The STEREO experiment, located at the high-flux research reactor at the Institut Laue-Langevin (ILL), Grenoble, is the latest to cast doubt on the existence of an additional, sterile neutrino state. Based on the full dataset collated from October 2017 until the experiment shut down in November 2020, the results support the conclusions of a global analysis of all neutrino data, that a normalisation bias in the beta-decay spectrum of 235U is the most probable explanation for a deficit of electron neutrinos seen at reactor experiments during the past decade.
The confirmation of neutrino oscillations 25 years ago showed that the lepton content of a given neutrino evolves as it propagates, generating a change of flavour. Numerous experiments based on solar, atmospheric, accelerator, reactor and geological neutrino sources have determined the oscillation parameters in detail, reaffirming the three-neutrino picture obtained by precise measurements of the Z boson’s decay width at LEP. However, several anomalies have also shown up, one of the most prominent being the so-called reactor antineutrino anomaly. Following a re-evaluation of the expected νe flux from nuclear reactors by a team at CEA and Subatech in 2011, a deficit in the number of νe detected by reactor neutrino experiments appeared. Combined with a longstanding anomaly reported by short-baseline accelerator-neutrino experiments such as LSND and a deficit in νe seen in calibration data for the solar-neutrino detectors GALLEX and SAGE, excitement grew that an additional neutrino state – a sterile or right-handed neutrino with non-standard interactions that arises in many extensions of the Standard Model – might be at play.
We anticipate that this result will allow progress towards finer tests of the fundamental properties of neutrinos
Designed specifically to investigate the sterile-neutrino hypothesis, STEREO was positioned about 10 m from the ILL reactor core to measure the evolution of the antineutrino energy spectrum from 235U fission at short distances with high precision. Comprising six cells filled with gadolinium-doped liquid scintillator positioned at different distances from the reactor core, producing six spectra, the setup allows the hypothesis that νeundergo a fast oscillation into a sterile neutrino to be tested independently of the predicted shape of the emitted νespectrum.
The measured antineutrino energy spectrum, based on 107,558 detected antineutrinos, suggests that the previously reported anomalies originate from biases in the nuclear experimental data used for the predictions, while rejecting the hypothesis of a light sterile neutrino with a mass of about 1 eV. “Our result supports the neutrino content of the Standard Model and establishes a new reference for the 235U antineutrino energy spectrum,” writes the team. “We anticipate that this result will allow progress towards finer tests of the fundamental properties of neutrinos but also to benchmark models and nuclear data of interest for reactor physics and for observations of astrophysical or geoneutrinos.”
Gallium remains
STEREO’s findings fit those reported recently by other neutrino-oscillation experiments. A 2021 analysis by the MicroBooNE collaboration at Fermilab, for example, favoured the Standard Model over an anomalous signal seen by its nearby experiment MiniBooNE, assuming the latter was due to the existence of a non-standard neutrino. Yet the story of the sterile neutrino is not over. In 2022, new results from the Baksan Experiment on Sterile Transitions (BEST) further confirmed the deficit in the νeflux emitted from radioactive sources as seen by the SAGE and GALLEX experiments – the so-called gallium anomaly – which, if interpreted in the context of neutrino oscillations, is consistent with νe → νs oscillations with a relatively large squared mass difference and mixing angle.
“Under the sterile neutrino hypothesis, a signal in MicroBooNE, MiniBooNE or LSND would require the sterile neutrino to mix with both νe and νμ, whereas for the gallium anomaly, mixing with νe alone is sufficient,” explains theorist Joachim Kopp of CERN. “Even though the reactor anomaly seems to be resolved, we’d still like to understand what’s behind the others.”
Antinuclei can travel vast distances through the Milky Way without being absorbed, concludes a novel study by the ALICE collaboration. The results, published in December, indicate that the search for 3He in space is a highly promising way to probe dark matter.
First observed in 1965 in the form of the antideuteron at CERN’s Proton Synchrotron and Brookhaven’s Alternating Gradient Synchrotron, antinuclei are exceedingly rare. Since they annihilate on contact with regular matter, no natural sources exist on Earth. However,light antinuclei have been produced and studied at accelerator facilities, including recent precision measurements of the mass difference between deuterons and antideuterons and between 3He and 3He by ALICE, and between the hypertriton and antihypertriton by the STAR collaboration at RHIC.
Antinuclei can in principle also be produced in space, for example in collisions between cosmic rays and the interstellar medium. However, the expected production rates are very small. A more intriguing possibility is that light antinuclei are produced by the annihilation of dark-matter particles. In such a scenario, the detection of antinuclei in cosmic rays could provide experimental evidence for the existence of dark-matter particles. Space-based experiments such as AMS-02 and PAMELA, along with the upcoming Antarctic balloon mission GAPS, are among a few experiments that are able to detect light antinuclei. But to be able to interpret future results, precise knowledge of the production and disappearance probabilities of antinuclei is vital.
The latter is where the new ALICE study comes in. The unprecedented energies of proton–proton and lead–lead collisions at the LHC produce, on average, as many nuclei as antinuclei. By studying the change in the rate of 3He as a function of the distance to the production point, the collaboration was able to determine the inelastic cross section, or disappearance probability, of 3He nuclei for the first time. These values were then used as input for astrophysics simulations.
Two models of the 3Heflux expected near Earth after the nuclei’s journey from sources in the Milky Way were considered: one assumes that the sources are cosmic-
ray collisions with the interstellar medium, and the other annihilations of hypothetical weakly interacting massive particles (WIMPs). For each model, the Milky Way’s transparency to 3He– that is, its ability to let the nuclei through without being absorbed – was estimated. The WIMP dark-matter model led to a transparency of about 50%, whereas for the cosmic-ray model the transparency ranged from 25 to 90%, depending on the energy of the antinucleus. These values show that 3Heoriginating from dark-matter or cosmic-ray collisions can travel distances of several kiloparsecs in the Milky Way without being absorbed, even from as far away as the galactic centre.
“This new result illustrates the close connection between accelerator-based experiments and observations of particles produced in the cosmos,” says ALICE spokesperson Marco van Leeuwen. “In the near future, these studies will be extended to 4He and to the lower-momentum region with much larger datasets.”
The Physics Beyond Colliders (PBC) study was launched in 2016 to explore the opportunities offered by CERN’s unique accelerator and experimental-area complex to address some of the outstanding questions in particle physics through experiments that are complementary to the high-energy frontier. Following the recommendations of the 2020 update of the European strategy for particle physics, the CERN directorate renewed the mandate of the PBC study, continuing it as a long-term activity.
The fourth PBC annual workshop took place at CERN from 7 to 9 November 2022. The aim was to review the status of the studies, with a focus on the programmes under consideration for the start of operations after Long Shutdown 3 (LS3), scheduled for 2026–2029.
The North Area (NA) at CERN, where experiments are driven by beams from the Super Proton Synchrotron (SPS), is at the heart of many present and proposed explorations for physics beyond the Standard Model. The NA includes an underground cavern (ECN3), which can host unique high-energy/high-intensity proton beams. Several proposals for experiments have been made, all of which require higher intensity proton beams than are currently available. It is therefore timely to identify the synergies and implications of a future ECN3 high-intensity programme on the otherwise ongoing NA technical consolidation programme.
The following proposals are being considered within the PBC study group:
• HIKE (High Intensity Kaon Experiment) is a proposed expansion of the current NA62 programme to study extremely rare decays of charged kaons and, in a second phase, those of neutral kaons. This would be complemented by searches for visible decays of feebly interacting particles (FIPs) that could emerge on-axis from the dump of an intense proton beam within a thick absorber that would contain all other known particles, except muons and neutrinos;
• SHADOWS (Search for Hidden And Dark Objects With the SPS) would search for visible FIP decays off-axis and could run in parallel to HIKE when operated in beam-dump mode. The proposed detector is compact and employs existing technologies to meet the challenges of reducing the muon background;
• SHiP (Search for Hidden Particles) would allow a full investigation of hidden sectors in the GeV mass range. Comprehensive design studies for SHiP and the Beam Dump Facility (BDF) in a dedicated experimental area were published in preparation for the European strategy update. During 2021, an analysis of alternative locations using existing infrastructure at CERN revealed ECN3 to be the most promising option;
• Finally, TauFV (Tau Flavour Violation) would conduct searches for lepton-flavour violating tau-lepton decays.
The HIKE, SHADOWS and BDF/SHiP collaborations have recently submitted letters of intent describing their proposals for experiments in ECN3. The technical feasibility of the experiments, their physics potential and implications for the NA consolidation are being evaluated in view of a possible decision by the beginning of 2023. A review of the experimental programme in the proposed high-intensityfacility will take place during 2023, in parallel with a detailed comparison of the sensitivity to FIPs in a worldwide context.
A vibrant programme
The NA could also host a vibrant ion-physics programme after LS3, with NA60++ aiming to measure the caloric curve of the strong-force phase transition with lead–ion beams, and NA61++ proposing to explore the onset of the deconfined nuclear medium, extending the scan in the momentum/ion space with collisions of lighter ion beams. The conceptual implementation of such schemes in the accelerators and experimental area is being studied and the results, together with the analysis of the physics potential, are expected during 2023.
The search for long-lived particles with dedicated experiments and the exploration of fixed-target physics is also open at the LHC. The proposed forward-physics facility, located in a cavern that could be built at a distance of 600 m along the beam direction from LHC Interaction Point 1, would take advantage of the large flux of high-energy particles produced in the very forward direction in LHC collisions. It is proposed to host a comprehensive set of detectors (FASER2, FASERν2, AdvSND, FORMOSA, FLArE) to explore a broad range of new physics and to study the highest energy neutrinos produced by accelerators. A conceptual design report of the facility, including detector design, background analysis and mitigation measures, civil engineering and integration studies is in preparation. Small prototypes of the MATHUSLA, ANUBIS and CODEX-b detectors aiming at the search for long-lived particles at large angles from LHC collisions are also being built for installation during the current LHC run.
The North Area at CERN is at the heart of many present and proposed explorations for physics beyond the Standard Model
A gas-storage cell (SMOG2) was installed in front of the LHCb experiment during the last LHC long shutdown, opening the way to high-precision fixed-target measurements at the LHC. The storage cell enhances the density of the gas and therefore the rate of the collisions by up to two orders of magnitude as compared to the previous internal gas target. SMOG2 has been successfully commissioned with neon gas, demonstrating that it can be operated in parallel to LHCb. Future developments include the injection of different types of gases and a polarised gas target to explore nucleon spin-physics at the LHC.
Crystal clear
Fixed-target experiments are also being developed that would extract protons from LHC beams by channelling the beam halo with a bent crystal.The extracted protons would impinge on a target and be used for measurements of proton structure functions (“single crystal setup”) or estimation of the magnetic and electric dipole moments of short-lived heavy baryons (“double crystal setup”). In the latter case, the measurement would be based on the baryon spin precession in the strong electric field of a second bent crystal installed immediately downstream from the baryon-production proton target. A proof-of-principle experiment of the double-crystal setup is being designed for installation in the LHC to determine the channelling efficiency for long crystals at TeV energies, as well as to demonstrate the control and management of the secondary halo and validate the estimate of the achievable luminosity.
The technology know-how at CERN can also benefit non-accelerator experiments
The technology know-how and experience available at CERN can also benefit non-accelerator experiments such as the Atom Interferometer Observatory and Network (AION), proposed to be installed in one of the shafts at Point 4 of the LHC for mid-frequency gravitational-wave detection and ultra-light dark-matter searches, as well as the development of superconducting cavities for the Relic Axion Detector Experimental Setup (RADES) and for the heterodyne detection of axion-like particles.
During the workshop, progress on the possible applications of a gamma factory at CERN, as well as the status of the design of a Charged-Particle EDM Prototype Ring and of the R&D for novel monitored or tagged neutrino beamlines, were also presented.
Highly energetic cosmic rays reach Earth from all directions and at all times, yet it has been challenging to conclusively identify their sources. Being charged, cosmic rays are easily deflected by interstellar magnetic fields during their propagation and thereby lose any information about where they originated from. On the other hand, highly energetic photons and neutrinos remain undeflected. Observations of high-energy photons and neutrinos are therefore crucial clues towards unravelling the mystery of cosmic-ray sources and accelerators.
Four years ago, the IceCube collaboration announced the identification of the blazar TXS 0506+056 as a source of high-energy cosmic neutrinos, the first of its kind (CERN Courier September 2018 p7). This was one of the early examples of multi-messenger astronomy wherein a high-energy neutrino event detected by IceCube, which was coincident in direction and time with a gamma-ray flare from the blazar, prompted an investigation into this object as a potential astrophysical neutrino source.
Point source
In the following years, IceCube made a full-sky scan for point-like neutrino sources, and in 2020, the collaboration found an excess coincident with the Seyfert II galaxy, NGC1068, that was inconsistent with a background-only hypothesis. However, with a statistical significance of only 2.9σ, it was insufficient to claim a detection. In November 2022, after a more detailed analysis with a longer live-time and improved methodologies, the collaboration confirmed NGC1068 to be a point source of high-energy neutrinos at a significance of 4.2σ.
IceCube’s measurements usher in a new era of neutrino astronomy
Messier 77, also known as the Squid Galaxy or NGC1068, is located 47 million light years away in the constellation Cetus and was discovered in 1780. Today, we know it to be an active galaxy: at its centre lies an active galactic nucleus (AGN), which is a luminous and compact region powered by a super massive black hole (SMBH), surrounded by an accretion disk. Specifically, it is a Seyfert II galaxy, which is an active galaxy that is viewed edge-on, with the line-of-sight passing through the accretion region that obscures the centre.
The latest search used data from the fully completed IceCube detector. Several calibrations and alignments were also made to the data-acquisition procedure and an advanced event reconstruction algorithm was deployed. The search was conducted in the Northern Hemisphere of the sky, i.e. by detecting neutrinos from “below”, so that Earth could screen background atmospheric muons.
Three different searches were carried out to locate possible point-like neutrino sources. The first involved scanning the sky for a statistically significant excess over background, while the other two used a catalogue of 110 sources that was developed in the 2020 study, the difference between the two being the statistical methods used. The results showed an excess of 79+22–20muon–neutrino events, with the main contribution coming from neutrinos in the energy range of 1.5 to 15 TeV, while the all-flavour flux is expected to be a factor of three higher. All the events contributing to the excess were well-reconstructed within the detector, with no signs of anomalies, and the results were found not to be dominated by just one or a few individual events. The results were also in line with phenomenological models that predict the production of neutrinos and gamma rays in sources such as NGC1068.
IceCube’s measurements usher in a new era of neutrino astronomy and take researchers a step closer to understanding not only the origin of high-energy cosmic rays but also the immense power of massive black holes, such as the one residing inside NGC1068.
In the Standard Model (SM) of particle physics, the only way the Higgs boson can decay without leaving any traces in the LHC detectors is through the four-neutrino decay, H → ZZ → 4ν, which has an expected branching fraction of only 0.1%. This very small value can be seen as a difficulty but is also an exciting opportunity. Indeed, several theories of physics beyond the SM predict considerably enhanced values for the branching fraction of invisible Higgs-boson decays. In one of the most interesting scenarios, the Higgs boson acts as a portal to the dark sector by decaying to a pair of dark matter (DM) particles. Measurements of the “Higgs to invisible” branching fraction are clearly among the most important tools available to the LHC experiments in their searches for direct evidence of DM particles.
The CMS collaboration recently reported the combined results of different searches for invisible Higgs-boson decays, using data collected at 7, 8 and 13 TeV centre-of-mass energies. To find such a rare signal among the overwhelming background produced by SM processes, the study considers events in most Higgs-boson production modes: via vector boson (W or Z) fusion, via gluon fusion and in association with a top quark–antiquark pair or a vector boson. In particular, the analysis looked at hadronically decaying vector bosons or top quark–antiquark pairs. A typical signature for invisible Higgs-boson decays is a large missing energy in the detector, so that the missing transverse energy plays a crucial role in the analysis. No significant signal has been seen, so a new and stricter upper limit is set on the probability that the Higgs boson decays to invisible particles: 15% at 95% confidence level.
This result has been interpreted in the context of Higgs-portal models, which introduce a dark Higgs sector and consider several dark Higgs-boson masses. The extracted upper limits on the spin-independent DM-nucleon scattering cross section, shown in figure 1 for a range of DM mass points, have better sensitivities than those of direct searches over the 1–100 GeV range of DM masses. Once the Run 3 data will be added to the analysis, much stricter limits will be reached or, if we are lucky, evidence for DM production at the LHC will be seen.
Lepton number is a quantum number that represents the difference in the number of leptons and antileptons participating in a process, while lepton flavour is a corresponding quantity that accounts for each generation of lepton (e, μ or τ) separately. Lepton number is always conserved but lepton flavour violation (LFV) is known to exist in nature, as this phenomenon has been observed in neutrino oscillations – the transition of a neutral lepton of a given flavour to one with a different flavour. This observation motivates searches for additional manifestations of LFV that may be the result of beyond-the-Standard Model (SM) physics, key among which is the search for LFV decays of the Higgs boson.
The ATLAS collaboration has recently announced the results of searches for H → eτ and H → μτ decays based on the full Run 2 data set, which was collected at a centre-of-mass energy of 13 TeV. The unstable τ lepton decays to an electron or a muon and two neutrinos, or to one or more hadrons and one neutrino. Most of the background events in these searches arise from SM processes such as Z →ττ, the production of top–antitop and weak-boson pairs, as well as from events containing misidentified or non-prompt leptons (fake leptons). These fake leptons originate from secondary decays, for example of charged pions. Several multivariate analysis techniques were used for each final state to provide the maximum separation between signal and background events.
To ensure the robustness of the measurement, two background estimation methods were employed: a Monte Carlo (MC) template method in which the background shapes were extracted from MC and normalised to data, and a “symmetry method”, which used only the data and relied on an approximate symmetry between prompt electrons and prompt muons. Any difference between the branching fractions B(H → eτμ) and B(H → μτe), where the subscripts μ and e represent the decay modes of the τ lepton, would break this symmetry. In both cases, contributions from events containing fake leptons were estimated directly from the data.
The MC-template method enables the measurement of the branching ratios of the LFV decay modes. Searches based on the MC-template method for background estimation involve both leptonic and hadronic decays of τ leptons. A simultaneous measurement of the H → eτ and H → μτ decay modes was performed. For the H → μτ (H → eτ) search, a 2.5 (1.6) standard deviation upward fluctuation above the SM background prediction is observed. The observed (expected) upper limits on the branching fractions B(H → eτ) and B(H → μτ) at 95% confidence level are slightly below 0.2% (0.1%), which are the most stringent limits obtained by the ATLAS experiment on these quantities. The result of the simultaneous measurement of the H → eτ and H → μτ branching fractions is compatible with the SM prediction within 2.2 standard deviations (see figure 1).
The observed upper limits on the branching fractions are the most stringent limits obtained by the ATLAS experiment
The symmetry method is particularly sensitive to the difference in the two LFV decay branching ratios. For this measurement, only the fully leptonic final states were used. Special attention was paid to correctly account for asymmetries induced by the different detector response to electrons and muons, especially regarding the trigger and offline efficiency values for lepton reconstruction, identification and isolation, as well as regarding contributions from fake leptons. The measurement of the branching ratio difference indicates a small but not significant upward deviation for H → μτ compared to H → eτ. The best-fit value for the difference between B(H → μτe) and B(H → eτμ) is (0.25 ± 0.10)%.
The expected twice-larger LHC Run 3 dataset at the higher centre-of-mass energy of 13.6 TeV will shed further light on these results.
The Cabibbo–Kobayashi–Maskawa (CKM) matrix describes the couplings between the quarks and the weak charged current, and contains within it a phase γ that changes sign under consideration of antiquarks rather than quarks. In the Standard Model (SM), this phase is the only known difference in the interactions of matter and anti-matter, a consequence of the breaking of charge-parity (CP) symmetry. While the differences within the SM are known to be far too small to explain the matter-dominated universe, it is still of paramount importance to precisely determine this phase to provide a benchmark against which any contribution from new physics can be compared.
A new measurement recently presented by the LHCb collaboration uses a novel method to determine γ using decays of the type B± → D[K∓π±π±π∓]h± (h = π, K). CP violation in such decays is a consequence of the interference between two tree-level processes with a weak phase that differs by γ, and thus provide a theoretically clean probe of the SM. The new aspect of this measurement compared to those performed previously lies in the partitioning of the five-dimensional phase space of the D-decay into a series of independent regions, or bins. In these bins, the asymmetries between B+ and B– meson decay rates can receive large enhancements from the hadronic interactions in the D-meson decay. The enhancement for one of such bins can be seen in figure 1, which shows the invariant mass spectrum of the B+ and B– meson candidates, where the correctly reconstructed decays peak at around 5.3 GeV. The observed asymmetry in this region is around 85%, which is the largest difference in the behaviour of matter and antimatter ever measured. Observables from the different bins are combined with information on the hadronic interactions in the D-meson decay from charm-threshold experiments to obtain γ = 55 ± 9°, which is compatible withprevious determinations and is the second most precise single measurement.
The matter–antimatter asymmetry reaches 85% in a certain region, the largest ever observed
The LHCb average value of γ is then determined by combining this analysis with the measurements in many other B and D decays, where in all cases the SM contribution is expected to be dominant. Measurements of charm decays are also included to better constrain both the parameters of charm mixing, which also play an important role in the measurements of B-meson decays at the current level of precision and help to constrain the hadronic interactions in some of the D decays. In particular, included for the first time in this combination is a measurement of yCP, which is proportional to the difference in lifetimes of the two neutral charm mesons, and was determined using two-body decays of the D meson using the entire LHCb data set collected so far.
The overall impact of these additional analyses reduces the uncertainty on γ by more than 10%, corresponding to adding around a year of data taking across all decay modes.
The improvements in the knowledge of yCP is also dramatic, reducing the uncertainty by around 40%. While the value of γ is found to be compatible with determinations that would be more susceptible to new physics, the precision of the comparison is starting to approach the level of a few degrees, at which discrepancies may start to be observable.
Given that the current uncertainties on many of the key input analyses to the combination are predominately statistical in nature, measurements of these fundamental flavour-physics parameters with the upgraded LHCb detector, and beyond, are an intriguing prospect for new-physics searches.
For almost 40 years, charmonium, a bound state of a heavy charm–anticharm pair (hence also called a hidden charm), has provided a unique probe to study the properties of the quark–gluon plasma (QGP), the state of matter composed by deconfined quarks and gluons present in the early instants of the universe and produced experimentally in ultrarelativistic heavy-ion collisions. Charmonia come in a rich variety of states. In a new analysis investigating how these different bound charmonium states are affected by the QGP, the ALICE collaboration has opened a novel way to study the strong interaction at extreme temperatures and densities.
In the QGP, the production of charmonium is suppressed due to “colour screening” by the large number of quarks and gluons present. The screening, and thus the suppression, increases with the temperature of the QGP and is expected to affect different charmonium states to different degrees. The production of the ψ(2S) state, for example, which is 10 times more weakly bound and two times larger in size than the most tightly bound state, the J/ψ, is expected to be more suppressed.
This hierarchical suppression is not the only fate of charmonia in the quark–gluon plasma. The large number of charm quarks and antiquarks in the plasma – up to about 100 in head-on lead–lead collisions – also gives rise to a mechanism, called recombination, that forms new charmonia and counters the suppression to a certain extent. This process is expected to depend on the type and momentum of the charmonia, with the more weakly bound charmonia being produced through recombination later in the evolution of the plasma and charmonia with the lowest (transverse) momentum having the highest recombination rate.
Previous studies, using data first from the Super Proton Synchrotron and then from the LHC, have shown that the production of the ψ(2S) state is indeed more suppressed than that of the J/ψ, and ALICE has also previously provided evidence of the recombination mechanism in J/ψ production. But so far, no studies of ψ(2S) production at low transverse particle momentum had been precise enough to provide conclusive results in this momentum regime, preventing a complete picture of ψ(2S) production from being obtained.
The ALICE collaboration has now reported the first measurements of ψ(2S) production down to zero transverse momentum, based on lead–lead collision data from the LHC collected in 2015 and 2018. The results indicate that the ψ(2S) yield is largely suppressed with respect to a proton–proton baseline, almost a factor of two more suppressed than the J/ψ. The suppression, shown as a function of the collision centrality (Npart) in the figure, is quantified through the nuclear modification factor (RAA), which compares the particle production in lead–lead collisions with respect to the expectations based on proton–proton collisions.
Theoretical predictions based on a transport approach that includes suppression and recombination of charmonia in the QGP (TAMU) or on the Statistical Hadronisation Model (SHMc), which assumes charmonia to be formed only at hadronisation, describe the J/ψ data, while the ψ(2S) production is underestimated in central events by the SHMc. This observation represents one of the first indications that dynamical effects in the QGP, as taken into account in the transport models, are needed to reproduce the yields of the various charmonium states. It also shows that precision studies, including these and those of other charmonia, and foreseen for Run 3 of the LHC, may lead to a final understanding of the modification of the force binding these states in the extreme environment of the QGP.
Special Topics in Accelerator Physics by Alexander Wu Chao introduces the global picture of accelerator physics, clearly establishing the scope of the book from the first page. The derivation and solution of concepts and equations is didactic throughout the chapters. Chao takes readers by the hand and guides them through important formulae and their limitations step-by-step, such that the reader does not miss the important parts – an extremely useful tactic for advanced masters or doctoral students when their topic of interest is among the eight special topics described.
In the first chapter, I particularly liked the way the author transitions from the Vlasov equation, a very powerful technique for studying beam–beam effects, towards the Fokker–Planck equation describing the statistical interaction of charged particles inside an accelerator. Chao pedagogically introduces the potential-well distortion, which is complemented by illustrations. The discussion on wakefield acceleration, taking readers deeper into the subject and extending it both for proton and electron beams, is timely. Extending the Fokker–Planck equation to 2D and 3D systems is particularly advanced but at the same time important. The author discusses the practical applications of the transient beam distribution in simple steps and introduces the higher order moments later. The proposed exercises, for some of which solutions are provided, are practical as well.
In chapter two, the concept of symplecticity, the conservation of phase space (a subject that causes much confusion), is discussed with concrete examples. Naming issues are meticulously explained, such as using the term short-magnet rather than thin-lens approximation in formula 2.6. Symplectic models for quadrupole magnets are introduced and the following discussion is extremely useful for students and accelerator physicists who will use symplectic codes such as MAD-X and who would like to understand the mathematical framework of their operation. This nicely conjuncts with the next chapter and the book offers useful insights to how these codes operate. In the discussion about third-order integration, Chao makes occasional mental leaps, which could be mitigated with an additional sentence. Although the discussion on higher order and canonical integrators is rather specialised, it is still very useful.
The author introduces the extremely convenient and broadly used truncated power series algebra (TPSA) technique, used to obtain maps, in chapter three. Chao explains in a simple manner the transition from the pre-TPSA algorithms (such as TRANSPORT or COSY) to symplectic algorithms such as MAD-X or PTC, as well as the reason behind this evolution. The clear “drawbacks” discussion is very useful in this regard.
The transition to Lie algebra in chapter four is masterful and pedagogical. Lie algebras, which can be an advanced topic and come with many formulas, are the main focus in this section of the book. In particular, the non-linearity of the drift space, which is absent of fields, should catch the reader’s attention. This is followed by specialised applications for expert readers only. One of this chapter’s highlights is the derivation of the sextupole pairing, which is complemented by that of Taylor maps up to the second order and its Lie algebra, although it would be better if the “Our plan” section was placed at the beginning of the chapter.
Chapter five covers proton-spin dynamics. Spinor formulas and the Froissart–Stora equation for the polarisation change are developed and explained. The Siberian snake technique remains one of the most well-known to retain beam polarisation, which the author discusses in detail. This links elegantly to chapter six, which introduces the reader to electron-spin dynamics where synchrotron radiation is the dominant effect and therefore constitutes a completely different research area. Chao focuses on the differences between the quantum and classical approach to synchrotron radiation, a phenomenon that cannot be ignored in high-brightness machines. Analogies between protons and electrons are then very well summarised in the recap figure 6.3. Section 6.5 is important for storage rings and leads smoothly to the Derbenev–Kondratenko formula and its applications.
Echoes
Chapter seven looks at echoes, a key technique when measuring diffusion in an accelerator, where the author introduces the reader to the generality of the term and the concept of echoes in accelerator physics. Transverse echoes (with and without diffusion) are quite analytical and the figures are didactic.
The book concludes with a very complete, concise and detailed chapter about beam–beam effects, which acts as an introduction to collider–accelerator physics for coherent- and incoherent-effects studies. Although synchro-betatron couplings causing resonant instabilities are advanced topics, they are often seen in practice when operating the machines, and the book offers the theoretical background for a deeper understanding of these effects.
Special Topics in Accelerator Physics is well written and develops the advanced subjects in a comprehensive, complete and pedagogical way.
High-energy physics spans a wide range of energies, from a few MeV to TeV, that are all relevant. It is therefore often difficult to take all phenomena into account at the same time. Effective field theories (EFTs) are designed to break down this range of scales into smaller segments so that physicists can work in the relevant range. Theorists “cut” their theory’s energy scale at the order of the mass of the lightest particle omitted from the theory, such as the proton mass. Thus, multi-scale problems reduce to separate and single-scale problems (see “Scales” image). EFTs are today also understood to be “bottom-up” theories. Built only out of the general field content and symmetries at the relevant scales, they allow us to test hypotheses efficiently and to select the most promising ones without needing to know the underlying theories in full detail. Thanks to their applicability to all generic classical and quantum field theories, the sheer variety of EFT applications is striking.
In hindsight, particle physicists were working with EFTs from as early as Fermi’s phenomenological picture of beta decay in which a four-fermion vertex replaces the W-boson propagator because the momentum is much smaller compared to the mass of the W boson (see “Fermi theory” image). Like so many profound concepts in theoretical physics, EFT was first considered in a narrow phenomenological context. One of the earliest instances was in the 1960s, when ad-hoc methods of current algebras were utilised to study weak interactions of hadrons. This required detailed calculations, and a simpler approach was needed to derive useful results. The heuristic idea of describing hadron dynamics with the most general Lagrangian density based on symmetries, the relevant energy scale and the relevant particles, which can be written in terms of operators multiplied by Wilson coefficients, was yet to be known. With this approach, it was possible to encode local symmetries in terms of the current algebra due to their association with conserved currents.
For strong interactions, physicists described the interaction between pions with chiral perturbation theory, an effective Lagrangian, which simplified current algebra calculations and enabled the low-energy theory to be investigated systematically. This “mother” of modern EFTs describes the physics of hadrons and remains valid to an energy scale of the proton mass. Heavy-quark effective theory (HQET), introduced by Howard Georgi in 1990, complements chiral perturbation theory by describing the interactions of charm and bottom quarks. HQET allowed us to make predictions on B-meson decay rates, since the corrections could now be classified. The more powers of energy are allowed, the more infinities appear. These infinities are cancelled by available counter-terms.
Similarly, it is possible to regard the Standard Model as the truncation of a much more general theory including non-renormalisable interactions, which yield corrections of higher order in energy. This perception of the whole Standard Model as an effective field theory started to be formed in the late 1970s by Weinberg and others (see “All things EFT: a lecture series hosted at CERN” panel). Among the known corrections to the Standard Model that do not satisfy its approximate symmetries are neutrino masses, postulated in the 1960s and discovered via the observation of neutrino oscillations in the late 1990s. While the scope of EFTs was unclear initially, today we understand that all successful field theories, with which we have been working in many areas of theoretical physics, are nothing but effective field theories. EFTs provide the theoretical framework to probe new physics and to establish precision programmes at experiments. The former is crucial for making accurate theoretical predictions, while the latter is central to the physics programme of CERN in general.
EFTs in particle physics
More than a decade has passed since the first run of the LHC, in which the Higgs boson and the mechanism for electroweak symmetry breaking were discovered. So far, there are no signals of new physics beyond the SM. EFTs are well suited to explore LHC physics in depth. A typical example for an event involving two scales is Higgs-boson production because there is a factor 10–100 between its mass and transverse momentum. The calculation of each Higgs-boson production process leads to large logarithms that can invalidate perturbation theory due to the large-scale separation. This is just one of many examples of the two-scale problem that arises when the full quantum field theory approach for high-energy colliders is applied. Traditionally, such two-scale problems have been treated in the framework of QCD factorisation and resummation.
Over the past two decades, it has been possible to recast two-scale problems at high-energy colliders with the advent of soft-collinear effective theory (SCET). SCET is nowadays a popular framework that is used to describe Higgs physics, jets and their substructure, as well as more formal problems, such as power corrections to reconstruct full amplitudes eventually. The difference between HQET and SCET is that SCET considers long-distance interactions between quarks and both soft and collinear particles, whereas HQET takes into account only soft interactions between a heavy quark and a parton. SCET is just one example where the EFT methodology has been indispensable, even though the underlying theory at much higher energies is known. Other examples of EFT applications include precision measurements of rare decays that can be described by QCD with its approximate chiral symmetry, or heavy quarks at finite temperature and density. EFT is also central to a deeper understanding of the so-called flavour anomalies, enabling comparisons between theory and experiment in terms of particular Wilson coefficients.
A novel global lecture series titled “All things EFT” was launched at CERN in autumn 2020 as a cross-cutting online series focused on the universal concept of EFT, and its application to the many areas where it is now used as a core tool in theoretical physics. Inaugurated in a formidable historical lecture by the late Steven Weinberg, who reviewed the emergence and development of the idea of EFT through to its perception nowadays as encompassing all of quantum field theory and beyond, the lecture series has amassed a large following that is still growing. The series featured outstanding speakers, world-leading experts from cosmology to fluid dynamics, condensed-matter physics, classical and quantum gravity, string theory, and of course particle physics – the birthing bed of the powerful EFT framework. The second year of the series was kicked off in a lecture dedicated to the memory of Weinberg by Howard Georgi, who looked back on the development of heavy-quark effective theory and its immediate aftermath.
Moreover, precision measurements of Higgs and electroweak observables at the LHC and future colliders will provide opportunities to detect new physics signals, such as resonances in invariant mass plots, or small deviations from the SM, seen in tails of distributions for instance at the HL-LHC – testing the perception of the SM as a low-energy incarnation of a more fundamental theory being probed at the electroweak scale. This is dubbed the SMEFT (SM EFT) or HEFT (Higgs EFT), depending on whether the Higgs fields are expressed in terms of the Higgs doublet or the physical Higgs boson. This particular EFT framework has recently been implemented in the data-analysis tools at the LHC, enabling the analyses across different channels and even different experiments (see “LHC physics” image). At the same time, the study of SMEFT and HEFT has sparked a plethora of theoretical investigations that have uncovered its remarkable underlying features, for example allowing EFT to be extended or placing constraints on the EFT coefficients due to Lorentz invariance, causality and analyticity.
EFTs in gravity
Since the inception of EFT, it was believed that the framework is applicable only to the description of quantum field theories for capturing the physics of elementary particles at high-energy scales, or alternatively at very small length scales. Thus, EFT seemed mostly irrelevant regarding gravitation, for which we are still lacking a full theory valid at quantum scales. The only way in which EFT seemed to be pertinent for gravitation was to think of general relativity as a first approximation to an EFT description of quantum gravity, which indeed provided a new EFT perspective at the time. However, in the past decade it has become widely acknowledged that EFT provides a powerful framework to capture gravitation occurring completely across large length scales, as long as these scales display a clear hierarchy.
The most notable application to such classical gravitational systems came when it was realised that the EFT framework would be ideal to handle gravitational radiation emitted at the inspiral phase of a binary of compact objects, such as black holes. At this phase in the evolution of the binary, the compact objects are moving at non-relativistic velocities. Using the small velocity as the expansion parameter exhibits the separation between the various characteristic length scales of the system. Thus, the physics can be treated perturbatively. For example, it was found that even couplings manifestly change in classical systems across their characteristic scales, which was previously believed to be unique to quantum field theories. The application of EFT to the binary inspiral problem has been so successful that the precision frontier has been pushed beyond the state of the art, quickly surpassing the reach of work that has been focused on the two-body problem for decades via traditional methods in general relativity.
This theoretical progress has made an even broader impact since the breakthrough direct discovery of gravitational waves (GWs) was announced in 2016. An inspiraling binary of black holes merged into a single black hole in less than a split second, releasing an enormous amount of energy in the form of GWs, which instigated even greater, more intense use of EFTs for the generation of theoretical GW data. In the coming years and decades, a continuous increase in the quantity and quality of real-world GW data is expected from the rapidly growing worldwide network of ground-based GW detectors, and future space-based interferometers, covering a wide range of target frequencies (see “Next generation” image).
EFTs in cosmology
Cosmology is inherently a cross-cutting domain, spanning scales over about 1060 orders of magnitude, from the Planck scale to the size of the observable universe. As such, cosmology generally cannot be expected to be tackled directly by each of the fundamental theories that capture particle physics or gravity. The correct description of cosmology relies heavily on the work in many disparate areas of research in theoretical and experimental physics, including particle physics and general relativity among many more.
The development of EFT applications in cosmology – including EFTs of inflation, dark matter, dark energy and even EFTs of large-scale structure – has become essential to make observable predictions in cosmology. The discovery of the accelerated expansion of the universe in 1998 shows our difficulty in understanding gravity both at the quantum regime and the classical one. The cosmological constant problem and dark-matter paradigm might be a hint for alternative theories of gravity at very large scales. Indeed, the problems with gravity in the very-high and very-low energy range may well be tied together. The science programme of next-generation large surveys, such as ESA’s Euclid satellite (see “Expanding horizons” image), rely heavily on all these EFT applications for the exploitation of the enormous data that is going to be collected to constrain unknown cosmological parameters, thus helping to pinpoint viable theories.
The future of EFTs in physics
The EFT framework plays a key role at the exciting and rich interface between theory and experiment in particle physics, gravity and cosmology as well as in other domains, such as condensed-matter physics, which were not covered here. The technology for precision measurements in these domains is constantly being upgraded, and in the coming years and decades we are heading towards a growing influx of real-world data of higher quality. Future particle-collider projects, such as the Future Circular Collider at CERN, or China’s Circular Electron Positron Collider, are being planned and developed. Precision cosmology is also thriving, with an upcoming next-generation of very large surveys, such as the ground-based LSST, or space-based Euclid. GW detectors keep improving and multiplying, and besides those that are currently operating many more are planned, aimed at measuring various frequency ranges, which will enable a richer array of sources and events to be found.
EFTs provide the theoretical framework to probe new physics and to establish precision programmes at experiments across all domains of physics
Half a century after the concept has formally emerged, effective field theory is still full of surprises. Recently, the physical space of EFTs has been studied as a fundamental entity in its own right. These studies, by numerous groups worldwide, have exposed a new hidden “totally positive’’ geometric structure dubbed the EFT-hedron that constrains the EFT expansion in any quantum field theory, and even string theory, from first principles, including causality, unitarity and analyticity, to be satisfied by any amplitudes of these theories. This recent formal progress reflects the ultimate leap in the perception of EFT nowadays as the most fundamental and most generic theory concept to capture the physics of nature at all scales. Clearly, in the vast array of formidable open questions in physics that still lie ahead, effective field theory is here to stay – for good.
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