in log-acceleration, with a 95 percent confidence interval of 0.204 to 0.253 dex. For comparison, general relativity with baryons alone yields 0.398 dex, MOND at its canonical acceleration constant yields 0.270 dex, and MOND with the constant re-fitted to the same selection yields 0.213 dex. The framework thus outperforms canonical MOND and baryons-only gravity while landing between the two MOND variants, all without a single parameter tuned to galaxies. Notably, its prediction shifts by only 0.005 dex when the stellar mass-to-light assumptions are changed, whereas the fitted MOND constant moves by a factor of 2.4 under the same variation.

On the cluster side, the story is more mixed but structurally interesting. Leave-one-cluster-out validation on X-COP yields an error of just 0.072 dex, and the calibrated plasma coefficient of 0.69 lies within a factor of 1.6 of an independent, parameter-free ionization estimate of 1.08. What distinguishes the framework from MOND here is not fit quality but internal consistency: MOND requires an acceleration constant 5.5 times larger to fit clusters than to fit galaxies, whereas the same kernel with the same fixed constants spans both regimes. However, applied unchanged to 22 clusters from the eROSITA sample, the framework roughly halves the central shortfall of baryons alone but retains a radially structured under-prediction of 0.435 dex overall, comparable in magnitude to MOND’s own central failure. Four of five dwarf spheroidal galaxies are also under-predicted, bracketing the model’s domain of validity at low baryonic density.

The framework survives the obvious local tests through its own screening structure. Predicted fractional anomalies in the Solar System range from 8.5 × 10^-14 at Mercury to 4.0 × 10^-8 at Neptune, between three and more than eight orders of magnitude below the Cassini sensitivity limit, with a steep radial increase that future ephemeris measurements at Neptune-to-Kuiper distances could probe directly. Wide-binary predictions depend on a stated transport convention for point-pair systems; under the ambient-disk reading, the predicted velocity excesses remain below current Gaia sensitivity, but measurements beyond 100 kAU would discriminate sharply between the two readings. As a conditional cosmological check, a matter-like scalar background reproduces the baryon-acoustic-oscillation sound horizon to within 0.04 percent under a matched drag-epoch prescription, though the full cosmological sector remains an open problem.

The author is explicit about what remains unproven. The rectified response of Assumption A2 has no microscopic derivation, and the Hubble-length causal column is an imposed simplification. The screening and transport functions are phenomenological, with demonstrated functional-form freedom at the 0.01 to 0.06 dex level. Yet the framework makes concrete, falsifiable predictions: the plasma coefficient must re-calibrate to the same value on independent cluster samples, ultra-wide-binary velocities beyond 100 kAU must match the stated curve, matched-radius lensing and dynamical masses must agree, and the scalar background’s energy density must evolve like non-relativistic matter through the drag epoch. All numerical results were produced with a single released analysis pipeline, making every modeling choice auditable. Whether the universe really generates its missing gravity from the interference statistics of ordinary matter is now a question that measurement, not philosophy, will decide.

Subject of Research: An emergent scalar-field model that derives Newtonian gravity and dark-matter phenomenology from random-phase waves emitted by ordinary matter

Article Title: Newtonian gravity and dark-matter phenomenology from an emergent scalar field sourced by ordinary matter

Article References: Stålhammar, G. (2026). Newtonian gravity and dark-matter phenomenology from an emergent scalar field sourced by ordinary matter. Frontiers in Astronomy and Space Sciences, 13, Article 1904894. https://doi.org/10.3389/fspas.2026.1904894

Image Credits: AI Generated

DOI: 10.3389/fspas.2026.1904894

Keywords: dark matter, scalar field, modified gravity, MOND, galaxy rotation curves, galaxy clusters, cosmology, SPARC, X-COP, baryonic matter, gravitation, emergent gravity

To understand what makes this possible, it helps to recall what torsion is. In general relativity, the connection that tells parallel-transported vectors how to move is the Levi-Civita connection, which is torsion-free and metric-compatible. In Einstein-Cartan theory, torsion is sourced algebraically by the spin density of matter and effectively vanishes in vacuum. Poincare gauge theory allows several independent torsion modes with multiple coupling constants, while teleparallel and f(T) gravity abandon curvature altogether and describe gravity purely through torsion. Semi-symmetric metric gravity, rooted in a class of connections introduced by Friedmann and Schouten in 1924, sits in an elegant middle ground: the spacetime retains both curvature and torsion, but the torsion tensor is completely determined by a single vector field, the torsion vector. In four dimensions this reduces the 24 independent components of a general torsion tensor to just 4, making it arguably the simplest torsional extension of general relativity.

The field equations of the theory are the vacuum Einstein equations built from the semi-symmetric Ricci tensor and scalar, which acquire extra contributions from the torsion vector and its derivatives. Csillag and Harko assumed a static, spherically symmetric metric and a purely radial torsion vector, and imposed the familiar Schwarzschild-like condition that the two metric functions sum to zero. Under these assumptions the coupled differential equations collapse into a solvable system. The outcome is a bi-parametric family of exact solutions whose metric function can be written compactly as a product of a quadratic factor in the radial coordinate and the standard Schwarzschild factor, normalized by a term involving the ratio of the gravitational radius to a new length scale. One integration constant reproduces the usual gravitational radius, while the second, denoted R_g, is a genuinely new cosmological-type length scale with no counterpart in Einstein’s theory.

The structure of the solution depends on a discrete sign choice. For one branch, the black hole possesses a single horizon at the gravitational radius, closely resembling Schwarzschild. For the other branch, a second, outer horizon appears at the radius R_g itself, and the torsion vector vanishes exactly at the inner horizon. In the limit where the new length scale vastly exceeds the gravitational radius, the metric smoothly reduces to the Schwarzschild solution, so general relativity is recovered whenever torsional effects are negligible. The authors also showed that the torsional contribution can be reinterpreted as an effective gravitational radius and an effective geometric density, quantities that behave as if the vacuum were filled with a smooth, geometry-generated mass distribution.

The real power of an exact solution is that it can be confronted with data, and the authors applied the three classical tests of general relativity. For the perihelion precession of Mercury, they derived the correction to the standard 42.94 arcseconds per century predicted by general relativity. Observations give 43.11 plus or minus 0.21 arcseconds per century, leaving a residual of 0.17 plus or minus 0.21 arcseconds that could be attributed to torsion. Assuming the entire residual comes from the new physics, the test fixes the sign of the new parameter and yields a lower bound of roughly 5 times 10 to the 26 centimeters for R_g, a scale far exceeding the Solar System and approaching cosmological proportions.

The deflection of light by the Sun and the radar echo delay between Earth and Mars tell a consistent story. Long-baseline radio interferometry constrains the fractional deviation of the light-deflection angle to at most a few parts in ten thousand, which translates into a torsional length scale of about 1.7 times 10 to the 25 centimeters. The Shapiro time delay measured in the Earth-Mars-Sun system gives a remarkably close value of about 2.1 times 10 to the 25 centimeters. Intriguingly, these bounds correspond to inverse-square values in the same ballpark as, though somewhat larger than, the observed cosmological constant, suggesting that the new length scale may be related to the dark energy scale that drives the accelerated expansion of the Universe, perhaps through a relation in which R_g scales as the inverse square root of the cosmological constant.

The thermodynamic analysis reveals genuinely new behavior. For the single-horizon branch, the Hawking temperature is shifted by a term proportional to one over R_g, and the Bekenstein-Hawking entropy takes the standard area form. For the two-horizon branch, the inner black hole horizon has a temperature reduced by the same kind of correction, while the outer horizon at R_g turns out to be a double root of the metric function. As a consequence, its Hawking temperature vanishes exactly, making it a genuinely cold horizon: it carries finite area and finite entropy but does not radiate thermally in the usual Hawking sense, a behavior reminiscent of extremal and cosmological horizons but even more extreme. In both branches the heat capacity of the black hole horizon is negative whenever the temperature is positive, reproducing the familiar thermodynamic instability of asymptotically flat black holes, whereby losing energy makes the hole hotter.

Stability was examined through linear perturbations. Scalar perturbations lead to a Schrodinger-like equation with an effective potential whose peak is determined by a quintic equation, so the scalar quasinormal spectrum must be computed numerically and is deferred to future work. The vector, or electromagnetic, sector, however, can be solved analytically. The effective potential remains non-negative throughout the physical region between the horizons, and a first-order WKB analysis shows that the imaginary parts of the quasinormal frequencies are negative, meaning vector perturbations decay in time. The vector sector is therefore linearly stable, an essential consistency check for any proposed black hole metric. Depending on the sign of the new parameter, the torsional correction either raises or lowers the potential barrier that governs how gravitational waves ring down from the hole, offering a potential observational signature.

Perhaps the most provocative implication lies at galactic and cluster scales. Because the new terms in the metric grow with radius, they become relevant only over megaparsec distances, precisely the scales where galaxies and clusters appear to contain far more gravitating mass than their visible stars and gas can supply. The torsion-generated effective density could mimic the gravitational effect of dark matter, and the authors outline how stellar velocity dispersions in clusters, analyzed through the Jeans equation with a Plummer stellar profile, could constrain the effective mass profile and the torsion vector directly. In cosmology, the same torsion sector modifies the Friedmann equations and admits de Sitter-type accelerated expansion without extra scalar fields, hinting at a geometric origin for inflation and dark energy alike. From Mercury’s orbit to the edge of galaxy clusters, a single torsion vector may quietly reshape gravity’s story, and the new exact solutions give astronomers a concrete target to test it against.

Subject of Research: Exact vacuum black hole solutions in semi-symmetric metric gravity with vectorial torsion and their observational constraints

Article Title: Exact black hole solutions with semi-symmetric vectorial torsion

Article References: Csillag, L., & Harko, T. (2026). Exact black hole solutions with semi-symmetric vectorial torsion. The European Physical Journal C, 86(8), Article 1015. https://doi.org/10.1140/epjc/s10052-026-16189-8

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16189-8

Keywords: black holes, torsion, semi-symmetric metric gravity, modified gravity, Schwarzschild solution, Solar System tests, perihelion precession, light deflection, radar echo delay, Hawking temperature, quasinormal modes, dark matter

The case for the upgrade rests on what the High-Luminosity LHC itself will deliver. When the accelerator completes its current upgrade programme, it will increase the integrated luminosity delivered to experiments by roughly an order of magnitude compared with Run 3, flooding the forward region with an unprecedented flux of neutrinos. These particles, born in the decays of heavy-flavour hadrons such as those containing charm quarks, are produced at extreme angles relative to the beamline, at pseudorapidities between about 7 and 8, and stream hundreds of metres along the tunnel. No general-purpose detector can catch them. SND@LHC, sitting off the collision axis, was conceived precisely to exploit this blind spot, and its first observations of both muon neutrinos and electron neutrinos from LHC collisions confirmed that collider neutrino physics has moved from theory to reality.

The upgraded detector, referred to in the paper as SND@HL-LHC while the collaboration keeps its original name, must contend with a fundamental technological problem: the emulsion-based tracking system that served the experiment during Run 3 cannot cope with the particle rates of the high-luminosity era. Emulsion films integrate everything that passes through them and offer no event-by-event electronic readout. The upgrade therefore replaces them with a fully electronic, silicon-based tracking system capable of real-time operation while preserving the spatial resolution needed to reconstruct neutrino interactions in a high-occupancy environment. The design also adds two capabilities the original detector never had: a precision timing system for rejecting background, and a magnetic spectrometer that measures the momentum and charge of outgoing muons, allowing, for the first time, a clean distinction between neutrino and antineutrino interactions.

The detector itself remains remarkably compact, roughly three metres long with a cross-section of about one square metre, a footprint dictated by the tight confines of the TI18 tunnel. Its heart is the neutrino target region, a stack of 58 tungsten plates, each seven millimetres thick, interleaved with silicon microstrip layers salvaged and repurposed from the CMS Microstrip Tracker. The stack weighs about 1.3 tons and corresponds to 116 radiation lengths and 4 nuclear interaction lengths, dense enough to stop and measure the showers produced when neutrinos strike tungsten nuclei. The silicon modules resolve positions to better than 30 micrometres, and consecutive layers are rotated by 90 degrees to provide precision tracking in both spatial coordinates. To keep the irradiated silicon stable, the target operates at approximately minus 20 degrees Celsius inside an insulated enclosure cooled by a closed-loop dry-air system with full redundancy and safety monitoring.

Downstream of the target sits the second major component: a magnetised hadronic calorimeter built from 34 layers of 50-millimetre-thick iron slabs interleaved with more recycled CMS silicon modules. The iron serves double duty, absorbing hadronic showers so their energy can be measured and providing the medium for a magnetic field of approximately 1.7 tesla, generated by a single-piece copper coil. This field bends the trajectories of muons leaving the target, allowing momentum measurements up to about 1 teraelectronvolt with a resolution of roughly 20 percent. Finite-element simulations confirm a homogeneous field within the active volume, with non-uniformities of only a few percent and negligible stray fields outside. Upstream, three planes of plastic scintillator bars read out by silicon photomultipliers form a veto system with a rejection efficiency at the level of one part in a billion against the few-kilohertz flux of beam muons, while a dedicated timing system, based on either fast scintillator tiles or thin-gap resistive plate chambers, aims at sub-50-picosecond resolution to tie every event to the correct LHC bunch crossing.

The most consequential part of the paper is its comparison of two installation scenarios, both using the identical detector. The Baseline configuration, which is the approved version of the upgrade, places the detector directly on the existing tunnel floor with no civil-engineering work, leaving its centre about 57 centimetres above and 39 centimetres to one side of the collision axis. That position yields an average pseudorapidity coverage of 6.9 to 7.7 but an azimuthal acceptance of only about 66 milliradians, squeezed by the clearance between detector and ceiling. The Extended configuration instead lowers the detector by 43 centimetres and shifts it 29 centimetres horizontally, requiring the removal of 4.5 cubic metres of concrete. The reward is dramatic: the transverse distance to the collision axis shrinks to roughly 14 by 10 centimetres, pseudorapidity coverage extends beyond 7.8, and the azimuthal acceptance grows roughly fourfold to about 250 milliradians, which the authors identify as the dominant contribution to the overall acceptance gain.

Simulations based on the DPMJET, FLUKA, GENIE and POWHEG generators, assuming the full 3000 inverse femtobarns of integrated luminosity expected over roughly a decade of HL-LHC operation, quantify what that geometric gain buys. In the Extended configuration the total neutrino interaction rate rises by approximately a factor of five, and the energy spectra shift toward higher values because the detector intercepts a more energetic component of the forward flux. The consequences ripple through the entire physics programme. For muon neutrino and antineutrino deep-inelastic scattering cross-sections above 350 gigaelectronvolts, a region never previously explored that bridges fixed-target experiments and IceCube, the statistical uncertainty falls from about 3 percent in the Baseline layout to below 1 percent in the Extended one, while the dominant flux systematic can be constrained to about 5 percent thanks to overlapping measurements by the LHCf experiment during Run 3.

The upgrade also promises precision tests of fundamental symmetries. Because electron neutrinos in the detector’s acceptance originate predominantly from charm decays, their measurement probes forward charm production and the gluon distribution of the proton at Bjorken-x values below ten to the minus five, a regime relevant both for future colliders such as the FCC and for predictions of ultra-high-energy atmospheric neutrinos. Per-bin statistical uncertainties on these charm-related measurements improve from about 10 percent in the Baseline to 5 percent in the Extended configuration. Tests of lepton flavour universality sharpen considerably: the ratio of electron-neutrino to tau-neutrino interactions, sensitive to the cross-sections of the two species, would be measured with a statistical uncertainty of about 6 percent in the Baseline and 2 percent in the Extended layout, compared with 30 percent in Run 3. Perhaps most tantalising, the Extended configuration could deliver the first direct observation of tau antineutrinos, which have never been seen experimentally: simulations predict roughly 120 tau antineutrino charged-current interactions in the target, about 9 observable signal events against a background of 2, yielding an observation significance of about 5 sigma, where the Baseline manages only around 3 sigma.

Beyond the Standard Model, the detector doubles as a hunting ground for feebly interacting particles such as dark photons, heavy neutral leptons and axion-like particles produced in the far-forward region, and the paper evaluates sensitivity to light dark matter scattering off protons via a leptophobic baryonic mediator. Here too the Extended geometry wins, since the larger acceptance and closer approach to the collision axis increase the dark matter flux intersecting the detector and extend the reach in mediator coupling into territory not excluded by other experiments. The collaboration also foresees roughly 600 to 1300 neutrino interactions coincident with events recorded by ATLAS, enabled by sub-50-picosecond timing synchronisation, which would directly link a neutrino interaction to its production mechanism. Whatever installation scenario is ultimately realised, the experience gained will feed directly into the SND detector at the proposed SHiP facility, for which the upgraded instrument serves as a full-scale prototype, making this modest tunnel experiment a testing ground for the next generation of collider neutrino physics.

Subject of Research: Upgrade of the SND@LHC forward neutrino detector for the High-Luminosity LHC, comparing installation scenarios and physics reach

Article Title: SND@LHC upgrade for the high-luminosity LHC: physics reach and installation scenarios

Article References: SND@LHC Collaboration, Abbaneo, D., Ahmad, S., Albanese, R., Alexandrov, A., Alicante, F., Aloschi, F., Androsov, K., Anokhina, A., Arellano, L. G., Asawatangtrakuldee, C., Torres, M. A. A., Bangaru, N., Battilana, C., Bay, A., Bertocco, A., Betancourt, C., Bick, D., Biswas, R., … Saá, J. Z. (2026). SND@LHC upgrade for the high-luminosity LHC: physics reach and installation scenarios. The European Physical Journal C, 86(9), Article 1030. https://doi.org/10.1140/epjc/s10052-026-15924-5

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-15924-5

Keywords: SND@LHC, High-Luminosity LHC, neutrinos, CERN, particle physics, forward physics, heavy-flavour decays, dark matter, lepton flavour universality, tau antineutrino, silicon trackers, magnetic spectrometer

Neutrino oscillations are one of the most remarkable phenomena in modern particle physics. Neutrinos come in three flavors, electron, muon and tau, but they do not travel as pure flavors. Instead, each flavor is a quantum superposition of three mass states, mixed together by the Pontecorvo-Maki-Nakagawa-Sakata matrix. As a neutrino races through space, these mass states accumulate slightly different quantum phases, and the relative phase difference determines the probability that the particle will be detected as a different flavor than the one it started as. The oscillation phase depends on the neutrino’s energy, the squared mass differences between the eigenstates, and the distance traveled. In flat spacetime the formula is elegant and well tested by experiments such as Super-Kamiokande, IceCube and Borexino. Curved spacetime, however, changes the game, because the phase must now be computed along the curved geodesic that the particle actually follows.

The team modeled a static, spherically symmetric Schwarzschild black hole immersed in what they call DMPF, dark matter within a phantom field background. This geometry, built from an Einstein-Hilbert action augmented with a scalar field, adds a logarithmic correction to the standard black hole metric, governed by a parameter a that encodes the density of the entire dark sector. The energy density of this dark component falls off as one over the cube of the distance from the hole, a profile consistent with the nearly flat rotation curves observed in spiral galaxies. By varying the dimensionless ratio a/M, where M is the black hole mass, the researchers could dial the strength of the dark matter influence up and down and watch how the neutrino oscillation patterns responded.

The first major result is a striking cancellation. For neutrinos traveling purely radially, straight outward from the black hole, the gravitational contributions to the oscillation phase exactly cancel. The phase difference between mass eigenstates ends up depending only on the radial distance, the mass-squared splitting and the neutrino energy, precisely as it would in flat spacetime. In other words, a neutrino beaming directly away from a black hole carries no memory of the gravitational maelstrom it just escaped, at least not in its oscillation phase. This result follows from expanding the covariant phase integral, built from the canonical momentum along the geodesic, in the ultra-relativistic limit where the neutrino mass is tiny compared with its energy, and it holds even in the presence of the dark matter logarithmic term.

The story changes dramatically for neutrinos whose paths are bent. When a trajectory is deflected by the gravitational field, characterized by a nonzero angular momentum and an impact parameter b, extra phase terms survive. The researchers derived analytical expressions showing that the dark matter parameter enters both as a small correction to the effective mass-splitting coefficient and as an additive logarithmic contribution to the total accumulated phase. When gravitational lensing splits the journey into two segments, from source to the point of closest approach and from there to the detector, the phase acquires further corrections involving the lens mass and the logarithm of the source and detector distances. Gravitational lensing thus does more than bend the neutrino’s path; it imprints measurable modifications on the interference pattern that determines which flavor arrives at the detector.

To make these abstract calculations concrete, the team computed two-flavor transition probabilities, electron to muon, for realistic astrophysical configurations. They considered three lensing objects: the Sun, Sagittarius A*, the four-million-solar-mass black hole at the center of our galaxy, and M87*, the 6.5-billion-solar-mass giant famously imaged by the Event Horizon Telescope. For Sagittarius A*, Event Horizon Telescope shadow observations constrain the dark sector parameter to values up to roughly 0.15 at two sigma, while for M87* the bound reaches about 0.33. The corresponding neutrino energies span an enormous range: solar neutrinos carry around 10 megaelectronvolts, astrophysical neutrinos detected by IceCube from sources such as the blazar TXS 0506+056 and the Seyfert galaxy NGC 1068 reach 10^8 to 10^10 megaelectronvolts, and hypothetical cosmogenic neutrinos, produced when ultra-high-energy cosmic rays collide with cosmic microwave background photons, could climb to the exaelectronvolt scale near M87*.

The numerical results reveal a rich structure. Plotting the transition probability as a function of the azimuthal angle of the source, the curves shift noticeably as the dark sector parameter is increased from zero, the pure Schwarzschild case, to a/M values of 0.05 and 0.1. The probability is highly sensitive to the dark sector density parameter, and it also depends on whether the neutrino mass hierarchy is normal or inverted. Intriguingly, the team uncovered a degeneracy: different combinations of lens mass and dark matter parameter can produce the same oscillation probability. For a fixed probability, achieving the same flavor transition under an inverted hierarchy requires a slightly larger a/M than under a normal hierarchy, and this difference grows with mass. This degeneracy is both a challenge and an opportunity, since breaking it with independent mass measurements could turn neutrino detectors into dark matter probes.

The study also tackled a subtler question: what happens when neutrinos are treated realistically as Gaussian wave packets rather than infinite plane waves? Wave packets of different mass states gradually separate in space, causing the oscillation pattern to wash out, a process called decoherence. Because gravity dilates proper time, neutrinos in curved spacetime must travel farther before their wave packets lose overlap. The researchers derived the effective damping factor for lensed trajectories and found that the dark matter background exerts only a minimal influence on decoherence. Instead, the absolute neutrino mass is the dominant factor determining the coherence length and the duration over which oscillations persist. Once decoherence sets in, the dark sector parameter has a negligible effect on the transition probability envelope, meaning that any dark matter signature must be extracted from neutrinos that are still coherent when detected.

The implications are tantalizing. In the Solar System, the dark matter density bound at one astronomical unit is so stringent that the parameter a/M is capped at roughly 7.5 times 10 to the minus 12, making dark matter effects on solar neutrino oscillations utterly unobservable with current techniques. But around supermassive black holes like Sagittarius A* and M87*, the allowed dark sector parameters are many orders of magnitude larger, and the extreme gravitational lensing amplifies the phase corrections. Future neutrino astronomy, whether through next-generation IceCube extensions, kilometer-cubic detectors in the Mediterranean, or hypothetical cosmogenic neutrino observatories, could in principle compare observed flavor ratios with the predictions of standard general relativity and detect the fingerprint of the dark halo surrounding these monsters.

Of course, this remains a theoretical edifice, resting on a two-flavor approximation and idealized geometries, and no one has yet observed a neutrino oscillation modified by dark matter. But the work demonstrates that the intersection of quantum interference and strong-field gravity is not merely a curiosity; it is a potential measurement channel. Any departure from the predictions of pure general relativity in neutrino flavor ratios arriving from the vicinity of compact objects would constitute compelling evidence for modified gravity or for the dark environments in which black holes are embedded. As detectors grow more sensitive and theoretical models more refined, the humble neutrino, the particle that barely interacts with anything, may become one of humanity’s sharpest tools for mapping the invisible universe that surrounds every black hole.

Subject of Research: Effects of dark matter in a phantom field background on neutrino flavor oscillations near black holes

Article Title: Probing dark matter and phantom field effects on neutrino oscillations around black holes

Article References: Ergashov, I., Narzilloev, B., Hussain, I., & Ahmedov, B. (2026). Probing dark matter and phantom field effects on neutrino oscillations around black holes. The European Physical Journal C, 86(9), Article 1032. https://doi.org/10.1140/epjc/s10052-026-16278-8

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16278-8

Keywords: neutrino oscillations, dark matter, black holes, phantom field, gravitational lensing, general relativity, neutrino astronomy, decoherence, Sagittarius A*, M87*, particle astrophysics, spacetime curvature

The theoretical backdrop is a family of low-scale baryogenesis scenarios collectively known as Mesogenesis. In these models, the matter-antimatter asymmetry of the universe and the dark matter abundance are generated together, at energy scales below the electroweak scale. That is a tantalizing feature, because it means the underlying interactions could be probed directly in laboratory experiments rather than only inferred from cosmology. The mechanism works through heavy colored mediators, scalar fields or vector fields, that couple Standard Model quarks to a dark baryon called psi, a fermion that is a complete singlet under the Standard Model gauge group. Because the mediators are heavy, with collider searches by ATLAS and CMS pushing their masses above roughly 0.52 teraelectronvolts, they can be integrated out, leaving behind compact effective interactions described by a handful of Wilson coefficients.

Experiments have already begun to squeeze those coefficients. The BABAR Collaboration has set upper limits of order ten to the minus six on B-meson decays into a baryon plus the invisible psi particle, while Belle has reached limits around ten to the minus five for a range of invisible B decays. More relevant for the new work, the BESIII Collaboration has searched for invisible decays of hyperons such as the Lambda and the Xi, establishing upper limits also at the level of ten to the minus five. Each null result translates directly into a tighter bound on the effective couplings that control how strongly quarks talk to the dark sector. The new analysis folds these constraints into a systematic calculation of what branching ratios the Mesogenesis framework actually predicts for hyperons.

The technical heart of the paper is an effective Lagrangian matched onto chiral perturbation theory, the standard framework for describing the low-energy interactions of light quarks, baryons and the pseudo-Goldstone mesons that encode chiral symmetry breaking. The three-quark operators that survive in the Mesogenesis model form a flavor octet, and the authors construct the most general flavor-invariant Hamiltonian for hyperon decays into a meson plus psi, or a photon plus psi. Angular momentum conservation plays a crucial role: in the Lambda hyperon the up-down quark pair carries spin zero, while in the Sigma-zero it carries spin one, so scalar and vector mediators predict different patterns of amplitudes for the radiative channels. The framework also yields approximate relations among decay rates that follow from SU(3) flavor symmetry, relations that the full calculation later shows to be only roughly obeyed.

Where the study departs from earlier work is in its treatment of one-loop triangle diagrams, which encode final-state interactions among ordinary hadrons. At first glance such loop processes should be suppressed, since every additional vertex typically costs a factor of the strong coupling divided by some large scale. But the authors point out that a triangle diagram has only one or two more strong vertices than the tree-level invisible decay, and the strong couplings among hadrons are vastly larger than the couplings between hadrons and the dark baryon. The loops are further regulated by phenomenological form factors that account for the internal structure of the exchanged particles, with a cutoff parameterized in terms of the QCD scale. The result is that these rescattering effects, far from being negligible, contribute corrections comparable in size to the tree diagrams.

The numerical consequences are laid out for a dark baryon mass near one gigaelectronvolt, within the kinematic window of roughly 0.94 to 1.18 gigaelectronvolts where all hyperon decays into psi plus a pion or photon remain allowed. For the hadronic channels, the branching ratios cluster around ten to the minus five. In the process Sigma-minus going to pi-minus plus psi, the tree diagrams alone give a branching ratio of 1.83 times ten to the minus five, while the triangle loops alone give 0.94 times ten to the minus five, and the combined result with interference is 1.25 times ten to the minus five. For Xi-zero going to pi-zero plus psi, the tree contribution is 5.24 times ten to the minus five and the loop contribution 1.05 times ten to the minus five. The loops are thus not a footnote but a co-star, and for Sigma-minus and Xi-zero they simply cannot be ignored.

The radiative channels, in which the hyperon emits a photon alongside the invisible dark baryon, fare considerably worse. Because the leading-order process requires radiative couplings of light hadrons, the predicted branching ratios fall below ten to the minus seven, at least two orders of magnitude smaller than the hadronic modes. The authors also extend the analysis to the neutron, which, if it can decay into a photon and a dark baryon, would offer a possible explanation for the well-known discrepancy between bottle and beam measurements of the neutron lifetime. That discrepancy, however, amounts to only about one percent, which constrains the decay width of the neutron into photon plus psi to roughly 7.41 times ten to the minus thirty gigaelectronvolts and forces the corresponding Wilson coefficient down to 6.87 times ten to the minus eleven inverse gigaelectronvolts squared, an extraordinarily tight bound.

One of the most interesting byproducts of the calculation is a stress test of SU(3) flavor symmetry. Simple symmetry arguments predict, for example, that the rate for Xi-minus decays should be exactly twice that for Xi-zero decays, and that the Sigma-minus rate should be a small fraction of the Xi-zero rate. The full effective Lagrangian calculation tells a different story: the Xi-minus to Xi-zero ratio comes out near 1.04 rather than 2, and the Sigma-minus to Xi-zero ratio near 0.40 rather than 0.07. The tree-level ratios by themselves agree well with the symmetry predictions, which pinpoints the deviation on the final-state interaction effects and the interference between tree and loop amplitudes. Flavor-symmetry breaking, in other words, is sizable in these decays, and analyses that rely on exact SU(3) may be misleading.

The practical upshot is a roadmap for experiments. The branching ratios decrease as the dark baryon mass increases across the allowed window, with Xi-zero going to pi-zero plus psi reaching the largest value, about 7.0 times ten to the minus five, at the lowest allowed mass, while Lambda decays give the smallest at 1.16 times ten to the minus five. Most channels are fairly insensitive to the cutoff parameter governing the form factors, but the Xi-zero and Sigma-minus modes grow strongly with it, a signature of their large loop contributions. Since current BESIII limits already sit at the same order of magnitude as these predictions, a modest improvement in sensitivity could either catch the first glimpse of a dark baryon or push the Mesogenesis parameter space into a much narrower corner. Either outcome would mark real progress in connecting the darkest question in cosmology to the humble decays of strange particles.

Subject of Research: Semi-invisible decays of hyperons into pions or photons plus a dark baryon in Mesogenesis models, computed with an effective Lagrangian approach

Article Title: Semi-invisible hyperon decays in the effective Lagrangian approach

Article References: Jiang, L., Xing, Y., Zhou, Y., & Hu, X.-H. (2026). Semi-invisible hyperon decays in the effective Lagrangian approach. The European Physical Journal C, 86(9), Article 1034. https://doi.org/10.1140/epjc/s10052-026-16292-w

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16292-w

Keywords: hyperon decays, dark matter, Mesogenesis, dark baryon, effective Lagrangian, chiral perturbation theory, branching ratios, BESIII, baryogenesis, final-state interactions, SU(3) flavor symmetry, neutron lifetime