When nucleons are bound within nuclei, their parton distribution functions (PDFs) differ from when they are free. The origin of these modifications, first discovered by the European Muon Collaboration in 1982 (CERN Courier November 1982 p362), remains one of the central open questions in nuclear physics, since the MeV-scale energies that bind nucleons together should have little bearing on the GeV-scale processes that probe their quarks and gluons. Results presented by the ATLAS collaboration at the Deep Inelastic Scattering (DIS) conference now provide the first observation that nucleons near the edge of a nucleus exhibit different PDFs from those near its centre.
The measurement relies on ultra-peripheral collisions (UPCs) of lead ions at the LHC, where – unlike a typical head-on collision – the ions glance past each other without their nucleons overlapping. They still interact, however, through the intense electromagnetic fields that surround each ion. Photonuclear UPCs occur when one nucleus emits a high-energy photon that strikes the other. One possible outcome is the production of jets through hard scattering between the photon and the nucleus, whose cross-section is sensitive to the parton distribution.
Such hard scatterings usually break the nucleus up, producing forward neutrons that are detected in the ATLAS zero-degree calorimeters located 140 metres from the interaction point. The key insight of this measurement is that, in about 4% of photonuclear scatterings, the photon strikes a single nucleon and leaves the rest of the nucleus whole. These events can be tagged by the absence of neutrons in the direction of the struck nucleus. Since nucleon densities are lower near the edge of the nucleus, collisions that leave it intact are also typically the more peripheral ones.
To study these collisions, the collaboration analysed lead–lead collision data collected in 2018 during Run 2 of the LHC, corresponding to an integrated luminosity of 1.72 nb–1. Events were selected by requiring at least two jets in the calorimeter with large rapidity gaps – regions of the detector devoid of particle production, characteristic of these photon-initiated processes. These were then categorised as “inclusive” or “peripheral” according to the presence or absence of forward neutrons, respectively.
To interpret the results, proxy variables for the parton kinematics were defined using the properties of the measured jets. One such variable is x+, which provides an estimate for the Bjorken-x of the struck parton, the fraction of the nucleon’s momentum that it carries. The measured ratio of the x+ distributions between inclusive and peripheral collisions has a clear slope (see figure 1), indicating a significant difference in the nuclear modification of the parton distributions between the two classes. The size of this effect is quantified through a statistical test of the difference between them, which reaches a significance of 6σ.
These results provide the first observation that nucleons near the edge of a nucleus have different PDFs from those near the centre, and mark a significant step forward in understanding the structure of nuclei. The analysis also has important implications for the interpretation of relativistic heavy-ion collisions, which are sensitive to the PDFs of the colliding ions, and demonstrates a novel methodology that could be applied at the future Electron-Ion Collider (EIC). While this analysis uses Run 2 data, the larger Run 3 lead–lead dataset and the HL-LHC programme will offer substantial opportunities to improve both the precision and scope of these measurements.
Since its discovery at CERN in 1983 (CERN Courier November 1983 p355), the W boson has been one of the most thoroughly studied particles in high-energy physics – yet some of its rarest decay modes remain unobserved. The CMS experiment has recently carried out a search for its decay into three light charged hadrons, using 420 fb–1 of proton–proton collision data recorded between 2016 and 2025. The result sets an upper limit on the branching fraction that excludes a large range within the theoretical expectation, constraining certain models of these rare decays.
While decays of the W boson into hadrons are the most common, they are also exceptionally complex. The process of hadronisation, in which quarks transform into detectable particles like pions and kaons, typically produces around 30 final-state particles in a single W-boson decay. Consequently, reconstructing the parent W boson and studying its properties with high precision is significantly more difficult than for leptonic decay modes.
In its recent study, the CMS experiment focused on a much cleaner and rarer signature: W-boson decays into three light charged hadrons. This decay offers the highest potential of observation among low-multiplicity exclusive modes, as it combines a clean, fully charged final state with a relatively high rate, well above that of competing processes such as decay into a photon and a pion. Observing it would provide valuable new insights into quantum chromodynamics, particularly the behaviour of factorisation and form factors at high energies.
To identify these events, charged hadrons are reconstructed either from isolated particle tracks in the detector or as hadronically-decaying tau leptons, since a common decay mode of the tau lepton produces a charged pion together with a neutrino.
The study focused on a much cleaner and rarer signature
The analysis requires events with at least three hadron candidates. The two candidates with the highest transverse momentum are reconstructed as hadronically-decaying tau leptons, whilst the third may also be reconstructed as an isolated charged-particle track. This strategy both expands the accessible phase space – by taking advantage of the lower transverse momentum threshold for isolated tracks – and suppresses background contributions through stricter momentum requirements for hadronically-decaying tau leptons. The sensitivity is further improved using a dedicated DeepTau machine-learning classifier, which helps distinguish hadronically-decaying tau leptons from jets.
The search is performed by examining the invariant mass of the hadrons (see figure 1). No significant excess of events with W bosons decaying into three charged hadrons is observed. The most stringent 95% CL upper limit on the branching fraction of the W boson to three light charged hadrons is set at 3.0 × 10–7, while theory estimates a branching fraction in the vicinity of 10–5–10–7.
The decay of the W boson into a low-multiplicity exclusive state probes an interesting dynamical domain at the boundary of perturbative and non-perturbative QCD physics, where theorists strongly need experimental input. Although the signal has not yet been observed, the result already constrains certain models of this rare W-boson decay. As larger datasets become available, these rare decay modes offer a new window on the dynamics of the strong interaction.
The LHCb collaboration has reported the observation of the doubly charmed baryon Ξ+cc, the first new particle found with the upgraded LHCb detector. The result completes the isospin doublet of the doubly charmed baryons, allowing the two states to be compared directly in mass, lifetime and decay channel. The Ξ+cc contains two charm quarks and a down quark, and is the isospin partner to the Ξ++cc baryon, much as the neutron is to the proton. Yet unlike the neutron, which is more massive than the proton, the Ξ+cc is expected to be lighter than the Ξ++cc, because electromagnetic effects outweigh the down–up quark mass difference.
The two states also differ in their lifetimes. The Ξ+cc is predicted to decay about six times faster than the Ξ++cc, owing to an additional W-exchange contribution and to interference between decay amplitudes. Precise measurements of their masses and lifetimes, therefore, test the heavy-quark dynamics at work inside baryons.
The experimental search for the Ξ+cc baryon has a long history. In 2002, the SELEX collaboration at Fermilab claimed to have observed it, a result that has not been confirmed by subsequent searches at FOCUS, BaBar, Belle and LHCb. Meanwhile, the LHCb collaboration observed the Ξ++cc baryon using proton–proton collisions recorded at a centre-of-mass energy of 13 TeV in 2016. The LHCb detector was then upgraded during the second long shutdown of the LHC (2019–2021), to maintain its performance while operating at around five times the instantaneous luminosity of Runs 1 and 2. The online trigger system, in which the interesting signals are selected from a huge number of proton–proton collisions at the LHC in real time, was also upgraded, increasing the efficiency for selecting hadronic decays by more than a factor of two.
The observation demonstrates the enhanced capabilities of the upgraded LHCb experiment
The new LHCb search used proton–proton collision data recorded at a centre-of-mass energy of 13.6 TeV in 2024. The Ξ+cc baryon was reconstructed through its decay to the Λ+cK–π+ final state in a blind analysis, designed to avoid any experimenter bias. A topologically similar decay of the Ξ++cc baryon, Ξ++cc→Λ+cK–π+π+, was used as a control mode for developing the event-selection strategy and calibrating the mass measurement. More than 8000 Ξ++cc candidates were reconstructed in the 2024 dataset, corresponding to an efficiency increase of about a factor of four relative to Run 2.The measured Ξ++cc mass was found to be consistent with the average of previous measurements.
Once the analysis was finalised, the Ξ+cc signal region was unblinded and examined. A structure with a statistical significance exceeding seven standard deviations was observed (see figure 1), corresponding to more than 900 Ξ+cc candidates. The corresponding efficiency is about two and a half times higher than that achieved during Run 2, with the smaller improvement relative to Ξ++cc reflecting the shorter lifetime of the Ξ+cc baryon.
The collaboration also performed a precision measurement of the Ξ+cc mass and the difference between the masses of the two doubly charmed baryons. The Ξ+cc mass was measured to be 3619.97 ± 0.83 (stat) ± 0.26 (syst)+1.90–1.30 (lifetime) MeV, with a difference of –1.77 ± 0.84 (stat) ± 0.15 (syst)+1.90–1.30(lifetime) MeV from that of the Ξ++cc, compatible with theoretical predictions. It was also about 100 MeV higher than the one reported by the SELEX collaboration, disfavouring the interpretation of that state as the Ξ+cc baryon.
The observation of the Ξ+cc baryon completes the isospin doublet of the doubly charmed baryons. It also demonstrates the enhanced capabilities of the upgraded LHCb detector and its trigger system, laying the groundwork for hadron spectroscopy studies with data taken in Run 3.
When lead nuclei collide at the LHC, they create tiny droplets of quark–gluon plasma, an extremely hot and dense state of matter in which quarks and gluons are no longer confined within protons and neutrons. Although these droplets exist for only a tiny fraction of a second, they expand collectively before cooling into the particles detected by the ALICE experiment. One of the clearest signatures of this collective motion is the elliptic flow, which quantifies how particles preferentially emerge along certain directions in the plane transverse to the collision axis.
ALICE has now measured, for the first time, the elliptic flow of the hypertriton (3ΛH) in lead–lead collisions at √sNN = 5.36 TeV, and compared the results with those of anti-3He, a more compact nucleus of similar mass (about 3 GeV). A bound state of a proton, a neutron and a Λ hyperon, the hypertriton is among the most weakly bound nuclei known. As a result, it is significantly larger than ordinary nuclei – while the radius of 3He is about 1.96 fm, the distance between the deuteron core and the Λ hyperon in the hypertriton is of the order of 10 fm. Measurements of the hypertriton flow thus provide a unique opportunity to test whether such a large and loosely bound nucleus follows the collective motion of the medium in the same way as more compact ones.
The analysis is based on approximately five billion lead–lead collisions recorded in 2023. 3He candidates are identified by measuring their specific energy loss in the ALICE Time-Projection Chamber, complemented by information from the Inner Tracking System. Hypertriton candidates are reconstructed through their decay into 3He and a charged pion. To distinguish the tiny signal from the much more abundant particles produced at the collision vertex, the analysis identifies a secondary vertex, displaced from the point of collision, where the hypertriton decay happened. Despite their very different sizes and binding energies, the measured elliptic flow of the hypertriton is found to be consistent with that of the 3He (see figure 1).
The 3He measurement reaches unprecedented precision and shows an increase in elliptic flow with transverse momentum, exceeding 0.5 at intermediate and high transverse momenta in the 40–60% centrality interval. Such large values suggest that larger azimuthal modulations contribute to the full angular pattern of 3He production. This behaviour arises naturally in coalescence models, in which light nuclei are formed near kinetic freeze-out by the coalescence of already formed nucleons. In this picture, their collective motion reflects the combined motion of their constituents. The combination of several flowing nucleons can then reshape the nucleus’s final azimuthal distribution, producing the large observed modulation.
Theoretical models reproduce the 3He flow only when a coalescence stage is included, providing strong evidence that light nuclei are not simply born as complete objects at hadronisation, but are assembled from nucleons at a later stage of the collision. Together, the new measurements provide a coherent picture of how composite objects emerge from the hot and dense medium created in high-energy nuclear collisions. Light nuclei appear to carry the collective motion of their constituents, and their elliptic flow is largely governed by the dynamics of the expanding medium. Even for the loosely bound hypertriton, the acquired flow remains insensitive to the large spatial size of the final nucleus. These results establish light nuclei as powerful probes of how and when composite matter forms in heavy-ion collisions.
The Quantum Observables for Collider Physics 2026 workshop, held at CERN from 20 to 24 April, was the third edition of a series that began at the Galileo Galilei Institute in Florence in 2023 – now brought to the heartland of high-energy physics. Around 100 invited specialists from across the world gathered to take stock of a programme that has grown, with surprising speed, from a mere theoretical curiosity into a substantial body of experimental results.
The study of quantum observables with colliders is not starting from scratch. Phenomena such as oscillations and CP violation in neutral meson systems, or quantum interference in decay amplitudes and entanglement between B mesons at the Υ(4S) resonance, have been under scrutiny for decades. The novelty lies in the systematic application of the conceptual vocabulary of quantum information science – entanglement witnesses, Bell inequalities, quantum state tomography, and magic and decoherence as observables – to the highest-energy collisions accessible today.
Catalogue of entanglement
The most sharply focused experimental news came from the Higgs sector, where both ATLAS and CMS reported evidence that the two Z bosons produced in Higgs decays are entangled. Tairan Xu (University of Michigan) presented the ATLAS result, with an observed significance of 4.7σ. Jeffrey Davis (Johns Hopkins University) reported the CMS analysis, which measured spin correlations and extracted helicity fractions within an effective-field-theory framework. Together, the two results mark the Higgs boson’s entry into the catalogue of entanglement sources at the LHC.
In the top sector, CMS presented a full tomographic characterisation of the top quark–antiquark quantum state, with Otto Hindrichs (University of Rochester) showing the reconstructed spin-density-matrix elements across the full kinematic range of Run 2. Fiona Jolly (DESY) presented complementary ATLAS measurements, probing quantum-information observables in top-quark pairs. What has changed since the first edition of the workshop is the ambition, with early proof-of-principle measurements giving way to precise reconstructions of the full quantum state.
What has changed since the first edition of the workshop is the ambition
One of the most striking results came from the STAR experiment at RHIC, presented by Zhoudunming Tu (BNL). The measurement reports spin correlations of Λ–Λ hyperon pairs in proton–proton collisions at a centre-of-mass energy of 200 GeV, with a clear angular dependence that existing predictions do not fully describe. Elsewhere, Dmitri Kharzeev (Stony Brook University) argued that partons within a proton approach maximal entanglement at high energies. Their entanglement entropy then becomes directly observable in final-state multiplicities, making structure functions themselves carriers of quantum information. Beatrix Hiesmayr (University of Vienna), whose earlier work on entanglement and Bell-inequality violations in neutral kaon systems helped lay the foundations of the field, provided perspectives from the meson sector that grounded the newer collider-based results.
Marcel Vos (IFIC Valencia) showed that, at a future lepton collider, the entanglement of the top spins in e+e–→ ttg events is expected to fall with the gluon’s energy, vanishing near the kinematic endpoint. This would be a computable, measurable signature of decoherence from real gluon emission. Lian-Tao Wang (University of Chicago) offered a striking reinterpretation, according to which decoherence due to soft, collinear radiation in high-energy collisions can be understood as a renormalisation-group flow.
Two-faced
Several talks explored whether entanglement suppression and enhanced symmetry are two faces of the same phenomenon. Ian Low (Northwestern University) showed, in an abstract spin-system setting, that entanglement reaches a minimum precisely where the Hamiltonian acquires an enlarged symmetry. Carlos Wagner (University of Chicago), Kamila Kowalska (NCBJ Warsaw), and Spencer Chang (University of Oregon) pressed the question from the collider side, asking whether the causal arrow runs from symmetry to entanglement or vice versa. The discussion remained productively unresolved.
A dedicated session on Bell tests reflected a field that has matured in its self-understanding. After a period of a rapid proliferation of proposals, there is now broad agreement on what is and is not achievable at a collider: entanglement can be established, Bell-violating quantum states can be witnessed, but a loophole-free Bell test – of the kind achieved with photons in a standard laboratory setting – is structurally out of reach with existing techniques. The community has, by and large, made peace with this distinction, and is now focusing on what can actually be done.
The next generation of colliders promises a significant step forward
Many contributions pushed the programme’s conceptual boundaries outward. Vlatko Vedral (University of Oxford) argued that laboratory interference experiments could test quantum effects in the gravitational field, while Nikos Mavromatos (King’s College London) explored entangled squeezed states of gravitons – associated with black-hole environments – as a potential probe of quantum gravity. David Kaiser (MIT) recounted how foundational debates about Bell inequalities, pursued by an unlikely group of physicists in 1970s California, eventually catalysed the cosmic Bell experiments. The account served as a reminder that questions dismissed as purely philosophical have a habit of becoming precision science.
On a longer timescale, the next generation of colliders promises a significant step forward. Tao Han (University of Pittsburgh) made the case that FCC-ee and CEPC would deliver large statistical samples in cleaner conditions than the LHC, and that beam polarisation in lepton colliders would open access to quantum process tomography of fermion pairs. Paweł Horodecki (Gdańsk University of Technology) emphasised that, by controlling the initial quantum state, this technique could enable tests of subtle deformations of quantum mechanics – possible extensions of the theory that state tomography alone cannot reach. Yoshitaka Hatta (BNL) and Kun Cheng (University of Pittsburgh) pointed to a further frontier at Brookhaven’s Electron–Ion Collider, where polarised beams will allow the partonic structure of the proton to be probed through its entanglement content.
Phrases overheard in the corridors, in the panel sessions and at the well-attended poster session captured the mood: “That’s fascinating,” “I disagree with you,” and “Let’s talk over coffee.” As Yoav Afik (University of Chicago) observed, the field has grown from a handful of proposals into a genuine international programme. The questions being asked are real ones, and the answers, when they come, will sharpen our understanding of quantum mechanics at the highest accessible energies. The next edition of the workshop will be in Chicago.
From 18 to 22 May 2026, the 28th annual PLANCK conference – held in conjunction with the 6th EuCAPT Symposium – brought more than 250 theoretical physicists to CERN to confront a set of dilemmas that are, at root, about scale. Where should the hunt for dark matter focus, when its mass might span 90 orders of magnitude? Why is the Higgs mass so tiny compared to the Planck scale, with no signs of a mechanism to stabilise the gap? Can one learn about particle production in the early universe, when evidence is spread thinly over the farthest sky?
Microscopic to galactic
Faced with these puzzles, theorists are seeking answers from systems ranging from the microscopic to the galactic. Jordy de Vries (NIKHEF) discussed novel methods to look for subtle differences in how the strong force affects matter and antimatter using tiny molecular dipole moments. At the opposite end, Kai Schmitz (Münster University) reported on work using the rhythms of pulsars spread across the Milky Way to detect gravitational waves produced in the first moments after the Big Bang.
The framework of effective field theory (EFT) threaded through the conference. By capturing the physics at a given scale and folding higher-scale effects into a handful of parameters, it proves ubiquitously powerful for advancing complex calculations. Giulia Isabella (UCLA) presented new results applying scattering methods – originally developed for particle physics – to calculate gravitational-wave signals from black hole mergers. Mikael Chala (University of Granada) discussed the use of EFTs in calculations of thermal phase transitions, such as those that occurred in the early universe. Anders Eller Thomsen (University of Bern) presented precision calculations of the Standard Model EFT used to predict subtle effects of undiscovered particles with masses beyond the energy range of the LHC.
The electroweak scale, at which electroweak symmetry breaks and particles acquire mass through the Brout–Englert–Higgs mechanism, continues to play a unique role across a variety of fundamental puzzles. The possibility that a strong electroweak phase transition led to a universe filled with matter was discussed in talks by Jorinde van de Vis (CERN), Dave Sutherland (University of Glasgow) and Maria Cristina Fiore (University of Granada), anticipating future tests of this scenario with gravitational waves, Higgs measurements and resonance searches.
A highly varied field, united around big questions
The idea of a “WIMP miracle”, in which the observed abundance of dark matter is due to a weakly interacting particle with mass around the electroweak scale, is one of the most compelling and long-standing dark-matter explanations. Weishuang Linda Xu (Stanford University) presented work interpreting gamma-ray observations of the galactic centre, arguing that this dark-matter framework can be fully tested once the next generation of telescopes comes online.
Many talks presented novel model-building ideas, including some related to the recent burst of activity around models explaining the observed hierarchies in fermion masses, many of which answer other theoretical puzzles. Marta Zamoro (Autonomous University of Madrid) showed how both the mass hierarchies and the strong CP problem could be explained through a model with extra copies of the Standard Model QCD group. Javier Lizana (University of Castilla–La Mancha) and Simone Marciano (University of Valencia) presented different models in which a dark-matter candidate arises within theories predicting hierarchical fermion masses. Each of these predicts novel phenomena, particularly in flavour-changing processes that could be measured at LHCb.
PLANCK 2026 presented a picture of a highly varied field, united around big questions and emerging techniques. Speakers and participants looked towards the new opportunities offered by upcoming measurements, colliders and telescopes, building a theoretical toolkit to interpret their insights across all scales.
The 16th Workshop on Critical Point and Onset of Deconfinement (CPOD26), held at CERN from 13 to 17 April 2026, brought together more than 100 researchers focused on the phase structure of strongly-interacting matter. The workshop continued the long-running CPOD series, which centres on understanding how and when ordinary hadronic matter transforms into quark–gluon plasma (QGP), and whether a critical point exists in the QCD phase diagram.
The series adopts a plenary-only format, to encourage unified discussion across theory and experiment and bridge gaps between different approaches to the same underlying questions. In this same spirit, the programme emphasised clarity and synthesis rather than specialised talks for a narrow audience. Many of the review talks were devoted to emerging subfields, making it easier to connect developments across traditionally separate areas.
Critical point
The central scientific theme was the search for the hypothetical QCD critical point, where the smooth crossover between hadronic matter and the QGP gives way to a genuine first-order transition, deconfining and chiral-restoring at once. Identifying it remains one of the most important open problems in high-energy nuclear physics.
Speakers examined how matter behaves under extreme temperature and density – conditions recreated in relativistic heavy-ion collisions. While lattice QCD provides invaluable results at vanishing net-baryon density, extending these calculations to high net-baryon density remains difficult due to the infamous “sign problem”. Still, new exclusion limits were presented, ruling out parts of the phase diagram as possible locations for the critical point.
On the experimental side, several contributions highlighted results from ongoing heavy-ion programmes, probing a wide range of observables with beam-energy and system-size scans. These efforts are designed to uncover non-trivial structures in the excitation functions of observables that might signal critical behaviour – or the onset of deconfinement. Particular attention was given to event-by-event fluctuations and correlations, as well as to methodology, since signals can be distorted by the dynamical evolution of the collision system.
Central were, of course, the properties of the QGP. Presentations addressed transport coefficients, collective flow, dileptons and the role of fluctuations in the QGP, aiming to understand how such properties vary across different regions of the phase diagram. The connection between early-time dynamics and final-state observables was a recurring theme, with hydrodynamic and transport models playing an important role.
A key takeaway from CPOD26 was the importance of integrating multiple approaches
Understanding hadronisation – the transition from QGP back to hadrons – is essential for linking theoretical descriptions of deconfined matter to experimental measurements. Various models of particle production and freeze-out were compared, with emphasis on how they affect fluctuation observables and potential signatures of critical phenomena. Subtler effects, such as possible indications of isospin-symmetry breaking, were also noted.
The workshop’s scope extended to dense QCD matter in astrophysical environments, particularly in neutron stars, with observations from modern astrophysics providing complementary constraints on the QCD equation of state at high density. This interdisciplinary perspective highlighted how insights from astrophysics and heavy-ion collisions can inform each other, contributing to a more complete picture of the phase diagram.
Looking to the future, several talks focused on new experimental facilities and detector upgrades. Speakers discussed developments at the FAIR complex at GSI – home to the CBM and HADES experiments – and at CERN, including the proposed new fixed-target experiment NA60+/DICE, the upgrade of NA61/SHINE and the next-generation ALICE 3 detector for the HL-LHC. The possibility of a fixed-target experiment at the Electron–Ion Collider (EIC) was also discussed. These efforts aim to improve sensitivity to rare signals and extend coverage into previously unexplored regions of the phase diagram.
Intriguing hints
A key takeaway from CPOD26 was the importance of integrating multiple approaches, especially given the uncertainty about the existence and location of the critical point. Experimental hints are intriguing but not yet conclusive, and theoretical predictions still face challenges in achieving quantitative agreement with data. The need for new, precise measurements at collision energies between 3 and 10 GeV was stressed throughout the workshop.
By bringing together diverse perspectives in a focused and collaborative setting, CPOD26 highlighted both how far the community has progressed in refining its tools and how much remains to be understood about the fundamental behaviour of strongly interacting matter. The next workshop is planned in Lanzhou (China), on 16–20 August 2027.
From 27 to 29 May 2026, LoopFest returned to Brookhaven National Laboratory, where the conference series started in 2002. Since then, LoopFest has been held each year across universities and national laboratories in the US and, more recently, Canada. With around 60 participants, this year’s edition provided a forum for discussing the latest results in precision quantum field theory (QFT), along with their applications to interpreting current experimental results and anticipating the precision reach of future experiments, primarily in collider physics. Its cousin event, the Loops and Legs symposium, was hosted last April in Bayreuth, Germany.
Talks highlighted impressive developments in multi-loop and multi-leg calculations, in matching fixed-order higher-order calculations with multi-purpose parton-shower event generators, and in the evaluation of parton distribution functions for precision measurements. Areas central to the precision-physics programme of the LHC, such as differential measurements of Higgs-boson and top-quark processes, received particular attention, while dedicated talks turned to future e+e– machines. There, the main challenge will be for theory to equal the extreme experimental accuracy expected for electroweak precision observables.
Exquisite control
Matching the precision of the High-Luminosity LHC and future e+e– colliders is vital for future discoveries. This endeavour will require exquisite control of theoretical predictions, at the (sub)percent and permille level, respectively, and already poses issues that are both technical and conceptual. Most importantly, aiming for extreme precision could not only enable the indirect discovery of new physics, but also lead to new insights into the fundamental structures of quantum field theory. Several talks stressed this point, some reviewing cutting-edge studies of amplitudes in N = 4 super Yang–Mills theories, others the impact of recent advances in quantum amplitudes for gravitational waves from black-hole scattering.
If anomalies emerge from precision studies, their interpretation will be equally challenging. Multiple contributions traced the state of the art of Standard Model effective field theory (SMEFT) calculations. SMEFT extends the Standard Model with a series of higher-dimensional operators built from its own fields, so that the imprint of unknown heavy particles is captured by small shifts in couplings. It is a common way to explore physics beyond the Standard Model under very general assumptions.
A dedicated effort to provide the dimension-6 SMEFT Lagrangian at the first non-trivial order of quantum corrections is reaching completion and will become a fundamental building block for future studies. Results from a global fit of the SMEFT Lagrangian – including, for the first time, a broad spectrum of electroweak, Higgs-boson, top-quark, Drell-Yan, di-boson and flavour observables – were presented as a proof of concept of how the SMEFT could help explore models of new physics.
New ways to apply artificial intelligence/machine learning and quantum information science have opened up
Finally, the focus shifted to how the groundbreaking ideas that have transformed the theoretical calculation of scattering amplitudes have also opened new ways to apply artificial intelligence/machine learning (AI/ML) and quantum information (QI) science. This is creating new opportunities to rethink how loop calculations are performed, potentially overcoming longstanding computational bottlenecks and enabling qualitatively new approaches and conceptual frameworks. For instance, recent work has explored the application of reinforcement learning, supervised regression and self-supervised learning to some of these problems.
At the same time, generative models – including normalising flows and diffusion-inspired methods – have already demonstrated impressive gains in Monte Carlo integration and importance sampling, the random-sampling methods used to evaluate the high-dimensional integrals underlying cross-section predictions. Since precision QFT calculations are quantum-mechanical at heart, a genuinely quantum computation of precision scattering opens the door to synergies with QI studies of collider processes. Some talks asked how far a future quantum computer could help study QFT processes from a QI perspective, to best exploit the precision data produced by colliders like the LHC.
Extended reach
Overall, LoopFest conveyed the impressive theoretical progress achieved in recent years, enabling the exploration of new physics through precision measurements at current and future experiments. Ground-breaking methods developed during the last two decades have progressed rapidly and are now entering a mature phase, providing a robust framework within which future technical and conceptual challenges can be identified and addressed. Combined with new emergent technologies such as AI/ML and QI, this could extend the reach of current precision-physics programmes far beyond expectations.
Cosmological filaments form the backbone of the cosmic web, the vast, interconnected network that defines the universe on the largest scales. Stretching across tens to hundreds of millions of light-years, they link galaxies and galaxy clusters along the pathways where matter assembles under gravity. They may also hold the key to one of the deepest questions in modern physics: the nature of dark matter.
For astrophysicists, filaments first drew attention as a potential reservoir of missing baryons. Big Bang nucleosynthesis and precision measurements of the cosmic microwave background agree on how much ordinary matter the universe should hold, but the census of stars, galaxies and hot gas comes up short. The leading explanation is a warm, diffuse gas permeating cosmic filaments, too faint to detect in any single observation but increasingly accessible through statistical techniques at X-ray and radio wavelengths.
More recently, dark-matter hunters have begun to recognise the potential of filaments as probes of new physics. Filaments are not only vast but overwhelmingly dark-matter-dominated, with lower astrophysical backgrounds than traditional search targets such as the galactic centre. New simulations are pinning down their dark-matter density profiles with enough precision to make quantitative predictions, and recent theoretical work has opened detection channels that could turn these structures into laboratories for physics beyond the Standard Model.
Dark matter and the cosmic web
Our scientific understanding of stars and the structures they inhabit has grown remarkably over the past century. We now know that galaxies are vast collections of stars, and clusters are collections of galaxies. These immense systems do not float randomly; they are woven into an intricate “cosmic web” resembling that of a spider. Gravity shapes this web and governs the motion of the celestial bodies within it. Yet many observations defy expectations. Galaxies rotate too quickly, clusters bend light too strongly, and the cosmic web holds together with more gravitational pull than visible matter would allow. Something unseen must be at work. A new, invisible “dark matter” component must dominate the mass of the universe.
Dark-matter candidates in the spotlight
Dark matter accounts for roughly 85% of the matter in the cosmos, and about 27% of its content once dark energy is included, yet its nature remains unknown. Several well-motivated candidates have emerged, each predicting distinct signatures that indirect searches, including those targeting cosmic filaments, could probe. Weakly interacting massive particles, sterile neutrinos, primordial black holes and axions are among the most prominent.
Weakly interacting massive particles These hypothetical particles naturally arise in several extensions of the Standard Model and possess two defining features: they are massive, and they interact only through gravity and the weak force.
Sterile neutrinos Unlike the three known active neutrino species, they do not interact through the weak force. Their existence is motivated by extensions of the Standard Model that aim to explain both neutrino masses and the matter–antimatter asymmetry of the universe.
Primordial black holes Unlike stellar black holes, which form from collapsing stars, primordial black holes are hypothetical relics of the early universe, born from the collapse of exceptionally dense regions of matter moments after the Big Bang.
Axions Originally proposed to solve the strong CP problem, axions are hypothetical particles whose production mechanism can account for the observed dark-matter abundance, elegantly linking two of modern physics’ greatest mysteries.
Dark matter accounts for roughly 85% of the matter in the cosmos and dictates how cosmic structures form and evolve. Yet, despite decades of international effort and extraordinary experimental ingenuity, its nature remains a puzzle. The Standard Model of particle physics, describing all known fundamental particles, can’t account for the observational effects of dark matter. In response, theorists have proposed a wide range of models that include dark-matter candidates (see “Dark-matter candidates in the spotlight” panel). A well-motivated dark-matter theory, one that truly excites theorists, typically meets three criteria. First, it accounts for the observed cosmic abundance of dark matter. Second, it yields clear, testable predictions. And third, it resolves multiple open questions in fundamental physics.
Rich landscape
While the theoretical landscape is rich, testing it requires identifying cosmic environments where dark matter’s signatures might be detectable. One of the most powerful strategies is indirect detection – the search for faint cosmic messengers produced when dark matter annihilates, decays or interacts with ordinary matter. These signatures may appear as electromagnetic waves, neutrinos or charged cosmic rays. Observing these messengers requires high sensitivity and careful modelling of both the dark-matter signal and the astrophysical backgrounds. Progress, therefore, depends on close collaboration between particle physicists, astrophysicists and cosmologists, integrating theoretical predictions with multi-messenger observations.
Choosing optimal targets is crucial for indirect dark-matter searches. Traditional efforts have focused on the galactic centre and on dwarf satellite galaxies of the Milky Way. The galactic centre is expected to host the highest dark-matter density, but it also contains intense and complex astrophysical backgrounds, which is why the origin of a long-debated gamma-ray excess observed by Fermi-LAT remains uncertain (see “Gamma-ray excess” figure). Dwarf galaxies, by contrast, are dark-matter-dominated and relatively free of astrophysical emission. However, their stellar populations are orders of magnitude smaller than that of the Milky Way. This limits the available kinematic tracers – observables whose spatial distribution correlates with the underlying matter density field – and leads to sizable uncertainties in the predicted signals.
Unconventional environments
Recently, unconventional but promising probes have gained attention, such as cosmological filaments. Filaments are a natural outcome of anisotropic gravitational collapse in an expanding universe. Matter can collapse under gravity in some directions while still expanding in others, producing elongated structures that are bound across their width but continue to grow along their length. Not all cosmic filaments are alike. Some lie within galaxy clusters, linking individual galaxies over relatively short distances. Others extend far beyond cluster boundaries, forming vast inter-cluster bridges that connect galaxy clusters and even superclusters across tens and hundreds of megaparsecs. The longer the filament, the thinner and more diffuse it tends to be. This reflects the way gravity draws matter out of underdense regions and funnels it into elongated bridges between massive nodes.
Together, galaxy clusters and the diffuse filaments that connect them form the cosmic web and make up most of the baryonic matter. Yet the very properties that make filaments so fundamental to cosmic structure also make them extraordinarily difficult to observe. Their emission is faint, diffuse and easily overwhelmed by brighter astrophysical sources, posing a major challenge for direct detection across the electromagnetic spectrum.
To overcome this limitation, astronomers have turned to a statistical technique known as “image stacking”. In stacking analyses, many observations of similar systems are superimposed. Any emission associated with filaments then adds coherently, while random noise and unrelated astrophysical signals average away. The result is a significant enhancement in sensitivity, allowing extremely weak, extended emission to emerge that otherwise would remain invisible.
A potent technique
The power of this approach relies on numbers: the larger the sample that can be stacked, the stronger and more reliable the resulting signal. Image stacking is therefore a potent but data-hungry technique, one that becomes increasingly effective as modern surveys deliver ever-larger datasets. This requirement poses a particular challenge for filaments, whose precise locations are generally unknown. Since cosmological filaments connect massive structures, a natural strategy is to use galaxy clusters as signposts: by stacking observations of regions between pairs of clusters, the faint emission from the filamentary bridges that link them can be statistically enhanced.
Cluster catalogues have expanded dramatically over the past decade. Today, surveys based on optical imaging, weak gravitational lensing and the Sunyaev–Zel’dovich effect, in which scattering with high-energy electrons distorts the cosmic microwave background, collectively identify tens of thousands of clusters across the sky. While progress is remarkable, it may still fall short of what is needed to robustly detect the extremely faint emission expected from typical filaments. This limitation motivates the search for alternative tracers. A reliable proxy for galaxy clusters available in far greater numbers, potentially in the millions, would enormously increase the statistical power of stacking analyses.
Particularly effective proxies for galaxy clusters are luminous red galaxies (LRGs). These massive, early-type galaxies have been observed and catalogued for decades and are known to be excellent tracers of the large-scale structure of the universe. LRGs typically reside in, or near, the centres of galaxy clusters, making them reliable signposts of the densest regions of the cosmic web. Pairs of LRGs that are close to one another in the sky and in physical distance can therefore be used as proxies for nearby cluster pairs. Statistically, such pairs are likely to be connected by inter-cluster bridges or filaments, even if the filaments themselves cannot be directly identified in individual observations.
By applying this stacking technique to pairs of LRGs drawn from the Sloan Digital Sky Survey, whose catalogues contain millions of such galaxies, together with radio maps from the GLEAM and OVRO-LWA surveys, researchers have identified an intriguing anomaly. The radio emission associated with stacked filaments (see “Stacked maps” figure) exceeds theoretical predictions for diffuse filamentary gas by more than an order of magnitude.
One possible interpretation is that this excess arises from secondary radiation produced by dark matter (see “Simulations, observations and theory” figure). In this scenario, weakly interacting massive particles with masses of a few GeV decay into electrons, which then spiral through filament magnetic fields and emit synchrotron radiation at radio wavelengths. For the magnetic field strengths inferred in the stacking analysis, the amplitude of the observed signal is consistent with that expected from a dark-matter flux of this kind.
As with other anomalies, this interpretation remains debated. A more conventional explanation attributes the emission to astrophysical particle acceleration in strong accretion shocks, generated as matter falls into filaments and galaxy clusters. While shocks can in principle produce radio synchrotron emission, reproducing the observed excess appears to require acceleration efficiencies higher than those typically assumed in simulations. Significant uncertainties persist in filament properties, such as their magnetic field strengths and shock characteristics, which complicate the modelling of expected signals and remain an active area of research.
Cosmic filaments may also open a window onto more exotic dark-matter scenarios. Recent work has shown that if heavy dark matter decays into gravitons – the hypothetical quantum carriers of the gravitational interaction – these can convert into photons via the Gertsenshtein effect (see “Graviton-to-photon” figure), closely analogous to the Primakoff conversion of axions, as they propagate through the large-scale magnetic fields threading filaments. This process generates an irreducible extragalactic gamma-ray background, allowing such scenarios to be constrained with Fermi-LAT data and offering promising sensitivity for future gamma-ray observatories.
A bright future for the dark universe
For millennia, humanity has been inspired by the starry sky. Philosophers, poets and scientists alike have gazed upward, their minds filled with questions, joy and awe. Dante, one of Italy’s greatest poets, expressed this enduring fascination in the closing line of Inferno in The Divine Comedy:
Centuries after Dante, the sky continues to guard many of its secrets. However, we are now entering a golden era for indirect dark-matter searches. Future facilities, most notably the Square Kilometre Array (SKA), currently under construction in South Africa and Australia, will deliver unprecedented sensitivity to the diffuse structures of the cosmic web, and may soon be capable of directly imaging large filaments, characterising their properties and turning these vast structures into powerful probes of physics beyond the Standard Model.
These observational advances are being matched by progress on the theoretical front. Cosmological simulations are reaching new levels of realism, while the growing use of machine-learning and artificial-intelligence techniques is beginning to transform how filamentary structures are identified, modelled and interpreted. These developments promise a far more precise characterisation of filament properties, sharpening their role as laboratories for fundamental physics. The cosmic web may not keep its secrets much longer.
Born of one kind, a neutrino can die another. Its three flavours, electron, muon and tau, do not correspond to states of definite mass, but to quantum superpositions of three distinct masses. As neutrinos propagate, the mixture reshuffles and the flavour at arrival can differ from the one at production. None of this is predicted by the Standard Model, making the observation of neutrino oscillations one of the clearest signals of physics beyond it.
Neutrino oscillations provide a unique probe of new physics, acting as an interferometer that is sensitive to neutrino mass differences down to the sub-eV level. Precise measurements at the next-generation accelerator-based oscillation experiments, Hyper-Kamiokande in Japan and DUNE in the US, are poised to answer several critical questions. What is the ordering of the three neutrino masses, given their two measured mass-squared differences? Do neutrinos and antineutrinos oscillate differently? Are there additional, as yet undetected, neutrino states? These long-baseline neutrino facilities, in which a beam of neutrinos is sent to a detector hundreds of kilometres away, will produce much larger datasets than current-generation experiments. However, they suffer from a fundamental limitation: we do not know the precise energy or intensity of the neutrino beams when they set out. Reaching ultimate precision on neutrino-oscillation parameters is therefore no longer a matter of statistics, but one of messy nuclear-physics questions related to the details of weak-interaction cross sections and proton-induced hadron production.
Modern neutrino beams use the famous “magnetic horn” design, developed by Simon van der Meer at CERN in 1961 (see “In focus” image). Protons strike a target to produce pions, which the horn focuses into a volume for them to decay to neutrinos and leptons. The trouble is, the resulting neutrino beam covers a wide range of energies (about 0.5 GeV and 2.5 GeV for Hyper-K and DUNE, respectively), with a shape and intensity that depend on the details of tough-to-model proton–nucleus collisions. To make matters worse, the broadband neutrino flux forces the neutrino energy to be estimated from the products of neutrino–nucleus interactions, which are notoriously difficult to model accurately. Together, these challenges form a barrier to ultimate precision in neutrino-oscillation measurements.
There is, in principle, a way around both problems: neutrino tagging. Proposed by Bruno Pontecorvo in 1979, this technique associates a measurement of the four momenta of the pion and muon in a π+→ μ+νμ decay with a measurement of a neutrino in a downstream detector. Four-momentum conservation then fixes the neutrino kinematics event-by-event. As a result, the neutrino energy is known for each interaction and the flux is perfectly constrained, nullifying the key challenges for neutrino-oscillation experiments and producing well-controlled muon, pion and kaon beams as byproducts. The idea was first attempted in the 1990s at the dedicated Tagged Neutrino Facility (TNF) at the Serpukhov accelerator in Protvino (see “Dream, deferred” image). TNF recorded two candidate events in its brief pilot run, before the dissolution of the Soviet Union brought the work to a halt.
The downside with neutrino tagging is one of scale: for every neutrino seen in a massive, 100-tonne detector close to the beam, there are about 1013 pion decays. To collect a reasonable 105 neutrino interactions per year, one would therefore need to identify at least 1011 individual muons per second and successfully identify the minute fraction of them that are associated with observed neutrinos. Such a measurement demands beamline detectors with timing resolutions of 10 to 100 ps and a neutrino detector with sub-ns timing resolution, with the beamline detectors operating in a high-radiation environment.
Promising performance
These challenges proved too much for the 1990s, and the idea lay dormant for three decades after the closure of TNF. However, a revolution in detector and electronics technology has since changed what is possible (see “The fast-timing revolution” panel) – beginning with the NA62 experiment at CERN.
The fast-timing revolution
R&D for the high-luminosity phase of the LHC are expected to push fast-timing sensors beyond the performance of NA62’s GigaTracker. With bunches crossing every 25 ns and up to 200 proton collisions in each, the ATLAS and CMS upgrades require timing resolutions below 50 ps to disentangle overlapping vertices. In a silicon detector, incoming particles release small electric charges, with internal electric fields then steering them toward electrodes to be collected and measured. Faster timing demands more charge, a shorter drift for the signal to form quickly and smaller collection electrodes for sharper and stronger pulses. In conventional planar sensors, these requirements are often in conflict with one another. Since the collected charge is proportional to the sensor thickness, which also sets the drift distance, thinner sensors give faster signals but fewer carriers. Potential solutions span a wide range of architectures. Low-gain avalanche detectors (LGADs), for instance, combine thin, 50 μm sensors with a gain layer to amplify charge, compensating for the lower number of carriers produced in a thin substrate while preserving a short drift. They achieve resolutions of 20 to 50 ps and will equip the new ATLAS and CMS timing layers.
Many roads to fast timing
For the upgrade of the LHCb vertex locator, which must resist radiation levels of 1016 to 1017 1 MeV neutron equivalents per cm2 (neq/cm2), a gain layer would erode too quickly. Three-dimensional sensors sidestep the problem geometrically. Their electrodes run along the sides of each pixel rather than on the top and bottom surfaces, so charges move sideways over distances below 50 μm while the sensor remains thick enough to generate large signals. Initially developed for radiation-hard pixel detectors for ATLAS and CMS, these sensors were later redesigned for timing and have reached resolutions as good as 10 ps. The remaining challenge lies in the electronics. Readout chips must match the sensors’ speed and radiation tolerance, and recent prototypes in 28 nm CMOS have achieved 30 ps resolution over areas of a few mm2. Large-area designs are currently underway.
Depleted monolithic active pixel sensors integrate the sensor and readout electronics on the same chip. With resolutions of 10 to 200 ps and pixels smaller than 100 × 100 μm2, they are much cheaper than three-dimensional sensors and LGADs, and therefore better suited to instrumenting large surfaces and achieving a lower material budget. Some R&D initiatives are also exploring the use of Cherenkov radiation to detect charged particles, a process much faster than ionisation in silicon. In these detectors, the prompt Cherenkov light is converted into photoelectrons and amplified in a thin gaseous detector, producing signals with time resolutions of a few tens of picoseconds. While highly promising, extending this approach to finely segmented detectors operating at very high rates remains an open problem. All these new tracking technologies offer promising perspectives beyond high-energy physics, for example in real-time monitoring of the proton and ion beams used in cancer therapy.
In order to study the very rare kaon decay K+→ π+νν, the NA62 collaboration faced a similar timing challenge in the late 2010s. At the time, pixel detectors, mainly developed for experiments at the LHC, were only recording the position of particles, their time being given by the proton bunch crossing (50–25 ns). New R&D was started to face the challenge of integrating timing capabilities into every pixel (of which there are more than one thousand per cm2). Within a few years, the “TDCPix” chip was designed (see “Pixel timekeeper” image), achieving a hit time resolution of 130 ps and starting a new field of 4D tracking (measuring particle trajectories in space and time). The price to pay for this performance was a significant increase in the power density absorbed by the pixel, exceeding 2W/cm2. Absorbing this power required developing an innovative cooling technology: a 200 μm-thin silicon plate integrating a dense microfluidic cooling circuit. These two innovations led to the GigaTracker beam spectrometer (see “Fourth dimension” figure) – the first 4D tracking detector in high-energy physics, which has been in operation since 2015.
With the GigaTracker in hand, the NA62 collaboration achieved the main goal of measuring the K → πνν decay, and was able to put neutrino tagging to the test. The facility’s high-intensity kaon beam also serves as a neutrino source, since the kaons predominantly decay as K+→ μ+ν. Due to the intensity of the neutrino beam and its mean energy of 40 GeV, a non-negligible number of neutrinos interact in the experiment’s electromagnetic calorimeter, a 20-tonne volume of liquid krypton. The analysis of data collected in 2022 revealed one neutrino interaction candidate that could be matched to a detected parent decay. The neutrino’s energy was estimated to be 52 GeV, with a record relative precision of 0.3%. For reference, with a few exceptions (such as pion and kaon decays at rest), neutrino energies from conventional neutrino beams are known with an uncertainty of at least 10%, and not event-by-event.
NA62’s proof-of-concept for neutrino tagging, combined with the broader advance of fast-timing detectors, have together made it possible to revisit the original TNF idea. Developed in parallel with the first tagged-neutrino analysis by NA62, the NuTag collaboration investigated the conditions under which a tagged beam would enable measurements inaccessible with conventional neutrino beams. These efforts have led to the proposed nuSCOPE facility at CERN, which emerged within CERN’s Physics Beyond Colliders study group by combining the tagged-beam concept from NuTag with the slow-extraction-driven monitored neutrino beam pioneered by the ENUBET collaboration. Rather than using a pulsed magnetic horn, the ENUBET setup relies on slow extraction from the SPS and lines the decay tunnel with particle detectors that identify the charged leptons produced with neutrinos, constraining the flux at the percent level.
Legacy measurements
The idea of nuSCOPE echoes that of TNF (see “Beam to neutrino” figure). The first step is to direct a slow-extracted proton beam from the SPS onto a target to produce secondary pions and kaons that are then momentum-selected, using a series of dipoles and quadrupoles, to form an 8.5 GeV meson beam with a narrow momentum range. The mesons then traverse a set of ultra-fast detectors before decaying to predominantly muons and neutrinos. The muons reach a second set of fast detectors, whilst a few neutrinos interact in a dedicated detector 25 metres downstream. With sufficient timing and spatial resolution, each neutrino interaction can be associated with a measured individual meson decay. For the first time, the energy of the incoming neutrino would be known at the sub-percent level on an event-by-event basis. Measurements of neutrino cross sections, currently the dominant source of systematic uncertainty projected for DUNE and Hyper-Kamiokande, may then reach an accuracy of about 1%. Such datasets could serve as reference, “legacy” measurements for neutrino physics for decades to come.
The implications extend well beyond standard oscillation physics. Short-baseline oscillations induced by sterile neutrinos, for instance, could produce rapid patterns that would get washed out by energy smearing in conventional beams. The facility would also deliver intense, well-characterised muon and pion beams, opening additional avenues for rare process searches and precision measurements. Looking further ahead, one can even imagine how such techniques might reshape future long-baseline experiments. Depending on what DUNE, Hyper-Kamiokande and the reactor-based JUNO experiment in China will discover, the next leap in precision may not come just from higher intensities, but from beams whose properties are known with exquisite accuracy.
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