Astrophysical gravitational waves have revolutionised astronomy; the eventual detection of cosmological gravitons promises to open an otherwise inaccessible window into the universe’s earliest moments. Such a discovery would offer profound insights into the hidden corners of the early universe and physics beyond the Standard Model. Relic Gravitons, by Massimo Giovannini of INFN Milan Bicocca, offers a timely and authoritative guide to the most exciting frontiers in modern cosmology and particle physics.
Giovannini is an esteemed scholar and household name in the fields of theoretical cosmology and early-universe physics. He has written influential research papers, reviews and books on cosmology, providing detailed discussions on several aspects of the early universe. He also authored 2008’s A Primer on the Physics of the Cosmic Microwave Background – a book most cosmologists are very familiar with.
In Relic Gravitons, Giovannini provides a comprehensive exploration of recent developments in the field, striking a remarkable balance between clarity, physical intuition and rigorous mathematical formalism. As such, it serves as an excellent reference – equally valuable for both junior researchers and seasoned experts seeking depth and insight into theoretical cosmology and particle physics.
Relic Gravitons opens with an overview of cosmological gravitons, offering a broad perspective on gravitational waves across different scales and cosmological epochs, while drawing parallels with the electromagnetic spectrum. This graceful introduction sets the stage for a well-contextualised and structured discussion.
Gravitational rainbow
Relic gravitational waves from the early universe span 30 orders of magnitude, from attohertz to gigahertz. Their wavelengths are constrained from above by the Hubble radius, setting a lower frequency bound of 10–18 Hz. At the lowest frequencies, measurements of the cosmic microwave background (CMB) provide the most sensitive probe of gravitational waves. In the nanohertz range, pulsar timing arrays serve as powerful astrophysical detectors. At intermediate frequencies, laser and atomic interferometers are actively probing the spectrum. At higher frequencies, only wide-band interferometers such as LIGO and Virgo currently operate, primarily within the audio band spanning from a few hertz to several kilohertz.
The theoretical foundation begins with a clear and accessible introduction to tensor modes in flat spacetime, followed by spherical harmonics and polarisations. With these basics in place, tensor modes in curved spacetime are also explored, before progressing to effective action, the quantum mechanics of relic gravitons and effective energy density. This structured progression builds a solid framework for phenomenological applications.
The second part of the book is about the signals of the concordance paradigm, which includes discussions of Sakharov oscillations, short, intermediate and long wavelengths, before entering technical interludes in the next section. Here, Giovannini emphasises that the evolution of the comoving Hubble radius is uncertain, spectral energy density and other observables require approximate methods. The chapter expands to include conventional results using the Wentzel–Kramers–Brillouin approach, which is particularly useful when early-universe dynamics deviate from standard inflation.
Phenomenological implications are discussed in the final section, starting with the low-frequency branch that covers the analysis of the phenomenological implications in the lowest-frequency domain. Giovannini then examines the intermediate and high-frequency ranges. The concordance paradigm suggests that large-scale inhomogeneities originate from quantum mechanics, where traveling waves transform into standing waves. The penultimate chapter addresses the hot topic of the “quantumness” of relic gravitons, before diving into the conclusion. The book finishes with five appendices covering all sorts of useful topics, from notation to basic related topics in general relativity and cosmic perturbations.
Relic Gravitons is a must-read for anyone intrigued by the gravitational-wave background and its unparalleled potential to unveil new physics. It is an invaluable resource for those interested in gravitational waves and the unique potential to explore the unknown parts of particle physics and cosmology.
The 31st Quark Matter conference took place from 6 to 12 April at Goethe University in Frankfurt, Germany. This edition of the world’s flagship conference for ultra-relativistic heavy-ion physics was the best attended in the series’ history, with more than 1000 participants.
A host of experimental measurements and theoretical calculations targeted fundamental questions in many-body QCD. These included the search for a critical point along the QCD phase diagram, the extraction of the properties of the deconfined quark–gluon plasma (QGP) medium created in heavy-ion collisions, and the search for signatures of the formation of this deconfined medium in smaller collision systems.
Probing thermalisation
New results highlighted the ability of the strong force to thermalise the out-of-equilibrium QCD matter produced during the collisions. Thermalisation can be probed by taking advantage of spatial anisotropies in the initial collision geometry which, due to the rapid onset of strong interactions at early times, result in pressure gradients across the system. These pressure gradients in turn translate into a momentum-space anisotropy of produced particles in the bulk, which can be experimentally measured by taking a Fourier transform of the azimuthal distribution of final-state particles with respect to a reference event axis.
An area of active experimental and theoretical interest is to quantify the degree to which heavy quarks, such as charm and beauty, participate in this collective behaviour, which informs on the diffusion properties of the medium. The ALICE collaboration presented the first measurement of the second-order coefficient of the momentum anisotropy of charm baryons in Pb–Pb collisions, showing significant collective behaviour and suggesting that charm quarks undergo some degree of thermalisation. This collective behaviour appears to be stronger in charm baryons than charm mesons, following similar observations for light flavour.
A host of measurements and calculations targeted fundamental questions in many-body QCD
Due to the nature of thermalisation and the long hydrodynamic phase of the medium in Pb–Pb collisions, signatures of the microscopic dynamics giving rise to the thermalisation are often washed out in bulk observables. However, local excitations of the hydrodynamic medium, caused by the propagation of a high-energy jet through the QGP, can offer a window into such dynamics. Due to coupling to the coloured medium, the jet loses energy to the QGP, which in turn re-excites the thermalised medium. These excited states quickly decay and dissipate, and the local perturbation can partially thermalise. This results in a correlated response of the medium in the direction of the propagating jet, the distribution of which allows measurement of the thermalisation properties of the medium in a more controlled manner.
In this direction, the CMS collaboration presented the first measurement of an event-wise two-point energy–energy correlator, for events containing a Z boson, in both pp and Pb–Pb collisions. The two-point correlator represents the energy-weighted cross section of the angle between particle pairs in the event and can separate out QCD effects at different scales, as these populate different regions in angular phase space. In particular, the correlated response of the medium is expected to appear at large angles in the correlator in Pb–Pb collisions.
The use of a colourless Z boson, which does not interact in the QGP, allows CMS to compare events with similar initial virtuality scales in pp and Pb–Pb collisions, without incurring biases due to energy loss in the QCD probes. The collaboration showed modifications in the two-point correlator at large angles, from pp to Pb–Pb collisions, alluding to a possible signature of the correlated response of the medium to the traversing jets. Such measurements can help guide models into capturing the relevant physical processes underpinning the diffusion of colour information in the medium.
Looking to the future
The next addition of this conference series will take place in 2027 in Jeju, South Korea, and the new results presented there should notably contain the latest complement of results from the upgraded Run 3 detectors at the LHC and the newly commissioned sPHENIX detector at RHIC. New collision systems like O–O at the LHC will help shed light on many of the properties of the QGP, including its thermalisation, by varying the lifetime of the pre-equilibrium and hydrodynamic phases in the collision evolution.
On 16 January, physicists and statisticians met in the CERN Council Chamber to celebrate 25 years of the PhyStat series of conferences, workshops and seminars, which bring together physicists, statisticians and scientists from related fields to discuss, develop and disseminate methods for statistical data analysis and machine learning.
The special symposium heard from the founder and primary organiser of the PhyStat series Louis Lyons (Imperial College London and University of Oxford), who together with Fred James and Yves Perrin initiated the movement with the “Workshop on Confidence Limits” in January 2000. According to Lyons, the series was to bring together physicists and statisticians, a philosophy that has been followed and extended throughout the 22 PhyStat workshops and conferences, as well as numerous seminars and “informal reviews”. Speakers called attention to recognition from the Royal Statistical Society’s pictorial timeline of statistics, starting with the use of averages by Hippias of Elis in 450 BC and culminating with the 2012 discovery of the Higgs boson with 5σ significance.
Lyons and Bob Cousins (UCLA) offered their views on the evolution of statistical practice in high-energy physics, starting in the 1960s bubble-chamber era, strongly influenced by the 1971 book Statistical Methods in Experimental Physics by W T Eadie et al., its 2006 second edition by symposium participant Fred James (CERN), as well as Statistics for Nuclear and Particle Physics (1985) by Louis Lyons – reportedly the most stolen book from the CERN library. Both Lyons and Cousins noted the interest of the PhyStat community not only in practical solutions to concrete problems but also in foundational questions in statistics, with the focus on frequentist methods setting high-energy physics somewhat apart from the Bayesian approach more widely used in astrophysics.
Giving his view of the PhyStat era, ATLAS physicist and director of the University of Wisconsin Data Science Institute Kyle Cranmer emphasised the enormous impact that PhyStat has had on the field, noting important milestones such as the ability to publish full likelihood models through the statistical package RooStats, the treatment of systematic uncertainties with profile-likelihood ratio analyses, methods for combining analyses, and the reuse of published analyses to place constraints on new physics models. In regards to the next 25 years, Cranmer predicted the increasing use of methods that have emerged from PhyStat, such as simulation-based inference, and pointed out that artificial intelligence (the elephant in the room) could drastically alter how we use statistics.
Statistician Mikael Kuusela (CMU) noted that Phystat workshops have provided important two-way communication between the physics and statistics communities, citing simulation-based inference as an example where many key ideas were first developed in physics and later adopted by statisticians. In his view, the use of statistics in particle physics has emerged as “phystatistics”, a proper subfield with distinct problems and methods.
Another important feature of the PhyStat movement has been to encourage active participation and leadership by younger members of the community.With its 25th anniversary, the torch is now passed from Louis Lyons to Olaf Behnke (DESY), Lydia Brenner (NIKHEF) and a younger team, who will guide Phystat into the next 25 years and beyond.
Since 1966 the Rencontres de Moriond has been one of the most important conferences for theoretical and experimental particle physicists. The Electroweak Interactions and Unified Theories session of the 59th edition attracted about 150 participants to La Thuile, Italy, from 23 to 30 March, to discuss electroweak, Higgs-boson, top-quark, flavour, neutrino and dark-matter physics, and the field’s links to astrophysics and cosmology.
Particle physics today benefits from a wealth of high-quality data at the same time as powerful new ideas are boosting the accuracy of theoretical predictions. These are particularly important while the international community discusses future projects, basing projections on current results and technology. The conference heard how theoretical investigations of specific models and “catch all” effective field theories are being sharpened to constrain a broader spectrum of possible extensions of the Standard Model. Theoretical parametric uncertainties are being greatly reduced by collider precision measurements and lattice QCD. Perturbative calculations of short-distance amplitudes are reaching to percent-level precision, while hadronic long-distance effects are being investigated both in B-, D- and K-meson decays, as well as in the modelling of collider events.
Comprehensive searches
Throughout Moriond 2025 we heard how a broad spectrum of experiments at the LHC, B factories, neutrino facilities, and astrophysical and cosmological observatories are planning upgrades to search for new physics at both low- and high-energy scales. Several fields promise qualitative progress in understanding nature in the coming years. Neutrino experiments will measure the neutrino mass hierarchy and CP violation in the neutrino sector. Flavour experiments will exclude or confirm flavour anomalies. Searches for QCD axions and axion-like particles will seek hints to the solution of the strong CP problem and possible dark-matter candidates.
The Standard Model has so far been confirmed to be the theory that describes physics at the electroweak scale (up to a few hundred GeV) to a remarkable level of precision. All the particles predicted by the theory have been discovered, and the consistency of the theory has been proven with high precision, including all calculable quantum effects. No direct evidence of new physics has been found so far. Still, big open questions remain that the Standard Model cannot answer, from understanding the origin of neutrino masses and their hierarchy, to identifying the origin and nature of dark matter and dark energy, and explaining the dynamics behind the baryon asymmetry of the universe.
Several fields promise qualitative progress in understanding nature in the coming years
The discovery of the Higgs boson has been crucial to confirming the Standard Model as the theory of particle physics at the electroweak scale, but it does not explain why the scalar Brout–Englert–Higgs (BEH) potential takes the form of a Mexican hat, why the electroweak scale is set by a Higgs vacuum expectation value of 246 GeV, or what the nature of the Yukawa force is that results in the bizarre hierarchy of masses coupling the BEH field to quarks and leptons. Gravity is also not a component of the Standard Model, and a unified theory escapes us.
At the LHC today, the ATLAS and CMS collaborations are delivering Run 1 and 2 results with beyond-expectation accuracies on Higgs-boson properties and electroweak precision measurements. Projections for the high-luminosity phase of the LHC are being updated and Run 3 analyses are in full swing. The LHCb collaboration presented another milestone in flavour physics for the first time at Moriond 2025: the first observation of CP violation in baryon decays. Its rebuilt Run 3 detector with triggerless readout and full software trigger reported its first results at this conference.
Several talks presented scenarios of new physics that could be revealed in today’s data given theoretical guidance of sufficient accuracy. These included models with light weakly interacting particles, vector-like fermions and additional scalar particles. Other talks discussed how revisiting established quantum properties such as entanglement with fresh eyes could offer unexplored avenues to new theoretical paradigms and overlooked new-physics effects.
In the Standard Model (SM), W and Z bosons acquire mass and longitudinal polarisation through electroweak (EW) symmetry breaking, where the Brout–Englert–Higgs mechanism transforms Goldstone bosons into their longitudinal components. One of the most powerful ways to probe this mechanism is through vector-boson scattering (VBS), a rare process represented in figure 1, where two vector bosons scatter off each other. At high (TeV-scale) energies, interactions involving longitudinally polarised W and Z bosons provide a stringent test of the SM. Without the Higgs boson’s couplings to these polarisation states, their interaction rates would grow uncontrollably with energy, eventually violating unitarity, indicating a complete breakdown of the SM.
Measuring the polarisation of same electric charge (same sign) W-boson pairs in VBS directly tests the predicted EW interactions at high energies through precision measurements. Furthermore, beyond-the-SM scenarios predict modifications to VBS, some affecting specific polarisation states, rendering such measurements valuable avenues for uncovering new physics.
Using the full proton–proton collision dataset from LHC Run 2 (2015–2018, 140 fb–1 at 13 TeV), the ATLAS collaboration recently published the first evidence for longitudinally polarised W bosons in the electroweak production of same-sign W-boson pairs in final states including two same-sign leptons (electrons or muons) and missing transverse momentum, along with two jets (EW W±W±jj). This process is categorised by the polarisation states of the W bosons: fully longitudinal (WL±WL±jj), mixed (WL±WT±jj), and fully transverse (WT±WT±jj). Measuring the polarisation states is particularly challenging due to the rarity of the VBS events, the presence of two undetected neutrinos, and the absence of a single kinematic variable that efficiently distinguishes between polarisation states. To overcome this, deep neural networks (DNNs) were trained to exploit the complex correlations between event kinematic variables that characterise different polarisations. This approach enabled the separation of the fully longitudinal WL±WL±jj from the combined WT±W±jj (WL±WT±jj plus WT±WT±jj) processes as well as the combined WL±W±jj (WL±WL±jj plus WL±WT±jj) from the purely transverse WT±WT±jj contribution.
To measure the production of WL±WL±jj and WL±W±jj processes, a first DNN (inclusive DNN) was trained to distinguish EW W±W±jj events from background processes. Variables such as the invariant mass of the two highest-energy jets provide strong discrimination for this classification. In addition, two independent DNNs (signal DNNs) were trained to extract polarisation information, separating either WL±WL±jj from WT±W±jj or WL±W±jj from WT±WT±jj, respectively. Angular variables, such as the azimuthal angle difference between the leading leptons and the pseudorapidity difference between the leading and subleading jets, are particularly sensitive to the scattering angles of the W bosons, enhancing the separation power of the signal DNNs. Each DNN is trained using up to 20 kinematic variables, leveraging correlations among them to improve sensitivity.
The signal DNN distributions, within each inclusive DNN region, were used to extract the WL±WL±jj and WL±W±jj polarisation fractions through two independent maximum-likelihood fits. The excellent separation between the WL±W±jj and WT±WT±jj processes can be seen in figure 2 for the WL±W±jj fit, achieving better separation for higher scores of the signal DNN, represented in the x-axis. An observed (expected) significance of 3.3 (4.0) standard deviations was obtained for WL±W±jj, providing the first evidence of same-sign WW production with at least one of the W bosons longitudinally polarised. No significant excess of events consistent with WL±WL±jj production was observed, leading to the most stringent 95% confidence-level upper limits to date on the WL±WL±jj cross section: 0.45 (0.70) fb observed (expected).
There is still much to understand about the electroweak sector of the Standard Model, and the measurement presented in this article remains limited by the size of the available data sample. The techniques developed in this analysis open new avenues for studying W- and Z-boson polarisation in VBS processes during the LHC Run 3 and beyond.
In 1989, Rocky Kolb and Mike Turner published The Early Universe – a seminal book that offered a comprehensive introduction to the then-nascent field of particle cosmology, laying the groundwork for a generation of physicists to explore the connections between the smallest and largest scales of the universe. Since then, the interfaces between particle physics, astrophysics and cosmology have expanded enormously, fuelled by an avalanche of new data from ground-based and space-borne observatories.
In Particle Cosmology and Astrophysics, Dan Hooper follows in their footsteps, providing a much-needed update that captures the rapid developments of the past three decades. Hooper, now a professor at the University of Wisconsin–Madison, addresses the growing need for a text that introduces the fundamental concepts and synthesises the vast array of recent discoveries that have shaped our current understanding of the universe.
Hooper’s textbook opens with 75 pages of “preliminaries”, covering general relativity, cosmology, the Standard Model of particle physics, thermodynamics and high-energy processes in astrophysics. Each of these disciplines is typically introduced in a full semester of dedicated study, supported by comprehensive texts. For example, students seeking a deeper understanding of high-energy phenomena are likely to benefit from consulting Longair’s High Energy Astrophysics or Sigl’s Astroparticle Physics. Similarly, those wishing to advance their knowledge in particle physics will find that more detailed treatments are available in Griffiths’ Introduction to Elementary Particles or Peskin and Schroeder’s An Introduction to Quantum Field Theory, to mention just a few textbooks recommended by the author.
A much-needed update that captures the rapid developments of the past three decades
By distilling these complex subjects into just enough foundational content, Hooper makes the field accessible to those who have been exposed to only a fraction of the standard coursework. His approach provides an essential stepping stone, enabling students to embark on research in particle cosmology and astrophysics with a well calibrated introduction while still encouraging further study through more specialised texts.
Part II, “Cosmology”, follows a similarly pragmatic approach, providing an updated treatment that parallels Kolb and Turner while incorporating a range of topics that have, in the intervening years, become central to modern cosmology. The text now covers areas such as cosmic microwave background (CMB) anisotropies, the evidence for dark matter and its potential particle candidates, the inflationary paradigm, and the evidence and possible nature of dark energy.
Hooper doesn’t shy away from complex subjects, even when they resist simple expositions. The discussion on CMB anisotropies serves as a case in point: anyone who has attempted to condense this complex topic into a few graduate lectures is aware of the challenge in maintaining both depth and clarity. Instead of attempting an exhaustive technical introduction, Hooper offers a qualitative description of the evolution of density perturbations and how one extracts cosmological parameters from CMB observations. This approach, while not substituting for the comprehensive analysis found in texts such as Dodelson’s Modern Cosmology or Baumann’s Cosmology, provides students with a valuable overview that successfully charts the broad landscape of modern cosmology and illustrates the interconnectedness of its many subdisciplines.
Part III, “Particle Astrophysics”, contains a selection of topics that largely reflect the scientific interests of the author, a renowned expert in the field of dark matter. Some colleagues might raise an eyebrow at the book devoting 10 pages each to entire fields such as cosmic rays, gamma rays and neutrino astrophysics, and 50 pages to dark-matter candidates and searches. Others might argue that a book titled Particle Cosmology and Astrophysics is incomplete without detailing the experimental techniques behind the extraordinary advances witnessed in these fields and without at least a short introduction to the booming field of gravitational-wave astronomy. But the truth is that, in the author’s own words, particle cosmology and astrophysics have become “exceptionally multidisciplinary,” and it is impossible in a single textbook to do complete justice to domains that intersect nearly all branches of physics and astronomy. I would also contend that it is not only acceptable but indeed welcome for authors to align the content of their work with their own scientific interests, as this contributes to the diversity of textbooks and offers more choice to lecturers who wish to supplement a standard curriculum with innovative, interdisciplinary perspectives.
Ultimately, I recommend the book as a welcome addition to the literature and an excellent introductory textbook for graduate students and junior scientists entering the field.
Since the discovery of the electron and proton over 100 years ago, physicists have observed a “zoo” of different types of particles. While some of these particles have been fundamental, like neutrinos and muons, many are composite hadrons consisting of quarks bound together by the exchange of gluons. Studying the zoo of hadrons – their compositions, masses, lifetimes and decay modes – allows physicists to understand the details of the strong interaction, one of the fundamental forces of nature.
The Ω(2012) was discovered by the Belle Collaboration in 2018. The ALICE collaboration recently released an observation of a signal consistent with it with a significance of 15σ in proton–proton (pp) collisions at a centre-of-mass energy of 13 TeV. This is the first observation of the Ω(2012) by another experiment.
While the details of its internal structure are still up for debate, the Ω(2012) consists, at minimum, of three strange quarks bound together. It is a heavier, excited version of the ground-state Ω baryon discovered in 1964, which also contains three strange quarks. Multiple theoretical models predicted a spectrum of excited Ω baryons, with some calling for a state with a mass around 2 GeV. Following the discovery of the Ω(2012), theoretical work has attempted to describe its internal structure, with hypotheses including a simple three-quark baryon or a hadronic molecule.
Using a sample of a billion pp collisions, ALICE has measured the decay of Ω(2012) baryons to Ξ–K0S pairs. After traveling a few centimetres, these hadrons decay in turn, eventually producing a proton and four charged pions that are tracked by the ALICE detector.
ALICE’s measurements of the mass and width of the Ω(2012) are consistent with Belle’s, and superior precision on the mass. ALICE has also confirmed the rather narrow width of around 6 MeV, which indicates that the Ω(2012) is fairly long-lived for a particle that decays via the strong interaction. Belle and ALICE’s width measurements also lend support to the conclusion that the Ω(2012) has a spin-parity configuration of JP = 3/2–.
ALICE also measured the number of Ω(2012) decays to Ξ–K0S pairs. By comparing this to the total Ω(2012) yield based on statistical thermal model calculations, ALICE has estimated the absolute branching ratio for the Ω(2012) → Ξ–K0 decay. A branching ratio is the probability of decay to a given mode. The ALICE results indicate that Ω(2012) undergoes two-body (ΞK–) decays more than half the time, disfavouring models of the Ω(2012) structure that require large branching ratios for three-body decays.
The present ALICE results will help to improve the theoretical description of the structure of excited baryons. They can also serve as baseline measurements in searches for modifications of Ω-baryon properties in nucleus–nucleus collisions. In the future, Ω(2012) baryons may also serve as new probes to study the strangeness enhancement effect observed in proton–proton and nucleus–nucleus collisions.
Among the fundamental particles, tau leptons occupy a curious spot. They participate in the same sort of reactions as their lighter lepton cousins, electrons and muons, but their large mass means that they can also decay into a shower of pions and they interact more strongly with the Higgs boson. In many new-physics theories, Higgs-like particles – beyond that of the Standard Model – are introduced in order to explain the mass hierarchy or as possible portals to dark matter.
Because of their large mass, tau leptons are especially useful in searches for new physics. However, identifying taus is challenging, as in most cases they decay into a final state of one or more pions and an undetected neutrino. A crucial step in the identification of a tau lepton in the CMS experiment is the hadrons-plus-strips (HPS) algorithm. In the standard CMS reconstruction, a minimum momentum threshold of 20 GeV is imposed, such that the taus have enough momentum to make their decay products fall into narrow cones. However, this requirement reduces sensitivity to low-momentum taus. As a result, previous searches for a Higgs-like resonance φ decaying into two tau leptons required a φ-mass of more than 60 GeV.
The CMS experiment has now been able to extend the φ-mass range down to 20 GeV. To improve sensitivity to low-momentum tau decays, machine learning is used to determine a dynamic cone algorithm that expands the cone size as needed. The new algorithm, requiring one tau decaying into a muon and two neutrinos and one tau decaying into hadrons and a neutrino, is implemented in the CMS Scouting trigger system. Scouting extends CMS’s reach into previously inaccessible phase space by retaining only the most relevant information about the event, and thus facilitating much higher event rates.
The sensitivity of the new algorithm is so high that even the upsilon (Υ) meson, a bound state of the bottom quark and its antiquark, can be seen. Figure 1 shows the distribution of the mass of the visible decay products of tau (Mvis), in this case a muon from one tau lepton and either one or three pions from the other. A clear resonance structure is visible at Mvis = 6 GeV, in agreement with the expectation for the Υ meson. The peak is not at the actual mass of the Υ meson (9.46 GeV) due to the presence of neutrinos in the decay. While Υ→ττ decays have been observed at electron–positron colliders, this marks the first evidence at a hadron collider and serves as an important benchmark for the analysis.
Given the high sensitivity of the new algorithm, CMS performed a search for a possible resonance in the range between 20 and 60 GeV using the data recorded in the years 2022 and 2023, and set competitive exclusion limits (see figure 2). For the 2024 and 2025 data taking, the algorithm was further improved, enhancing the sensitivity even more.
CERN’s Large Hadron Collider continues to deliver surprises. While searching for additional Higgs bosons, the CMS collaboration may have instead uncovered evidence for the smallest composite particle yet observed in nature – a “quasi-bound” hadron made up of the most massive and shortest-lived fundamental particle known to science and its antimatter counterpart. The findings, which do not yet constitute a discovery claim and could also be susceptible to other explanations, were reported this week at the Rencontres de Moriond conference in the Italian Alps.
Almost all of the Standard Model’s shortcomings motivate the search for additional Higgs bosons. Their properties are usually assumed to be simple. Much as the 125 GeV Higgs boson discovered in 2012 appears to interact with each fundamental fermion with a strength proportional to the fermion’s mass, theories postulating additional Higgs bosons generally expect them to couple more strongly to heavier quarks. This puts the singularly massive top quark at centre stage. If an additional Higgs boson has a mass greater than about 345 GeV and can therefore decay to a top quark–antiquark pair, this should dominate the way it decays inside detectors. Hunting for bumps in the invariant mass spectrum of top–antitop pairs is therefore often considered to be the key experimental signature of additional Higgs bosons above the top–antitop production threshold.
The CMS experiment has observed just such a bump. Intriguingly, however, it is located at the lower limit of the search, right at the top-quark pair production threshold itself, leading CMS to also consider an alternative hypothesis long considered difficult to detect: a top–antitop quasi-bound state known as toponium (see “Threshold excess” figure).
The toponium hypothesis is very exciting as we previously did not expect to be able to see it at the LHC
“When we started the project, toponium was not even considered as a background to this search,” explains CMS physics coordinator Andreas Meyer (DESY). “In our analysis today we are only using a simplified model for toponium – just a generic spin-0 colour-singlet state with a pseudoscalar coupling to top quarks. The toponium hypothesis is very exciting as we previously did not expect to be able to see it at the LHC.”
Though other explanations can’t be ruled out, CMS finds the toponium hypothesis to be sufficient to explain the observed excess. The size of the excess is consistent with the latest theoretical estimate of the cross section to produce pseudoscalar toponium of around 6.4 pb.
“The cross section we obtain for our simplified hypothesis is 8.8 pb with an uncertainty of about 15%,” explains Meyer. “One can infer that this is significantly above five sigma.”
The smallest hadron
If confirmed, toponium would be the final example of quarkonium – a term for quark–antiquark states formed from heavy charm, bottom and perhaps top quarks. Charmonium (charm–anticharm) mesons were discovered at SLAC and Brookhaven National Laboratory in theNovember Revolution of 1974. Bottomonium (bottom–antibottom) mesons were discovered at Fermilab in 1977. These heavy quarks move relatively slowly compared to the speed of light, allowing the strong interaction to be modelled by a static potential as a function of the separation between them. When the quarks are far apart, the potential is proportional to their separation due to the self-interacting gluons forming an elongating flux tube, yielding a constant force of attraction. At close separations, the potential is due to the exchange of individual gluons and is Coulomb-like in form, and inversely proportional to separation, leading to an inverse-square force of attraction. This is the domain where compact quarkonium states are formed, in a near perfect QCD analogy to positronium, wherein an electron and a positron are bound by photon exchange. The Bohr radii of the ground states of charmonium and bottomonium are approximately 0.3 fm and 0.2 fm, and bottomonium is thought to be the smallest hadron yet discovered. Given its larger mass, toponium’s Bohr radius would be an order of magnitude smaller.
For a long time it was thought that toponium bound states were unlikely to be detected in hadron–hadron collisions. The top quark is the most massive and the shortest-lived of the known fundamental particles. It decays into a bottom quark and a real W boson in the time it takes light to travel just 0.1 fm, leaving little time for a hadron to form. Toponium would be unique among quarkonia in that its decay would be triggered by the weak decay of one of its constituent quarks rather than the annihilation of its constituent quarks into photons or gluons. Toponium is expected to decay at twice the rate of the top quark itself, with a width of approximately 3 GeV.
CMS first saw a 3.5 sigma excess in a 2019 search studying the mass range above 400 GeV, based on 35.9 fb−1 of proton–proton collisions at 13 TeV from 2016. Now armed with 138 fb–1 of collisions from 2016 to 2018, the collaboration extended the search down to the top–antitop production threshold at 345 GeV. Searches are complicated by the possibility that quantum interference between background and Higgs signal processes could generate an experimentally challenging peak–dip structure with a more or less pronounced bump.
“The signal reported by CMS, if confirmed, could be due either to a quasi-bound top–antitop meson, commonly called ‘toponium’, or possibly an elementary spin-zero boson such as appears in models with additional Higgs bosons, or conceivably even a combination of the two,” says theorist John Ellis of King’s College London. “The mass of the lowest-lying toponium state can be calculated quite accurately in QCD, and is expected to lie just below the nominal top–antitop threshold. However, this threshold is smeared out by the short lifetime of the top quark, as well as the mass resolution of an LHC detector, so toponium would appear spread out as a broad excess of events in the final states with leptons and jets that generally appear in top decays.”
Quantum numbers
An important task of the analysis is to investigate the quantum numbers of the signal. It could be a scalar particle, like the Higgs boson discovered in 2012, or a pseudoscalar particle – a different type of spin-0 object with odd rather than even parity. To measure its spin-parity, CMS studied the angular correlations of the top-quark-pair decay products, which retain information on the original quantum state. The decays bear all the experimental hallmarks of a pseudoscalar particle, consistent with toponium (see “Angular analysis” figure) or the pseudoscalar Higgs bosons common to many theories featuring extended Higgs sectors.
“The toponium state produced at the LHC would be a pseudoscalar boson, whose decays into these final states would have characteristic angular distributions, and the excess of events reported by CMS exhibits the angular correlations expected for such a pseudoscalar state,” explains Ellis. “Similar angular correlations would be expected in the decays of an elementary pseudoscalar boson, whereas scalar-boson decays would exhibit different angular correlations that are disfavoured by the CMS analysis.”
Whatever the true cause of the excess, the analyses reflect a vibrant programme of sensitive measurements at the LHC – and the possibility of a timely discovery
Two main challenges now stand in the way of definitively identifying the nature of the excess. The first is to improve the modelling of the creation of top-quark pairs at the LHC, including the creation of bound states at the threshold. The second challenge is to obtain consistency with the ATLAS experiment. “ATLAS had similar studies in the past but with a more conservative approach on the systematic uncertainties,” says ATLAS physics coordinator Fabio Cerutti (LBNL). “This included, for example, larger uncertainties related to parton showers and other top-modelling effects. To shed more light on the CMS observation, be it a new boson, a top quasi-bound state, or some limited understanding of the modelling of top–antitop production at threshold, further studies are needed on our side. We have several analysis teams working on that. We expect to have new results with improved modelling of the top-pair production at threshold and additional variables sensitive to both a new pseudo-scalar boson or a top quasi-bounded state very soon.”
Whatever the true cause of the excess, the analyses reflect a vibrant programme of sensitive measurements at the LHC – and the possibility of a timely discovery.
“Discovering toponium 50 years after the November Revolution would be an unanticipated and welcome golden anniversary present for its charmonium cousin that was discovered in 1974,” concludes Ellis. “The prospective observation and measurement of the vector state of toponium in e+e– collisions around 350 GeV have been studied in considerable theoretical detail, but there have been rather fewer studies of the observability of pseudoscalar toponium at the LHC. In addition to the angular correlations observed by CMS, the effective production cross section of the observed threshold effect is consistent with non-relativistic QCD calculations. More detailed calculations will be desirable for confirmation that another quarkonium family member has made its appearance, though the omens are promising.”
Just like particle physics, cosmology has its own standard model. It is also powerful in prediction, and brings new mysteries and profound implications. The first was the realisation in 1917 that a homogeneous and isotropic universe must be expanding. This led Einstein to modify his general theory of relativity by introducing a cosmological constant (Λ) to counteract gravity and achieve a static universe – an act he labelled his greatest blunder when Edwin Hubble provided observational proof of the universe’s expansion in 1929. Sixty-nine years later, Saul Perlmutter, Adam Riess and Brian Schmidt went further. Their observations of Type Ia supernovae (SN Ia) showed that the universe’s expansion was accelerating. Λ was revived as “dark energy”, now estimated to account for 68% of the total energy density of the universe.
On large scales the dominant motion of galaxies is the Hubble flow, the expansion of the fabric of space itself
The second dominant component of the model emerged not from theory but from 50 years of astrophysical sleuthing. From the “missing mass problem” in the Coma galaxy cluster in the 1930s to anomalous galaxy-rotation curves in the 1970s, evidence built up that additional gravitational heft was needed to explain the formation of the large-scale structure of galaxies that we observe today. The 1980s therefore saw the proposal of cold dark matter (CDM), now estimated to account for 27% of the energy density of the universe, and actively sought by diverse experiments across the globe and in space.
Dark energy and CDM supplement the remaining 5% of normal matter to form the ΛCDM model. ΛCDM is a remarkable six-parameter framework that models 13.8 billion years of cosmic evolution from quantum fluctuations during an initial phase of “inflation” – a hypothesised expansion of the universe by 26 to 30 orders of magnitude in roughly 10–36 seconds at the beginning of time. ΛCDM successfully models cosmic microwave background (CMB) anisotropies, the large-scale structure of the universe, and the redshifts and distances of SN Ia. It achieves this despite big open questions: the nature of dark matter, the nature of dark energy and the mechanism for inflation.
Cosmologists are eager to guide beyond-ΛCDM model-building efforts by testing its end-to-end predictions, and the model now seems to be failing the most important: predicting the expansion rate of the universe.
One of the main predictions of ΛCDM is the average energy density of the universe today. This determines its current expansion rate, otherwise known as the Hubble constant (H0). The most precise ΛCDM prediction comes from a fit to CMB data from ESA’s Planck satellite (operational 2009 to 2013), which yields H0 = 67.4 ± 0.5 km/s/Mpc. This can be tested against direct measurements in our local universe, revealing a surprising discrepancy (see “The Hubble tension” figure).
At sufficiently large distances, the dominant motion of galaxies is the Hubble flow – the expansion of the fabric of space itself. Directly measuring the expansion rate of the universe calls for fitting the increase in the recession velocity of galaxies deep within the Hubble flow as a function of distance. The gradient is H0.
Receding supernovae
While high-precision spectroscopy allows recession velocity to be precisely measured using the redshifts (z) of atomic spectra, it is more difficult to measure the distance to astrophysical objects. Geometrical methods such as parallax are imprecise at large distances, but “standard candles” with somewhat predictable luminosities such as cepheids and SN Ia allow distance to be inferred using the inverse square-law. Cepheids are pulsating post-main-sequence stars whose radius and observed luminosity oscillate over a period of one to 100 days, driven by the ionisation and recombination of helium in their outer layers, which increases opacity and traps heat; their period increases with their true luminosity. Before going supernova, SN Ia were white dwarf stars in binary systems; when the white dwarf accretes enough mass from its companion star, runaway carbon fusion produces a nearly standardised peak luminosity for a period of one to two weeks. Only SN Ia are deep enough in the Hubble flow to allow precise measurements of H0. When cepheids are observable in the same galaxies, they can be used to calibrate them.
At present, the main driver of the Hubble tension is a 2022 measurement of H0 by the SH0ES (Supernova H0 for the Equation of State) team led by Adam Riess. As the SN Ia luminosity is not known from first principles, SH0ES built a “distance ladder” to calibrate the luminosity of 42 SN Ia within 37 host galaxies. The SN Ia are calibrated against intermediate-distance cepheids, and the cepheids are calibrated against four nearby “geometric anchors” whose distance is known through a geometric method (see “Distance ladder” figure). The geometric anchors are: Milky Way parallaxes from ESA’s Gaia mission; detached eclipsing binaries in the large and small magellanic clouds (LMC and SMC); and the “megamaser” galaxy host NGC4258, where water molecules in the accretion disk of a supermassive black hole emit Doppler-shifting microwave maser photons.
The great strength of the SH0ES programme is its use of NASA and ESA’s Hubble Space Telescope (HST, 1990–) at all three rungs of the distance ladder, bypassing the need for cross-calibration between instruments. SN Ia can be calibrated out to 40 Mpc. As a result, in 2022 SH0ES used measurements of 300 or so high-z SN Ia deep within the Hubble flow to measure H0 = 73.04 ± 1.04 km/s/Mpc. This is in more than 5σ tension with Planck’s ΛCDM prediction of 67.4 ± 0.5 km/s/Mpc.
The value of H0 obtained from fitting Planck CMB data has been shown to be robust in two key ways.
First, Planck data can be bypassed by combining CMB data from NASA’s WMAP probe (2001–2010) with observations by ground-based telescopes. WMAP in combination with the Atacama Cosmology Telescope (ACT, 2007–2022) yields H0 = 67.6 ± 1.1 km/s/Mpc. WMAP in combination with the South Pole Telescope (SPT, 2007–) yields H0 = 68.2 ± 1.1 km/s/Mpc. Second, and more intriguingly, CMB data can be bypassed altogether.
In the early universe, Compton scattering between photons and electrons was so prevalent that the universe behaved as a plasma. Quantum fluctuations from the era of inflation propagated like sound waves until the era of recombination, when the universe had cooled sufficiently for CMB photons to escape the plasma when protons and electrons combined to form neutral atoms. This propagation of inflationary perturbations left a characteristic scale known as the sound horizon in both the acoustic peaks of the CMB and in “baryon acoustic oscillations” (BAOs) seen in the large-scale structure of galaxy surveys (see “Baryon acoustic oscillation” figure). The sound horizon is the distance travelled by sound waves in the primordial plasma.
While the SH0ES measurement relies on standard candles, ΛCDM predictions rely instead on using the sound horizon as a “standard ruler” against which to compare the apparent size of BAOs at different redshifts, and thereby deduce the expansion rate of the universe. Under ΛCDM, the only two free parameters entering the computation of the sound horizon are the baryon density and the dark-matter density. Planck evaluates both by studying the CMB, but they can be obtained independently of the CMB by combining BAO measurements of the dark-matter density with Big Bang nucleosynthesis (BBN) measurements of the baryon density (see “Sound horizon” figure). The latest measurement by the Dark Energy Spectroscopic Instrument in Arizona (DESI, 2021–) yields H0 = 68.53 ± 0.80 km/s/Mpc, in 3.4σ tension with SH0ES and fully independent of Planck.
The next few years will be crucial for understanding the Hubble tension, and may decide the fate of the ΛCDM model. ACT, SPT and the Simons Observatory in Chile (2024–) will release new CMB data. DESI, the Euclid space telescope (2023–) and the forthcoming LSST wide-field optical survey in Chile will release new galaxy surveys. “Standard siren” measurements from gravitational waves with electromagnetic counterparts may also contribute to the debate, although the original excitement has dampened with a lack of new events after GW170817. More accurate measurements of the age of the oldest objects may also provide an important new test. If H0 increases, the age of the universe decreases, and the SH0ES measurement favours less than 13.1 billion years at 2σ significance.
The SH0ES measurement is also being checked directly. A key approach is to test the three-step calibration by seeking alternative intermediate standard candles besides cepheids. One candidate is the peak-luminosity “tip” of the red giant branch (TRGB) caused by the sudden start of helium fusion in low-mass stars. The TRGB is bright enough to be seen in distant galaxies that host SN Ia, though at distances smaller than that of cepheids.
Settling the debate
In 2019 the Carnegie–Chicago Hubble Program (CCHP) led by Wendy Freedman and Barry Madore calibrated SN Ia using the TRGB within the LMC and NGC4258 to determine H0 = 69.8 ± 0.8 (stat) ± 1.7 (syst). An independent reanalysis including authors from the SH0ES collaboration later reported H0 = 71.5 ± 1.8 (stat + syst) km/s/Mpc. The difference in the results suggests that updated measurements with the James Webb Space Telescope (JWST) may settle the debate.
Launched into space on 25 December 2021, JWST is perfectly adapted to improve measurements of the expansion rate of the universe thanks to its improved capabilities in the near infrared band, where the impact of dust is reduced (see “Improved resolution” figure). Its four-times-better spatial resolution has already been used to re-observe a subsample of the 37 hosts galaxies home to the 42 SN Ia studied by SH0ES and the geometric anchor NGC4258.
So far, all observations suggest good agreement with the previous observations by HST. SH0ES used JWST observations to obtain up to a factor 2.5 reduction in the dispersion of the period-luminosity relation for cepheids with no indication of a bias in HST measurements. Most importantly, they were able to exclude the confusion of cepheids with other stars as being responsible for the Hubble tension at 8σ significance.
Meanwhile, the CCHP team provided new measurements based on three distance indicators: cepheids, the TRGB and a new “population based” method using the J-region of the asymptotic giant branch (JAGB) of carbon-rich stars, for which the magnitude of the mode of the luminosity function can serve as a distance indicator (see the last three rows of “The Hubble tension” figure).
The new CCHP results suggest that cepheids may show a bias compared to JAGB and TRGB, though this conclusion was rapidly challenged by SH0ES, who identified a missing source of uncertainty and argued that the size of the sample of SN Ia within hosts with primary distance indicators is too small to provide competitive constraints: they claim that sample variations of order 2.5 km/s/Mpc could explain why the JAGB and TRGB yield a lower value. Agreement may be reached when JWST has observed a larger sample of galaxies – across both teams, 19 of the 37 calibrated by SH0ES have been remeasured so far, plus the geometric anchor NGC 5468 (see “The usual suspects” figure).
At this stage, no single systematic error seems likely to fully explain the Hubble tension, and the problem is more severe than it appears. When calibrated, SN Ia and BAOs constrain not only H0, but the entire redshift range out to z ~ 1. This imposes strong constraints on any new physics introduced in the late universe. For example, recent DESI results suggest that the dynamics of dark energy at late times may not be exactly that of a cosmological constant, but the behaviour needed to reconcile Planck and SH0ES is strongly excluded.
Rather than focusing on the value of the expansion rate, most proposals now focus on altering the calibration of either SN Ia or BAOs. For example, an unknown systematic error could alter the luminosity of SN Ia in our local vicinity, but we have no indication that their magnitude changes with redshift, and this solution appears to be very constrained.
The most promising solution appears to be that some new physics may have altered the value of the sound horizon in the early universe. As the sound horizon is used to calibrate both the CMB and BAOs, reducing it by 10 Mpc could match the value of H0 favoured by SH0ES (see “Sound horizon” figure). This can be achieved either by increasing the redshift of recombination or the energy density in the pre-recombination universe, giving the sound waves less time to propagate.
The best motivated models invoke additional relativistic species in the early universe such as a sterile neutrino or a new type of “dark radiation”. Another intriguing possibility is that dark energy played a role in the pre-recombination universe, boosting the expansion rate at just the right time. The wide variety and high precision of the data make it hard to find a simple mechanism that is not strongly constrained or finely tuned, but existing models have some of the right features. Future data will be decisive in testing them.
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