The 21st International Conference on Strangeness in Quark Matter (SQM 2024) will focus on new experimental and theoretical developments on the role of strange and heavy-flavour quarks in high energy heavy-ion collisions and in astrophysical phenomena.
Scientific topics include:
Strangeness and heavy-quark production in nuclear collisions and hadronic interactions
Hadron resonances in the strongly-coupled partonic and hadronic medium
Bulk matter phenomena associated with strange and heavy quarks
To advance our understanding of gluonic saturated matter at the LHC, the ALICE collaboration has presented a new study using photon-induced interactions in ultra-peripheral collisions (UPCs). In this type of collision, one beam emits a very high energetic photon that strikes the other beam, giving rise to photon–proton, photon–nucleus and even photon–photon collisions.
While we know that the proton – and most of the visible matter of the universe – is made of quarks bound together by gluons, quantum chromodynamics (QCD)has not yet provided a complete understanding of the rich physics phenomena that occur in high-energy interactions involving hadrons. For example, it is not known how the distribution of gluons evolve at low values of Bjorken-x. The rapid increase in gluon density observed with decreasing x cannot continue forever as it would eventually violate unitarity. At some point “gluon saturation” must set in to curb this growth.
So far, it has been challenging to experimentally establish when saturation sets in. One can expect, however, that it should occur at lower energies for heavy nuclei than for protons. Thus, the ALICE Collaboration has studied the energy dependence of UPC processes for both protons and heavy nuclei. At the same time, other physics phenomena, such as gluon shadowing originating from multi-scattering processes, can exist with similar experimental signatures. The interplay between these phenomena is still an open problem in QCD.
ALICE has presented new results on J/ψ meson-production UPC, where the photon probes the whole nucleus. The new ALICE results, analysed using LHC Run 1 and Run 2 data, probe a wide range of photon-nucleus collision energies from around 10 GeV to 1000 GeV. These results confirm previous measurements by ALICE, obtained at lower energies, that indicated a strong nuclear suppression when such photon–nucleus data are compared to expectations from photon–proton interactions. The present analysis employs novel methods for extracting the energy dependence, providing new information to test theoretical models. The present data at high energies can be described by both saturation-based and gluon shadowing models. The coherent J/ψ meson production at low energy, in the anti-shadowing region, is not described by these models, nor can available models fully describe the energy dependence of this process over the explored energy range.
ALICE will continue to investigate these phenomena in LHC Runs 3 and 4, where high-precision measurements with larger data samples and upgraded detectors will provide more powerful tools to better understand gluonic saturated matter.
Charge-parity (CP) violation parameters in tree-dominated b → c c s quark transitions are a powerful probe of physics beyond the Standard Model (SM). When B0(s) and B0(s) mesons decay through these transitions to the same final-state particles, an interference between mixing and decay amplitudes occurs, making these processes particularly sensitive to CP violation.
In the SM, B0(s) – B0(s) mixing is possible because the flavour eigenstates are not the (physical) mass eigenstates: a neutral B meson, once produced, evolves as a quantum superposition of B0(s) and B0(s) states. Due to this time-dependent mixing amplitude, an interference between mixing and decay amplitudes can lead to an observable time-dependent CP asymmetry in the decay rates. It was through the observation of this phenomenon in the “golden mode” B0→ J/ψ K0s that, in 2001, the BaBar and Belle collaborations reported the first unequivocal evidence for CP violation in B decays, for which Kobayashi and Maskawa were awarded the 2008 Nobel Prize in Physics.
As the 3 × 3 Cabibbo–Kobayashi–Maskawa (CKM) matrix that describes quark mixing in the SM is expected to be unitary, it leads to relations among its complex elements. These can be represented as triangles in a complex plane, all of them with the same area (which is a measure of the amount of CP violation in the SM). The most famous of them, the so-called unitary triangle, has sides of roughly the same size and internal angles denoted as α, β and γ. Since individually none of the CKM parameters are predicted by theory, the search for new physics relies on over-constraining them by looking for any hint of internal inconsistency. For that, precision is the key.
LHCb has become a major actor in precision studies of CP violation
Having analysed the full proton–proton collision data set with 13 TeV, and adding it to previous measurements at 7 and 8 TeV, LHCb recently brought the CP-violating parameters in B0→ J/ψ K0sand in another golden channel, B0s→ J/ψ K+K–, to a new level of precision. These parameters (sin2β and φs, respectively) are predicted with high accuracy through global CKM fits and, given their clean experimental signatures, are paramount for new-physics searches. The measured time-dependent CP asymmetry of B0 and B0 decay rates is shown in figure 1 with the resulting amplitude proportional to sin2β. Similarly, the update of the B0s→ J/ψ K+K– analysis with the 13 TeV data resulted in the world’s most precise φs measurement. Both angles agree with SM expectations and with previous measurements.
These legacy results for sin2β and φs from the first LHC runs represent a new milestone in LHCb’s hunt for physics beyond the SM. Along with the world-leading determination of γ (with a current precision of less than four degrees), and the discovery of CP violation in charm in 2019, LHCb has fulfilled and exceeded its own goals of more than a decade ago, becoming the major actor in precision studies of CP violation. LHCb is taking data with a brand new detector at larger interaction rates than before, boosting the experimental sensitivity and tightening the grip around the Standard Model.
Since the discovery of the Higgs boson in 2012, its di-photon and four-lepton decays have played a crucial role in characterising its properties. Despite their small branching ratios, these decay channels are ideal for accurate measurements due to the excellent resolution and efficient identification of photons and leptons provided by the ATLAS detector.
The Higgs-boson mass (mH) is a free parameter of the Standard Model (SM) that must be determined experimentally. Its value governs the coupling strengths of the Higgs boson with the other SM particles. It also enters as logarithmic corrections to the SM predictions of the W-boson mass and effective weak mixing angle, whose precise measurements allow the electroweak model to be tested. Moreover, the Higgs mass determines the shape and energy evolution of the Brout–Englert–Higgs potential and thus the stability of the electroweak vacuum. A precise measurement of mH is therefore of paramount importance.
ATLAS has recently published a new result of the Higgs-boson mass in the H → γγ decay channel using proton–proton collision data from LHC Run 2 (2015–2018). The measurement requires a careful control of systematic uncertainties, primarily arising from the photon energy scale. The new analysis has achieved a substantial reduction by more than a factor of three of these uncertainties compared to the previous ATLAS result based on the 2015 and 2016 dataset. That improvement became possible after extensive efforts to refine the photon energy-scale calibration and associated uncertainties.
The calibration benefited from an improved understanding of the energy response across the longitudinal ATLAS electromagnetic calorimeter layers and of nonlinear electronics readout effects. A new correction was implemented in the extrapolation of the precisely measured electron-energy scale in Z → e+e– events to photons, to account for differences in the lateral shower development between electrons and photons. These improvements reduced the systematic uncertainty in the mass measurement by about 40%. Moreover, the extrapolation of the electron energy scale from Z → e+e– events to photons originating from the Higgs boson was further refined, and transverse-momentum dependent effects were corrected. Taken together, the improvements allowed ATLAS to measure the Higgs-boson mass in the di-photon channel with a precision of 1.1 per mille.
The new di-photon result was combined with the mH measurement in the H → ZZ*→ 4ℓ decay using the full Run 2 dataset, published by ATLAS in 2022, and with the corresponding Run 1 (2011–2012) measurements (see figure 1). The resulting combined Higgs-boson mass mH = 125.11 ± 0.11 GeV has a precision of 0.9 per mille and is dominated by statistical uncertainties that will further reduce with the Run 3 data.
The high level of readiness and excellent performance of the ATLAS detector also allowed first measurements of the fiducial Higgs-boson production cross-sections in the H → γγ and H → ZZ*→ 4ℓ decay channels using up to 31.4 fb–1 of data collected in 2022. Their extrapolation to full phase space and combination gives σ(pp → H) = 58.2 ± 8.7 pb, which agrees with the SM prediction of 59.9 ± 2.6 pb (see figure 2).
With the continuation of Run 3 data taking, the precision of the 13.6 TeV cross-section measurements will improve and the combination with the Run 2 data will allow the exploration of Higgs-boson properties with growing sensitivity.
Despite its exceptional success, we know that the standard model (SM) is incomplete. To date, the LHC has not yet found clear indications of physics beyond the SM (BSM), which might mean that the BSM energy scale is above what can be directly probed at the LHC. An alternative way to probe BSM physics is through searches of off-shell effects, which can be done using the effective field theory framework (EFT). By treating the SM Lagrangian as the lowest order term in a perturbative expansion, EFT allows us to include higher-dimension operators in the Lagrangian, while respecting the experimentally verified SM symmetries.
Operators
The CMS collaboration recently performed a search for BSM physics using EFT, analysing data containing top quarks with additional final-state leptons. The top quark is of particular interest because of its large mass, resulting in a Higgs–Yukawa coupling of order unity. Many BSM models connect the top-quark mass to large couplings to new physics. In the context of top quark EFT, there are 59 total operators at dimension six, controlled by the so-called Wilson coefficients, 26 of which produce final-state leptons. These coefficients enter the model as corrections to the SM matrix element, with a first term corresponding to the interference between the SM and BSM contributions, and a second term reflecting pure BSM effects.
The analysis was performed on the Run 2 proton–proton collisions sample, corresponding to an integrated luminosity of 138 fb–1. It obtained limits on those 26 dimension-six coefficients, simulated at detector level with leading order precision (plus an additional parton when possible), exploiting six final-state signals, with different numbers of top quarks and leptons: ttH, ttℓν, ttℓℓ, tℓℓq, tHq and tttt. The analysis splits the data into 43 discrete categories, based primarily on lepton multiplicity, total lepton charge, and total jet or b-quark jet multiplicities. The events are analysed as differential distributions in the kinematics of the final-state leptons and jets.
A statistical analysis is performed using a profiled likelihood to extract the 68% and 95% confidence intervals for all 26 Wilson coefficients by varying one of them while profiling the other 25. All the coefficients are compatible with zero (i.e. in agreement with the SM) at the 95% confidence level. For many of them, these results are the most competitive to date, even when compared to analyses that fit only one or two coefficients. Figure 1 shows how the 95% confidence intervals (2σ limit) translate into upper limits on the energy scale of the probed BSM interaction.
The CMS collaboration will continue to refine these measurements by expanding upon the final-state observables and leveraging the Run 3 data sample. With the HL-LHC quickly approaching, the future of BSM physics searches is full of potential.
The GBAR experiment at CERN has joined the select club of experiments that have succeeded in synthesising antihydrogen atoms. Located at the Antiproton Decelerator (AD), GBAR aims to test Einstein’s equivalence principle by measuring the acceleration of an antihydrogen atom in Earth’s gravitational field and comparing it with that of normal hydrogen.
Producing and slowing down an antiatom enough to see it in free fall is no mean feat. To achieve this, the AD’s 5.3 MeV antiprotons are decelerated and cooled in the ELENA ring and a packet of a few million 100 keV antiprotons is sent to GBAR every two minutes. A pulsed drift tube further decelerates the packet to an adjustable energy of a few keV. In parallel, a linear particle accelerator sends 9 MeV electrons onto a tungsten target, producing positrons, which are accumulated in a series of electromagnetic traps. Just before the antiproton packet arrives, the positrons are sent to a layer of nanoporous silica, from which about one in five positrons emerges as a positronium atom. When the antiproton packet crosses the resulting cloud of positronium atoms, a charge exchange can take place, with the positronium giving up its positron to the antiproton, forming antihydrogen.
At the end of 2022, during an operation that lasted several days, the GBAR collaboration detected some 20 antihydrogen atoms produced in this way, validating the “in-flight” production method for the first time. The collaboration will now improve the production of antihydrogen atoms to enable precision measurements, for example, of its spectroscopic properties.
The first antihydrogen atoms were produced at CERN’s LEAR facility in 1995, but at an energy too high for any measurement to be made. Following this early success, CERN’s Antiproton Accumulator (used for the discovery of the W and Z bosons in 1983) was repurposed as a decelerator, becoming the AD, which is unique worldwide in providing low-energy antiprotons to antimatter experiments. After the demonstration of storing antiprotons by the ATRAP and ATHENA experiments, ALPHA, a successor of ATHENA, was the first experiment to merge trapped antiprotons and positrons and to trap the resulting antihydrogen atoms. Since then, ATRAP and ASACUSA have also achieved these two milestones, and AEgIS has produced pulses of antiatoms. GBAR now joins this elite club, having produced 6 keV antihydrogen atoms in-flight.
GBAR is also not alone in its aim of testing Einstein’s equivalence principle with atomic antimatter. ALPHA and AEgIS are also working towards this goal using complementary approaches.
Within astronomy and cosmology, the idea that the universe is continuously expanding is a cornerstone of the standard cosmological model. For example, when measuring the distance of astronomical objects one often uses their redshift, which is induced by their velocity with respect to us due to the expansion. The expansion itself has, however, never been directly measured, i.e. no measurement exists that shows the increasing redshift with time of a single object. Although not far beyond the current capabilities of astrophysics, such a measurement is unlikely to be performed soon. Rather, evidence for it is based on correlations within populations of astrophysical objects. However, not all studies agree with this standard assumption.
One population study that supports the standard model concerns type 1A supernovae, specifically the observed correlation between their duration and distance. Such a correlation is predicted to be the result of time dilation induced by the higher velocity of more distant objects. Supporting this picture, gamma-ray bursts occurring at larger distances appear to, on average, last longer than those that occur nearby. However, similar studies of quasars thus far did not show any dependence of the length in their variability with their distance, thereby contradicting special relativity and leading to an array of alternative hypotheses.
Detailed studies
Quasars are active galaxies containing a supermassive blackhole surrounded by a relativistic accretion disk. Due to their brightness they can be observed with redshifts up to about z = 8, which, based on special relativity should show variabilities occurring √8 times slower than those that occur nearby. As previous studies did not observe such time dilation, alternative theories proposed included those that cast doubt on the extragalactic nature of quasars. A new, detailed study now removes the need for such theories.
These results do not provide hints of new physics but rather resolve one of the main problems with the standard cosmological model
In order to observe time dilation one requires a standard clock. Supernovae are ideal for this purpose because these explosions are all nearly identical, allowing their duration to be used to measure time dilation. For quasars the issue is more complicated as the variability of their brightness appears almost random. However, the variability can be modelled using a so-called dampened random walk (DRW), a random process combined with an exponential dampening component. This complex model does not allow the brightness of a quasar to be predicted, but contains a characteristic timescale in the exponent that should correlate to the redshift due to time dilation.
This idea has now been tested by Geraint Lewis and Brenden Brewer of the universities of Sydney and Auckland, respectively. The pair studied 190 quasars with redshifts up to z = 4, observed over a 20 year period by the Sloan Digital Sky Survey and PanSTARRS-1, and applied a Bayesian analysis to look for a correlation between the DRW parameters and their redshift. The data was found to match best a universe where the DRW parameters scale according to (1 + z)n with n = 1.28 ±0.29, thereby making it compatible with n = 1, the value expected by standard physics. This contradicts previous measurements, something the authors attribute to the smaller quasar sample used in previous studies. The complex nature of quasars and the large variability in their population requires long observations of a similar population to make the time dilation effect visible.
These new results, which were made possible due to the large amounts of data becoming available from large observatories, do not provide hints of new physics but rather resolve one of the main problems with the standard cosmological model.
At around 1 a.m. on 17 July, the LHC beams were dumped after only nine minutes in collision due to a radiofrequency interlock caused by an electrical perturbation. Approximately 300 milliseconds after the beams were cleanly dumped, several superconducting magnets lost their superconducting state, or quenched. Among them were the inner-triplet magnets located to the left of Point 8, which focus the beams for the LHCb experiment. While occasional quenches of some LHC magnets are to be expected, the large forces resulting from this particular event led to a breach of the vacuum helium pressure vessel, rapidly degrading the insulation vacuum and prompting a series of interventions with implications for the 2023 Run 3 schedule.
The leak occurred between the LHC’s cryogenic circuit, which contains the liquid helium, and the insulation vacuum that separates the cold magnet from the warm outer vessel (the cryostat) – a crucial barrier for preventing heat transfer from the surrounding LHC tunnel to the interior of the cryostat. As a result of the leak, the insulation vacuum filled with helium gas, cooling down the cryostat and causing condensation to form and freeze on the outside.
By 24 July the CERN teams had traced the leak to a crack in one of more than 2500 bellows that compensate for thermal expansion and contraction on the cryogenic distribution lines. Measuring just 1.6 mm long, it is thought to have been caused by a sudden increase in vacuum pressure when the magnet quench protection system (QPS) kicked in. Following the electrical perturbation, the QPS had dutifully triggered the quench heaters (which are designed to bring the whole magnet out of the superconducting state in a controlled and homogenous manner) of the magnets concerned, generating a heat wave according to expectations.
It is the first time that such a breachevent has occurred; the teamwork between many working groups, including safety, accelerator operations, vacuum, cryogenics, magnets, survey, beam instrumentation, machine protection, electrical quality assurance as well as material and mechanical engineering, made a quick assessment and action plan possible. On 25 July the affected bellow was removed. A new bellow was installed on 28 July, the affected modules were closed, and the insulation vacuum was pumped.
The electrical perturbation turned out to be caused by an uprooted tree falling on power lines in the nearby Swiss municipality of Morges. In early August, as the Courier went to press, the repairs were finished and the implications for Run physics were being assessed. The choice is between preparing the machine for a short-term proton–proton phase to account for some of the missed run time or sticking to the planned heavy-ion run at the end of the run year, since in 2022 there was no full heavy-ion run. The favoured scenario is to go with the latter and was presented to the LHC machine committee on 26 July.
The discovery of the W boson at CERN in 1983 can well be considered the birth of precision electroweak physics. Measurements of the W boson’s couplings and mass have become ever more precise, progressively weaving in knowledge of other particle properties through quantum corrections. Just over a decade ago, the combination of several Standard Model (SM) parameters with measurements of the W-boson mass led to a prediction of a relatively low Higgs-boson mass, of order 100 GeV, prior to its discovery. The discovery of the Higgs boson in 2012 with a mass of about 125 GeV was hailed as a triumph of the SM. Last year, however, an unexpectedly high value of the W-boson mass measured by the CDF experiment threw a spanner into the works. One might say the 40-year-old W boson encountered a midlife crisis.
The mass of the W boson, mW, is important because the SM predicts its value to high precision, in contrast with the masses of the fermions or the Higgs boson. The mass of each fermion is determined by the strength of its interaction with the Brout–Englert–Higgs field, but this strength is currently only known to an accuracy of approximately 10% at best; future measurements from the High-Luminosity LHC and a future e+e– collider are required to achieve percent-level accuracy. Meanwhile, mW is predicted with an accuracy better than 0.01%. At tree level, this mass depends only on the mass of the Z boson and the weak and electromagnetic couplings. The first measurements of mW by the UA1 and UA2 experiments at the SppS collider at CERN were in remarkable agreement with this prediction, within the large uncertainties. Further measurements at the Tevatron at Fermilab and the Large Electron Positron collider (LEP) at CERN achieved sufficient precision to probe the presence of higher-order electroweak corrections, such as from a loop containing top and bottom quarks.
Increasing sophistication
Measurements of mW at the four LEP experiments were performed in collisions producing two W bosons. Hadron colliders, by contrast, can produce a single W-boson resonance, simplifying the measurement when utilising the decay to an electron or muon and an associated neutrino. However, this simplification is countered by the complication of the breakup of the hadrons, along with multiple simultaneous hadron–hadron interactions. Measurements at the Tevatron and LHC have required increasing sophistication to model the production and decay of the W boson, as well as the final-state lepton’s interactions in the detectors. The average time between the available datasets and the resulting published measurement have increased from two years for the first CDF measurement in 1991 to more than 10 years for the most recent CDF measurement announced last year (CERN Courier May/June 2022 p9). The latter benefitted from a factor of four more W bosons than the previous measurement, but suffered from a higher number of additional simultaneous interactions. The challenge of modelling these interactions while also increasing the measurement precision required many years of detailed study. The end result, mW = 80433.5 ± 9.4 MeV, differs from the SM prediction of mW = 80357 ± 6 MeV by approximately seven standard deviations (see “Out of order” figure).
The SM calculation of mW includes corrections from single loops involving fermions or the Higgs boson, as well as from two-loop processes that also include gluons. The splitting of the W boson into a top- and bottom-quark loop produces the largest correction to the mass: for every 1 GeV increase in top-quark mass the predicted W mass increases by a little over 6 MeV. Measurements of the top-quark mass at the Tevatron and LHC have reached a precision of a few hundred MeV, thus contributing an uncertainty on mW of only a couple of MeV. The calculated mW depends only logarithmically on the Higgs-boson mass mH, and given the accuracy of the LHC mH measurements, it contributes negligibly to the uncertainty on mW. The tree-level dependence of mW on the Z-boson mass and on the electromagnetic coupling strength contribute an additional couple of MeV each to the uncertainty. The robust prediction of the SM allows an incisive test through mW measurements, and it would appear to fail in the face of the recent CDF measurement.
Since the release of the CDF result last year, physicists have held extensive and detailed discussions, with a recurring focus on the measurement’s compatibility with the SM prediction and with the measurements of other experiments. Further discussions and workshops have reviewed the suite of Tevatron and LHC measurements, hypothesising effects that could have led to a bias in one or more of the results. These potential effects are subtle, as fundamentally the W-boson signature is strikingly unique and simple: a single charged electron or muon with no observable particle balancing its momentum. Any source of bias would have to lie in a higher-order theoretical or experimental effect, and the analysts have studied and quantified these in great detail.
Progress
In the spring of this year ATLAS contributed an update to the story. The collaboration re-analysed its data from 2011 to apply a comprehensive statistical fit using a profile likelihood, as well as the latest global knowledge of parton distribution functions (PDFs) – which describe the momentum distribution functions of quarks and gluons inside the proton. The preliminary result (mW = 80360 ± 16 MeV) reduces the uncertainty and the central value of its previous result published in 2017, further increasing the tension between the ATLAS result and that of CDF.
Meanwhile, the Tevatron+LHC W-mass combination working group has carried out a detailed investigation of higher-order theoretical effects affecting hadron-collider measurements, and provided a combined mass value using the latest published measurement from each experiment and from LEP. These studies, due to be presented at the European Physical Society High-Energy Physics conference in Hamburg in late August, give a comprehensive and quantitative overview of W-boson mass measurements and their compatibilities. While no significant issues have been identified in the measurement procedures and results, the studies shed significant light on their details and differences.
LHC versus Tevatron
Two important aspects of the Tevatron and LHC measurements are the modelling of the momentum distribution of each parton in the colliding hadrons, and the angular distribution of the W boson’s decay products. The higher energy of the LHC increases the importance of the momentum distributions of gluons and of quarks from the second generation, though these can be constrained using the large samples of W and Z bosons. In addition, the combination of results from centrally produced W bosons at ATLAS with more forward W-boson production at LHCb reduces uncertainties from the PDFs. At the Tevatron, proton–antiproton collisions produced a large majority of W bosons via the valence up and down (anti)quarks inside the (anti)proton, and these are also constrained by measurements at the Tevatron. For the W-boson decay, the calculation is common to the LHC and the Tevatron, and precise measurements of the decay distributions by ATLAS are able to distinguish several calculations used in the experiments.
In any combination of measurements, the primary focus is on the uncertainty correlations. In the case of mW, many uncertainties are constrained in situ and are therefore uncorrelated. The most significant source of correlated uncertainty is the PDFs. In order to evaluate these correlations, the combination working group generated large samples of events and produced simplified models of the CDF, DØ and ATLAS detectors. Several sets of PDFs were studied to determine their compatibility with broader W- and Z-boson measurements at hadron colliders. For each of these sets the correlations and combined mW values were determined, opening a panorama view of the impact of PDFs on the measurement (see “Measuring up” figure).
The mass of the W boson is important because the SM predicts its value to high precision, in contrast with the masses of the fermions or the Higgs boson
The first conclusion from this study is that the compatibility of all PDF sets with W- and Z-boson measurements is generally low: the most compatible PDF set, CT18 from the CTEQ collaboration, gives a probability of only 1.5% that the suite of measurements are consistent with the predictions. Using this PDF set for the W-boson mass combination gives an even lower compatibility of 0.5%. When the CDF result is removed, the compatibility of the combined mW value is good (91%), and when comparing this “N-1” combined value to the CDF value for the CT18 set, the difference is 3.6σ. The results are considered unlikely to be compatible, though the possibility cannot be excluded in the absence of an identified bias. If the CDF measurement is removed, the combination yields a mass of mW = 80369.2 ± 13.3 MeV for the CT18 set, while including all measurements results in a mass of mW = 80394.6 ± 11.5 MeV. The former value is consistent with the SM prediction, while the latter value is 2.6σ higher.
Two scenarios
The results of the preliminary combination clearly separate two possible scenarios. In the first, the mW measurements are unbiased and differ due to large fluctuations and the PDF dependence of the W- and Z-boson data. In the second, a bias in one or more of the measurements produces the low compatibility of the measured values. Future measurements will clarify the likelihood of the first scenario, while further studies could identify effect(s) that point to the second scenario. In either case the next milestone will take time due to the exquisite precision that has now been reached, and to the challenges in maintaining analysis teams for the long timescales required to produce a measurement. The W boson’s midlife crisis continues, but with time and effort the golden years will come. We can all look forward to that.
The existence of dark matter in the universe is one of the most important puzzles in fundamental physics. It is inferred solely by means of its gravitational effects, such as on stellar motions in galaxies or on the expansion history of the universe. Meanwhile, non-gravitational interactions between dark matter and the known particles described by the Standard Model have not been detected, despite strenuous and advanced experimental efforts.
Such a situation suggests that new particles and fields, possibly similar to those of the Standard Model, may have been similarly present across the entire cosmological history of our universe, but with only very tiny interactions with visible matter. This intriguing idea is often referred to as the paradigm of dark sectors and is made even more compelling by the lack of new particles seen at the LHC and laboratory experiments so far.
Dark universe
Cosmological observations, above all those of the cosmic microwave background (CMB), currently represent the main tool to test such a paradigm. The primary example is that of dark radiation, i.e. putative new dark particles that, unlike dark matter, behave as relativistic species at the energy scales probed by the CMB. The most recent data collected by the Planck satellite constrain such dark particles to make at most around 30% of the energy of a single neutrino species at the recombination epoch (when atoms formed and the universe became transparent, around 380,000 years after the Big Bang).
While such observations represent a significant advance, the early universe was characterised by temperatures in the MeV range and above (enabling nucleosynthesis), possibly as large as 1016 GeV. Some of these temperatures correspond to energy scales that cannot be probed via the CMB, nor directly with current or prospective particle colliders. Even if new particles had significant interactions with SM particles at such high temperatures, any electromagnetic radiation in the hot universe was continuously scattered off matter (electrons), making it impossible for any light from such early epochs to reach our detectors today. The question then arises: is there another channel to probe the existence of dark sectors in the early universe?
We are entering a golden era of GW observations across the frequency spectrum
For more than a century, a different signature of gravitational interactions has been known to be possible: waves, analogous to those of the electromagnetic field, carrying fluctuations of gravitational fields. The experimental effort to detect gravitational waves (GWs) had a first amazing success in 2015, when waves generated by the merger of two black holes were first detected by the LIGO and Virgo interferometers in the US and Italy.
Now, the GW community is on the cusp of another incredible milestone: the detection of a GW background, generated by all sources of GWs across the history of our universe. Recently, based on more than a decade of observations, several networks of radio telescopes called pulsar timing arrays (PTAs) – NANOGrav in North America, EPTA in Europe, PPTA in Australia and CPTA in China – produced tentative evidence for such a stochastic GW background based on the influence of GWs on pulsars (see “Hints of low-frequency gravitational waves found” and “Clocking gravity” image). Together with next-generation interferometer-based GW detectors such as LISA and the Einstein Telescope, and new theoretical ideas from particle physics, the observations suggest that we are entering an exciting new era of observational cosmology that connects the smallest and largest scales.
Particle physics and the GW background
Once produced, GWs interact only very weakly with any other component of the universe, even at the high temperatures present at the earliest times. Therefore, whereas photons can tell us about the state of the universe at recombination, the GW background is potentially a direct probe of high-energy processes in the very early universe. Unlike GWs that reach Earth from the locations of binary systems of compact objects, the GW background is expected to be mostly isotropic in the sky, very much like the CMB. Furthermore, rather than being a transient signal, it should persist in the sensitivity bands of GW detectors, similar to a noise component but with peculiarities that are expected to make a detection possible.
As early as 1918, Einstein quantified the power emitted in GWs by a generic source. Compared to electromagnetic radiation, which is sourced by the dipole moment of a charge distribution, the power emitted in GWs is proportional to the third time derivative of the quadrupole moment of the mass-energy distribution of the source. Therefore, the two essential conditions for a source to emit GWs are that it should be sufficiently far from spherical symmetry and that its distribution should change sufficiently quickly with time.
What possible particle-physics sources would satisfy these conditions? One of the most thoroughly studied phenomena as a source of GWs is the occurrence of a phase transition, typically associated with the breaking of a fundamental symmetry. Specifically, only those phase transitions that proceed via the nucleation, expansion and collision of cosmic bubbles (analogous to the phase transition of liquid water to vapour) can generate a significant amount of GWs (see “Ringing out” image). Inside any such bubble the universe is already in the broken-symmetry phase, whereas beyond the bubble walls the symmetry is still unbroken. Eventually, the state of lowest energy inside the bubbles prevails via their rapid expansion and collisions, which fill up the universe. Even though such bubbles may initially be highly spherical, once they collide the energy distribution is far from being so, while their rapid expansion provides a time variation.
The occurrence of two phase transitions is in fact predicted by the Standard Model (SM): one related to the spontaneous breaking of the electroweak SU(2) × U(1) symmetry, the other associated with colour confinement and thus the formation of hadronic states. However, dedicated analytical and numerical studies in the 1990s and 2000s concluded that the SM phase transitions are not expected to be of first order in the early universe. Rather, they are expected to proceed smoothly, without any violent release of energy to source GWs.
This leads to a striking conclusion: a detection of the GW background would provide evidence for physics beyond the SM – that is, if its origin can be attributed to processes occurring in the early universe. This caveat is crucial, since astrophysical processes in the late universe also contribute to a stochastic GW background.
In order to claim a particle-physics interpretation for any stochastic GW background, it is thus necessary to appropriately account for astrophysical sources and characterise the expected (spectral) shape of the GW signal from early-universe sources of interest. These tasks are being undertaken by a diverse community of cosmologists, particle physicists and astrophysicists at research institutions all around the world, including in the cosmology group in the CERN TH department.
Precise probing
For particle physicists and cosmologists, it is customary to express the strength of a given stochastic GW signal in terms of the fraction of the energy (density) of the universe today carried by those GWs. The CMB already constraints this “relic abundance” to be less than roughly 10% of ordinary radiation, or about one millionth of that of the dominant component of the universe today, dark energy. Remarkably, current GW detectors are already able to probe stochastic GWs that produce only one billionth of the energy density of the universe.
Generally, the stochastic GW signal from a given source extends over a broad frequency range. The spectrum from many early-universe sources typically peaks at a frequency linked to the expansion rate at the time the source was active, redshifted to today. Under standard assumptions, the early universe was dominated by radiation and the peak frequency of the GW signal increases linearly with the temperature. For instance, the GW frequency range in which LIGO/Virgo/KAGRA are most sensitive (10–100 Hz) corresponds to sources that were active when the universe was as hot as 108 GeV – six orders of magnitude higher than the LHC. The other currently operating GW observatories, PTAs, are sensitive to GWs of much smaller frequencies, around 10–9–10–7 Hz, which correspond to temperatures around 10 MeV to 1 GeV (see “Broadband” figure). These are the temperatures at which the QCD phase transition occurred. While, as mentioned above, a signal from the latter is not expected, dark sectors may be active at those temperatures and source a GW signal. In the near (and long-term) future, it is conceivable that new GW observatories will allow us to probe the stochastic GW background across the entire range of frequencies from nHz to 100 Hz.
Together with bubble collisions, another source of peaked GW spectra due to symmetry breaking in the early universe is the annihilation of topological defects, such as domain walls separating different regions of the universe (in this case the corresponding symmetry is a discrete symmetry). Violent (so-called resonant) decays of new particles, such as is predicted by some early-universe scenarios, may also strongly contribute to the GW background (albeit possibly only at very large frequencies, beyond the sensitivity reach of current and forecasted detectors). Yet another discoverable phenomenon is the collapse of large energy (density) fluctuations in the early universe, such as is predicted to occur in scenarios where the dark matter is made of primordial black holes.
On the other hand, particle-physics sources can also be characterised by very broad GW spectra without large peaks. The most important such source is the inflationary mechanism: during this putative phase of exponential expansion of the universe, GWs would be produced from quantum fluctuations of space–time, stretched by inflation and continuously re-entering the Hubble horizon (i.e. the causally connected part of the universe at any given time) throughout the cosmological evolution. The amount of such primordial GWs is expected to be small. Nonetheless, a broad class of inflationary models predicts GWs with frequencies and amplitudes such that they can be discovered by future measurements of the CMB. In fact, it is precisely via these measurements that Planck and BICEP/Keck Array have been able to strongly constrain the simplest models of inflation. The GWs that can be discovered via the CMB would have very small frequencies (around 10–17 Hz, corresponding to ~eV temperatures). The full spectrum would nonetheless extend to large frequencies, only with such a small amplitude that detection by GW observatories would be unfeasible (except perhaps for the futuristic Big Bang Observer – a proposed successor to the Laser Interferometer Space Antenna, LISA, currently being prepared by the European Space Agency).
Feeling blue
Certain classes of inflationary models could also lead to “blue-tilted” (i.e. rising with frequency) spectra, which may then be observable at GW observatories. For instance, this can occur in models where the inflaton is a so-called axion field (a generalisation of the predicted Peccei–Quinn axion in QCD). Such scenarios naturally produce gauge fields during inflation, which can themselves act as sources of GWs, with possible peculiar properties such as circular polarisation and non-gaussianities. A final phenomenon that would generate a very broad GW spectrum, unrelated to inflation, is the existence of cosmic strings. These one-dimensional defects can originate, for instance, from the breaking of a global (or gauge) rotation symmetry and persist through cosmological history, analogous to cracks that appear in an ice crystal after a phase transition from water.
Astrophysical contributions to the stochastic GW background are certainly expected from binary black-hole systems. At the frequencies relevant for LIGO/Virgo/KAGRA, such background would be due to black holes with masses of tens of solar masses, whereas in the PTA sensitivity range the background is sourced by binaries of supermassive black holes (with masses up to millions of solar masses), such as those that are believed to exist at the centres of galaxies. The current PTA indications of a stochastic GW background require detailed analyses to understand whether the signal is due to a particle physics or an astrophysics source. A smoking gun for the latter origin would be the observation of significant anisotropies in the signal, as it would come from regions where more binary black holes are clustered.
We are entering a golden era of GW observations across the frequency spectrum, and thus in exploring particle physics beyond the reach of colliders and astrophysical phenomena at unprecedented energies. The first direct detection of GWs by LIGO in September 2015 was one of the greatest scientific achievements of the 21st century. The first generation of laser interferometric detectors (GEO600, LIGO, Virgo and TAMA) did not detect any signal and only constrained the gravitational-wave emission from several sources. The second generation (Advanced LIGO and Advanced Virgo) made the first direct detection and has observed almost 100 GW signals to date. The underground Kamioka Gravitational Wave Detector (KAGRA) in Japan joined the LIGO–VIRGO observations in 2020. As of 2021, the LIGO–Virgo–KAGRA collaboration is working to establish the International Gravitational Wave Network, to facilitate coordination among ground-based GW observatories across the globe. In the near future, LIGO India (IndIGO) will also join the network of terrestrial detectors.
Despite being sensitive to changes in the arm length of the order of 10–18 m, the LIGO, Virgo and KAGRA detectors are not sensitive enough for precise astronomical studies of GW sources. This has motivated the new generation of detectors. The Einstein Telescope (ET) is a proposed design concept for a European third-generation GW detector underground, which will be 10 times more sensitive than the current advanced instruments (see “Joined-up thinking in vacuum science”). On Earth, however, gravitational waves with frequencies lower than 1 Hz are inaccessible due to terrestrial gravity gradient noise and limitations to the size of the device. Space-based detectors, on the other hand, can access frequencies as low as 10–4 Hz. Several space-based GW observatories are proposed that will ultimately form a network of laser interferometers in space. They include LISA (planned to launch around 2035), the Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) led by the Japan Aerospace Exploration Agency and two Chinese detectors, TianQin and Taiji (see “In synch” figure).
Precision detection of the gravitational-wave spectrum is essential to explore particle physics beyond the reach of particle colliders
A new kid on the block, atom interferometry, offers a complementary approach to laser interferometry for the detection of GWs. Two atom interferometers coherently manipulated by the same light field can be used as a differential phase meter tracking the distance traversed by the light field. Several terrestrial cold-atom experiments are under preparation, such as MIGA, ZAIGA and MAGIS, or being proposed, such as ELGAR and AION. These experiments will provide measurements in the mid-frequency range between 10–2–1 Hz. Moreover, a space-based cold-atom GW detector called the Atomic Experiment for Dark Matter and Gravity Exploration (AEDGE) is expected to probe GWs in a much broader frequency range (10–7–10 Hz) compared to LISA.
Astrometry provides yet another powerful way to explore GWs that is not accessible to other probes, i.e. ultra-low frequencies of 10 nHz or less. Here, the passage of a GW over the Earth-star system induces a deflection in the apparent position of a star, which makes it possible to turn astrometric data into a nHz GW observatory. Finally, CMB missions have a key role to play in searching for possible imprints on the polarisation of CMB photons caused by a stochastic background of primordial GWs (see “Acoustic imprints” image). The wavelength of such primordial GWs can be as large as the size of our horizon today, associated with frequencies as low as 10–17 Hz. Whereas current CMB missions allow upper bounds on GWs, future missions such as the ground-based CMB-S4 (CERN Courier March/April 2022 p34) and space-based LiteBIRD observatories will improve this measurement to either detect primordial GWs or place yet stronger upper bounds on their existence.
Outlook
Precision detection of the gravitational-wave spectrum is essential to explore particle physics beyond the reach of particle colliders, as well as for understanding astrophysical phenomena in extreme regimes. Several projects are planned and proposed to detect GWs across more than 20 decades of frequency. Such a wealth of data will provide a great opportunity to explore the universe in new ways during the next decades and open a wide window on possible physics beyond the SM.
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