Physics Archives – Page 32 of 144

Electroweak baryogenesis

**Bubble nucleation** Simulation of Higgs-bubble nucleation and expansion history during a ﬁrst-order electroweak phase transition. Source: *JCAP* 04 014

Precision measurements of the Higgs boson open the possibility to explore the moment in cosmological history when electroweak symmetry broke and elementary particles acquired mass. Ten years after the Higgs-boson discovery, it remains a possibility that the electroweak phase transition happened as a rather violent process, with a large departure from thermal equilibrium, via Higgs-bubble nucleations and collisions. This is a fascinating scenario for three reasons: it provides a framework for explaining the matter–antimatter asymmetry of the universe; it predicts the existence of at least one new weak-scale scalar ﬁeld and thus is testable at colliders; and it would leave a unique signature of gravitational waves detectable by the future space-based interferometer LISA.

One major failure of the Standard Model (SM) is its inability to explain the baryon-to-photon ratio in the universe: η ≈ 6 × 10^–10. Measurements of this ratio from two independent approaches – anisotropies in the cosmic microwave background and the abundances of light primordial elements – are in beautiful agreement. In a symmetric universe, however, the prediction for η is a billion times smaller; big-bang nucleosynthesis could not have occurred and structures could not have formed. This results from strong annihilations between nucleons and antinucleons, which deplete their number densities very efficiently. Only in a universe with a primordial asymmetry between nucleons and antinucleons can these annihilations be prevented. There are many different models to explain such “baryogenesis”. Interestingly, however, the Higgs boson plays a key role in essentially all of them.

Accidental symmetry

It is worth recalling how baryon number B gets violated by purely SM physics. B is an “accidental” global symmetry in the SM. There are no B-violating couplings in the SM Lagrangian. But the chiral nature of electroweak interactions, combined with the non-trivial topology of the SU(2) gauge theory, results in non-perturbative, B-violating processes. Technically, these are induced by extended gauge-ﬁeld conﬁgurations called sphalerons, whose energy is proportional to the value of the Brout–Englert–Higgs (BEH) field. The possibility of producing these conﬁgurations is totally suppressed at zero temperature, such that B is an extremely good symmetry today. However, at high temperature, and in particular at 100 GeV or so, when the electroweak symmetry is unbroken, the baryon number is violated intensively as there is no energy cost. Since both baryons and antibaryons are created by sphalerons, charge–parity (CP) violation is needed. Indeed, as enunciated by Sakharov in 1967, a theory of baryogenesis requires three main ingredients: B violation, CP violation and a departure from equilibrium, otherwise the baryon number will relax to zero.

The conclusion is that baryogenesis must take place either from a mechanism occurring before the electroweak phase transition (necessitating new sources of B violation beyond the SM) or from a mechanism where B-violation relies exclusively on SM sphalerons and occurring precisely at the electroweak phase transition (provided that it is sufficiently out-of-equilibrium and CP-violating). The most emblematic example in the ﬁrst category is leptogenesis, where a lepton asymmetry is produced from the decay of heavy right-handed neutrinos and “reprocessed” into a baryon asymmetry by sphalerons. This is a popular mechanism motivated by the mystery of the origin of neutrino masses, but is difficult to test experimentally. The second category, electroweak baryogenesis, involves electroweak-scale physics only and is therefore testable at the LHC.

Electroweak baryogenesis requires a ﬁrst-order electroweak phase transition to provide a large departure from thermal equilibrium, otherwise the baryon asymmetry is washed out. A prime example of this type of phase transition is boiling water, where bubbles of gas expand into the liquid phase. During a ﬁrst-order electroweak phase transition, symmetric and broken phases coexist until bubbles percolate and the whole universe is converted into the broken phase (see “Bubble nucleation” image). Inside the bubble, the BEH field has a non-zero vacuum expectation value; outside the bubble, the electroweak symmetry is unbroken. As the wall is passing, chiral fermions in the plasma scatter off the Higgs at the phase interface. If some of these interactions are CP-violating, a chiral asymmetry will develop inside and in front of the bubble wall. The resulting excess of left-handed fermions in front of the bubble wall can be converted into a net baryon number by the sphalerons, which are unsuppressed in the symmetric phase in front of the bubble. Once inside the bubble, this baryon number is preserved as sphalerons are frozen there. In this picture, the baryon asymmetry is determined by solving a diffusion system of coupled differential equations.

New scalar required

The nature of the electroweak phase transition in the SM is well known: for a 125 GeV Higgs boson, it is a smooth crossover with no departure from thermal equilibrium. This prevents the possibility of electroweak baryogenesis. It is, however, easy to modify this prediction to produce a ﬁrst-order transition by adding an electroweak-scale singlet scalar ﬁeld that couples to the Higgs boson, as predicted in many SM extensions. Notably, this is a general feature of composite-Higgs models, where the Higgs boson emerges as a “pseudo Nambu–Goldstone” boson of a new strongly-interacting sector.

Stochastic gravitational-wave background — **Primordial peak** The stochastic gravitational-wave background inherited from a ﬁrst-order electroweak phase transition (red) compared to the much broader backgrounds expected from inﬂation (black) and cosmic strings (blue), as well as sensitivity curves of future experiments. Credit: P Simakachorn

An important consequence of such models is that the BEH field is generated only at the TeV scale; there is no field at temperatures above that. In the minimal composite Higgs model, the dynamics of the electroweak phase transition can be entirely controlled by an additional scalar Higgs-like ﬁeld, the dilaton, which has experimental signatures very similar to the SM Higgs boson. In addition, we expect modiﬁcations of the Higgs boson’s couplings (to gauge bosons and to itself) induced by its mixing with this new scalar. LHC Run 3 thus has excellent prospects to fully test the possibility of a ﬁrst-order electroweak phase transition in the minimal composite Higgs model.

The properties of the additional particle required to modify the electroweak phase transition also suggest new sources of CP violation, which is welcome as CP-violating SM processes are not sufficient to explain the baryon asymmetry. In particular, this would generate non-zero electric dipole moments (EDMs). The most recent bounds on the electron EDM from the ACME experiment in the US placed stringent constraints on a large number of electroweak baryogenesis models, in particular two-Higgs-doublet models. This is forcing theorists to consider new paths such as dynamical Yukawa couplings in composite Higgs models, a higher temperature for the electroweak phase transition, or the use of dark particles as the new source of CP violation. Here, there is a tension. To evade the stringent EDM bounds, the new scalar has to be heavy. But if it is too heavy, it reheats the universe too much at the end of the electroweak phase transition and washes out the just-produced baryon asymmetry. During the next decade, precise measurements of the Higgs boson at the LHC will enable a deﬁnitive test of the electroweak baryogenesis paradigm.

Gravitational waves

There is a further striking consequence of a ﬁrst-order electroweak phase transition: fluid velocities in the vicinity of colliding bubbles generate gravitational waves (GWs). Today, these would appear as a stochastic background that is homogeneous, isotropic, Gaussian and unpolarised – the superposition of GWs generated by an enormous number of causally-independent sources, arriving at random times and from random directions. It would appear as noise in GW detectors with a frequency (in the mHz region) corresponding to the typical inverse bubble size, redshifted to today (see “Primordial peak” figure). There has been a burst of activity in the past few years to evaluate the chances of detecting such a peaked spectrum at the future space interferometer LISA, opening the fascinating possibility of learning about Higgs physics from GWs.

The results from the LHC so far have pushed theorists to question traditional assumptions about where new physics beyond the SM could lie. Electroweak baryogenesis relies on rather conservative and minimal assumptions, but more radical approaches are now being considered, such as the intriguing possibility of a cosmological interplay between the Higgs boson and a very light and very weakly-coupled axion-like particle. Through complementarity of studies in theory, collider experiments, EDMs, GWs and cosmology, probing the electroweak phase transition will keep us busy for the next two decades. There are exciting times ahead.

Synergy at the Higgs frontier

**Joined up** Sally Dawson is leader of the high-energy theory group at Brookhaven National Laboratory. Credit: BNL

What impact did the discovery of the Higgs boson have on your work?

It was huge because before then it was possible that maybe there was no Higgs. You could have some kind of dynamical symmetry breaking, or maybe a heavy Higgs, at 400 GeV say, which would be extremely interesting but completely different. So once you knew that the Higgs was at the same mass scale as the W and the Z, our thinking changed because that comes out of only a certain kind of model. And of course once you had it, everyone, including myself, was motivated to calculate everything we could.

I am working on how you tease out new physics from the Higgs boson. It’s the idea that even if we don’t see new particles at the LHC, precision measurements of the Higgs couplings are going to tell us something about what is happening at very high energy scales. I’m using what’s called an effective field theory approach, which is the standard these days for trying to find out what we can learn from combining Higgs measurements with other types of measurements, such as gauge-boson pair production and top-quark physics.

Aside from the early formal work, what was the role of Standard Model calculations in the discovery of the Higgs boson?

You had to know what you were looking for, because there’s so many events at the LHC. Otherwise, it would be like looking for a needle in a haystack. The Higgs was discovered, for example, by its decay to two photons and there are millions of two-photon events at the LHC that have nothing to do with the Higgs. Theory told you how to look for this particle, and I think it was really important that a trail was set out to follow. This involves calculating how often you make a Higgs boson and what the background might look like. It wasn’t until the late 1980s that people began taking this seriously. It was really the Superconducting Super Collider that started us thinking about how to observe a Higgs at a hadron collider. And then there were the LEP and Tevatron programmes that actively searched for the Higgs boson.

To what order in perturbation theory were those initial calculations performed?

For the initial searches you didn’t need the complicated calculations because you weren’t looking for precision measurements such as those required at the Z-pole, for example. You really just needed the basic rate and background information. We weren’t inspired to do higher order calculations until later in the game. When I was a postdoc at Berkeley in 1986, that’s when I really started to calculate things about the Higgs. But there was a long gap between the time when the Brout–Englert–Higgs mechanism was proposed and when people really started doing some hard calculations. There’s the famous paper in 1976 by Ellis, Gaillard and Dimopoulos that calculated how the Higgs might be observed, but in essence it said: why bother looking for this thing, we don’t know where it is! So people were thinking we could see the Higgs in kaon decays, if it was very light, and in other ways, and were looking at the problem in a global kind of way.

**Was this what drove your involvement with The Higgs Hunter’s Guide in 1990?**

We were further along in terms of calculating things precisely by then, and I suppose there was a bit of a generation gap. It was a wonderful collaboration to produce the guide. We still went through the idea of how you would find the Higgs at different energy scales because we still had no idea where it was. The calculations went into high gear around that time, which was well before the Higgs was discovered. Partly it was the motivation that we were pretty sure we would see it at the LHC. But partly it was developments in theory which meant we could calculate things that we never would have imagined was possible 30 years earlier. The capability of theorists to calculate has grown exponentially.

What have these improvements been?

It’s what they call the next-to-next-to-leading order (NNLO) revolution – a new frontier in perturbative QCD where diagrams with two extra emissions of real or extra loops of virtual partons are accounted for. These were new mathematical techniques for evaluating the integrals that come into the quantum field theory, so not just turning the crank computationally but really an intellectual advance in understanding the structure of these calculations. It started with Bern, Dixon and Kosower, who understood the needed amplitudes in a formal way. This enabled all sorts of calculations, and now we have N³LO calculations for certain Higgs-boson production modes.

What is driving greater precision on Higgs calculations today?

Actually it’s really exciting because at the high-luminosity LHC (HL-LHC), experimentalists will be limited in their understanding of the Higgs boson by theory – the theory and experimental uncertainties will be roughly the same. This is truly impressive. You might think that these higher order corrections, which have quite small errors, are enough but they need to be even smaller to match the expected experimental precision. As theorists we have to keep going and do even better, which from my point of view is wonderful. It’s the synergy between experiment and theory that is the real story. We’re co-dependent. Even now, theory is not so different from ATLAS and CMS in terms of precision. Theory errors are hard things to pin down because you never really know what they are. Unlike an absolute statistical uncertainty, they’re always an estimate.

How do the calculations look for measurements beyond the LHC?

It’s a very different situation at e⁺e^– colliders compared to hadron colliders. The LHC runs with protons containing gluons, so that’s why you need the higher order corrections. At a future e⁺e⁺ collider, you need higher-order corrections but they are much more straightforward because you don’t have parton distribution functions to worry about. We know how to do the calculations needed for an e⁺e^– Future Circular Collider, for example, but there is not a huge community of people working on them. That’s because they are really hard: you can’t just sit down and do them as a hobby, they really need a lot of skills.

You are currently leading the Higgs properties working group of the current Snowmass planning exercise. What has been the gist of discussions?

This is really exciting because our job has essentially been to put together the pieces of the puzzle after the European strategy update in 2020. That process did a very careful job of looking at the future Higgs programme, but there have been developments in our understanding since then. For example, the muon collider might be able to measure the Higgs couplings to muons very precisely, and there has been some good work on how to measure the couplings to strange quarks, which is very hard to do.

**Essential reading** At 425 pages, *The Higgs Hunters Guide* (Basic Books, 1990) offered a comprehensive guide to the physics of Higgs bosons. Credit: Basic Books

I would like to see an e⁺e^– collider built somewhere, anywhere. In point of fact, when you look at the proposals they’re roughly the same in terms of Higgs physics. This was clear from the European strategy report and will be clear from the upcoming Snowmass report. Personally, I don’t much care whether there is a precision of 1% or 1.5% on some coupling. I care that you can get down to that order of magnitude, and that e⁺e^– machines will significantly improve on the precision of HL-LHC measurements. The electroweak programme of large circular e⁺e^– colliders is extremely interesting. At the Z-pole you get some very precise measurements of Standard Model quantities that feed into the whole theory because everything is connected. And at the WW threshold you get very precise measurements in the effective field theory of things that connect the Higgs and WW pairs. As a theorist, it doesn’t make sense to think of the Higgs in a vacuum. The Higgs is part of this whole electroweak programme.

What are the prospects for finding new physics via the Higgs?

The fact that we haven’t seen anything unexpected yet is probably because we haven’t probed enough. I’m absolutely convinced we are going to see something, I just don’t know what (or where) it is. So I can’t believe in the alternative “nightmare” scenario of a Standard-Model Higgs and nothing else because there are just so many things we don’t know. You can make pretty strong arguments that we haven’t yet reached the precision where we would expect to see something new in precision measurements. It’s a case of hard work.

What’s next in the meantime?

The next big thing is measuring two Higgs bosons at a time. That’s what theorists are super excited about because we haven’t yet seen the production of two Higgses and that’s a fundamental prediction of our theory. If we don’t see it, and it’s extremely difficult to do so experimentally, it tells us something about the underlying model. It’s a matter of getting the statistics. If we actually saw it, then we would do more calculations. For the trilinear Higgs coupling we now have a complete calculation at next-to-leading order, which is a real tour de force. The calculations are sufficient for a discovery, and because it’s so rare it’s unlikely we will be doing precision measurements, so it is probably okay for the foreseeable future. For the quartic coupling there are some studies that suggest you might see it at a 100 TeV hadron collider.

With all the Standard Model particles in the bag, does theory take more of a back seat from here?

The hope is that we will see something that doesn’t fit our theory, which is of course what we’re really looking for. We are not making these measurements at ever higher precisions for the sake of it. We care about measuring something we don’t expect, as an indicator of new physics. The Higgs is the only tool we have at the moment. It’s the only way we know how to go.

Top quark weighs in with unparalleled precision

A top-quark pair at the LHC — **Top marks** The classic signature of a top-quark pair at the LHC is four jets (yellow cones), one muon (red line and boxes) and missing energy from a neutrino (pink arrow). Credit: CMS

The CMS collaboration has substantially improved on its measurement of the top-quark mass. The latest result, 171.77 ± 0.38 GeV, presented at CERN on 5 April, represents a precision of about 0.22% – compared to the 0.36% obtained in 2018 with the same data. The gain comes from new analysis methods and improved procedures to consistently treat uncertainties in the measurement simultaneously.

As the heaviest elementary particle, precise knowledge of the top-quark mass is of paramount importance to test the internal consistency of the Standard Model. Together with accurate knowledge of the masses of the W and Higgs bosons, the top-quark mass is no longer a free parameter but a clear prediction of the Standard Model. Since the top-quark mass dominates higher-order corrections to the Higgs-boson mass, a precise measurement of the top mass also places strong constraints on the stability of the electroweak vacuum (see The Higgs and the fate of the universe).

Since its discovery at Fermilab in 1995, the mass of the top quark has been measured with increasing precision using the invariant mass of different combinations of its decay products. Measurements by the Tevatron experiments resulted in a combined value of 174.30 ± 0.65 GeV, while the ATLAS and CMS collaborations measured 172.69 ± 0.48 GeV and 172.44 ± 0.48 GeV, respectively, from the combination of their most precise results from LHC Run 1 recorded at a centre-of-mass energy of 8 TeV. The latter measurement achieved a relative precision of about 0.28%. In 2019, the CMS collaboration also experimentally investigated the running of the top quark mass – a prediction of QCD that causes the mass to vary as a function of energy – for the first time at the LHC.

The LHC produces top quarks predominantly in quark–antiquark pairs via gluon fusion, which then decay almost exclusively to a bottom quark and a W boson. Each tt event is classified by the subsequent decay of the W bosons. The latest CMS analysis uses semileptonic events – where one W decays into jets and the other into a lepton and a neutrino – selected from 36 fb^–1 of Run 2 data collected at a centre-of-mass energy of 13 TeV. Five kinematical variables, as opposed to up to three in previous analyses, were used to extract the top-quark mass. While the extra information in the fit improved the precision of the measurement in a novel and unconventional way, it made the analysis significantly more complicated. In addition, the measurement required an extremely precise calibration of the CMS data and an in-depth understanding of the remaining experimental and theoretical uncertainties and their interdependencies.

The final result, 171.77 ± 0.38 GeV, which includes 0.04 GeV statistical uncertainty, is a considerable improvement compared to all previously published top-quark mass measurements and supersedes the previously published measurement in this channel using the same data set.

“The cutting-edge statistical treatment of uncertainties and the use of more information have vastly improved this new measurement from CMS,” says Hartmut Stadie of the University of Hamburg, who contributed to the result. “Another big step is expected when the new approach is applied to the more extensive dataset recorded in 2017 and 2018.”

Dead-cone effect exposed by ALICE

**Showering** A charm quark in a parton shower loses energy by emitting gluons. The shower displays a “dead cone” of suppressed radiation around the quark for angles smaller than the ratio of the quark’s mass and energy, causing the cone size to increase at each stage of the shower. Credit: D Dominguez/CERN-GRAPHICS-2022-015-7

More than 30 years after it was predicted, a phenomenon in quantum chromodynamics (QCD) called the dead-cone effect has been directly observed by the ALICE collaboration. The result, reported in Nature on 18 May, not only confirms a fundamental feature of the theory of the strong force, but enables a direct experimental observation of the non-zero mass of the charm quark in the partonic phase.

In QCD, the dead-cone effect predicts a suppression of gluon bremsstrahlung from a quark within a cone centred on the quark’s flight direction. This cone has an angular size m_q/E, where m_q is the mass of the quark and E is its energy. The effect arises due to the conservation of angular momentum during the gluon emission and is significant for low-energy heavy-flavour quarks.

The dead cone has been indirectly observed at particle colliders. A direct observation from the parton shower’s radiation pattern has remained challenging, however, because it relies on the determination of the emission angle of the gluon, as well as the emitting heavy-flavour quark’s energy, at each emission vertex in the parton shower (see “Showering” figure). This requires a dynamic reconstruction of the cascading quarks and gluons in the shower from experimentally accessible hadrons, which had not been possible until now. In addition, the dead-cone region can be obscured and filled by other sources such as the decay products of heavy-flavour hadrons, which must be removed during the measurement.

To observe the dead-cone effect directly, ALICE used jets tagged with a reconstructed D⁰-meson in a 25 nb^–1sample of pp collisions at a centre-of-mass-energy of 13 TeV collected between 2016 and 2018. The D⁰-mesons were reconstructed with transverse momenta between 2 and 36 GeV/c through their decay into a kaon and pion pair. Jet-finding was then performed on the events with the “anti-k_T” algorithm, and jets with the reconstructed D⁰-meson amongst their constituents were tagged. The team used recursive jet-clustering techniques to reconstruct the gluon emissions from the radiating charm quark by following the branch containing the D⁰-meson at each de-clustering step, which is equivalent to following the emitting charm quark through the shower. A similar procedure was carried out on a flavour-untagged sample of jets, which contain primarily gluon and light-quark emissions and form a baseline where the dead-cone effect is absent.

Comparisons between the gluon emissions from charm quarks and from light quarks and gluons directly reveal the dead-cone effect through a suppression of gluon emissions from the charm quark at small angles, compared to the emissions from light quarks and gluons. Since QCD predicts a mass-dependence of the dead cones, the result also directly exposes the mass of the charm quark, which is otherwise inaccessible due to confinement. ALICE’s successful technique to directly observe a parton shower’s dead cone may therefore offer a way to measure quark masses.

The upgraded ALICE detector in LHC Run 3 will enable an extension of the measurement to jets tagged with a B⁺ meson. This will allow the reconstruction of gluon emissions from beauty quarks which, due to their larger mass, are expected to have a larger dead cone than charm quarks. Comparisons between the angular distribution of gluon emissions from beauty quarks and those from charm quarks will isolate mass-dependent effects in the shower and remove the contribution from effects pertaining to the differences between quark and gluon fragmentation, bringing deeper insights into the intriguing workings of the strong force.

Probing new physics with the Higgs boson

ATLAS figure 1 — **Fig. 1.** Observed (solid) and expected (dashed) upper limits at 95% CL on the production-cross section for pp → Wʹ → WH. The green (yellow) band indicates ±1 (±2) standard deviations from the expected limits. Source: ATLAS-CONF-2021-026

Due to its connection to the process of electroweak symmetry breaking, the Higgs boson plays a special role in the Standard Model (SM). Its properties, such as its mass and its couplings to fermions and bosons, have been measured with increasing precision. For these reasons, the Higgs boson has become an ideal tool to conduct new-physics searches. Prominent examples are direct searches for new heavy particles decaying into Higgs bosons or searches for exotic decays of the Higgs boson. Such phenomena have been predicted in many extensions of the SM motivated by long-standing open questions, including the hierarchy problem, dark matter and electroweak baryogenesis. Examples of new particles that couple to the Higgs boson are heavy vector bosons (as in models with Higgs compositeness or warped extra dimensions) and additional scalar particles (as in supersymmetric models or axion models).

Searches for resonances

The ATLAS collaboration recently released results of a search for a new heavy particle decaying into a Higgs and a W boson. The search was performed by probing for a localised excess in the invariant mass distribution of the ℓνbb final state. As no such excess was found, upper limits at 95% confidence level were set on the production-cross section times branching ratio of the new heavy resonance (figure 1). The results were also interpreted in the context of the heavy vector triplet (HVT) model, which extends the SM gauge group by an additional SU(2) group, to constrain the coupling strengths of heavy vector bosons to SM particles. In two HVT benchmark models, W′ masses below 2.95 and 3.15 TeV are excluded.

ATLAS figure 2 — **Fig. 2.** Invariant mass distribution of the two jets considered in the search for Higgs-boson decays into invisible particles for the vector-boson fusion production process. The signal (dashed red line) scaled to a branching ratio of 15% for Higgs-boson decays tends to higher masses, corresponding to large angular separation of the jets. Source: arXiv:2202.07953

Rare or exotic decays are excellent candidates to search for weakly coupled new physics. The Higgs boson is particularly sensitive to such new physics owing to its narrow total width, which is three orders of magnitude smaller than that of the W and Z bosons and the top quark. Several searches for exotic decays of the Higgs boson have been carried out by ATLAS, and they may be broadly classified as those scenarios where the possible new daughter particle decays promptly to SM particles, and those where it would be long-lived or stable.

A recent search from ATLAS targeted exotic decays of the Higgs boson into a final state into four electrons or muons, which benefit from a very clean experimental signature. Although a signal was not observed, the search put stringent constraints on decays to new light scalar bosons – particularly in the low mass range of a few GeV – and to new vector bosons, dubbed dark Z bosons or dark photons, in the mass range up to a few tens of GeV. Depending on the new-physics model, this search can exclude branching ratios of the Higgs boson to new particles as low as O(10^–5).

Invisibles

Another interesting possibility is the case where the Higgs boson decays to particles that are invisible in the detector, such as dark-matter candidates. To select such events, different strategies are pursued depending on the particles produced in association with the Higgs boson. The most powerful channel for such a search is the vector-boson fusion production process, where two energetic jets from quarks are produced with large angular separation alongside the invisibly decaying Higgs boson (figure 2). Another sensitive channel is the associated production of a Higgs boson with a Z boson that decays to a pair of leptons. Improvements in background predictions have made it possible to reach a sensitivity down to 10% on the branching ratio of invisible Higgs-boson decays, while the corresponding observed limit amounts to 15%.

These searches will greatly benefit from the large datasets expected in Run 3 and later High-Luminosity LHC runs, and will enable searches for even more feeble couplings of new particles to the Higgs boson.

Upsilon suppression in heavy-ion collisions

CMS figure 1 — **Fig. 1.** The nuclear modification factor R_AA of the three ϒ states, as a function of <N_part> (besides the centrality-integrated values). The error bars (boxes) represent the statistical (systematic) uncertainties. The boxes at unity represent global systematic uncertainties, for both the ϒ(2S) and ϒ(3S) points (open), and for only the ϒ(2S) (purple) or ϒ(3S) (green) mesons. Source: CMS-PAS-HIN-21-007

The bound states of a heavy quark and its antiquark, called quarkonia, have long been regarded as ideal probes to study the quark–gluon plasma (QGP) formed in high-energy heavy-ion collisions. The golden signature is the suppression of their production yield in lead–lead (PbPb) collisions with respect to extrapolations from proton–proton (pp) collisions, caused by modifications of the binding potential in the QGP. The suppression of the different quarkonium states is expected to depend on their binding energies. Quarkonia can also be produced by recombination processes. The ϒ states (bound states of b quarks and antiquarks) are much less affected by recombination effects than charmonium states, given the very small probability that b quarks are produced. A comparison of their suppression patterns is particularly informative because of the different binding energies of the ϒ(1S), ϒ(2S) and ϒ(3S) states.

The suppression of quarkonium production is quantified via the nuclear modification factor R_AA, defined as the ratio between the yield in nucleus–nucleus (AA) collisions and the yield extrapolated from pp data. Previous measurements of R_AA for the ϒ mesons by experiments at RHIC and the LHC revealed a significant suppression of the ϒ(1S) state and a larger suppression for the ϒ(2S) state. However, these experiments could only set upper limits for the ϒ(3S) state due to its very low production yield. The CMS experiment recently changed this situation by presenting the first observation of the ϒ(3S) meson in heavy-ion collisions. The ϒ mesons are detected using their decay to two muons. The analysis used the large PbPb data sample collected in 2018 and extracted the ϒ(3S) signals from the large background of muon pairs by using a boosted decision tree algorithm.

The new R_AA results are shown together with the previously published ϒ(1S) values as a function of the average number of nucleons participating in the PbPb collisions, <N_part> (figure 1). Collisions with larger <N_part> show a bigger overlap between the two nuclei, producing a larger and hotter QGP. As previously observed, the degree of suppression increases from peripheral to central collisions, i.e. as N_part increases, indicating a more substantial dissociation effect at higher QGP temperatures. The new ϒ(3S) suppression measurement completes the picture of suppression patterns for five different quarkonium states, which was started 35 years ago at the CERN SPS with the J/ψ and ψ(2S) results of NA38. The stage is set for a deeper understanding of deconfinement in the QGP.

X-ray polarisation probes extreme physics

Accretion disk around magnetar 4U 0142+61 — **Magnetar** Artistic depiction of the accretion disk around the magnetar 4U 0142+61, located in the Cassiopeia constellation 13,000 lights years away. Credit: NASA/JPL-Caltech/R Hurt (SSC)

X-ray astronomy has been around for more than 50 years and remains responsible for a wealth of discoveries. Astronomical breakthroughs have been the result of detailed measurements of the X-ray arrival time, direction and energy. But the fourth measurable parameter of X-rays, their polarisation, remains largely unexplored. Following the first rough measurements of a handful of objects in the 1970s by Martin Weisskopf and co-workers, there was a hiatus in X-ray polarimetry due to the complexity of the detection mechanism. In recent years, in parallel with the emergence of gamma-ray polarimetry, interest in the field has returned. Indeed, after some initial measurements using the Chinese–Italian PolarLight Cubesat launched in October 2018, X-ray polarimetry has reached full maturity with the launch of the first large-scale dedicated observatory in December 2021: the Imaging X-ray Polarimetry Explorer (IXPE), a joint project by NASA and the Italian Space Agency, led by Weisskopf.

The IXPE mission uses gas pixel detectors to measure the polarisation for a range of astronomical sources in the 2-8 keV energy range. Incoming X-rays are absorbed in a gas which results in the emission of a photoelectron, the azimuthal emission direction of which is correlated with the polarisation vector of the incoming photon. Tracking the path of the electron therefore allows the polarisation to be inferred. Accurately measuring the emission direction of the low-energy photoelectron, especially in a space-based detector, has been one of the main IXPE challenges and required decades of detector development.

X-ray polarimetry has reached full maturity with the launch of the first large-scale dedicated observatory

IXPE has already observed a range of sources. Its first public results, posted on arXiv on 18 May, concern a magnetar, a highly magnetic neutron star, called 4U 0142+61, which rotates around its axis in about 8 s and has a magnetic field of 10¹⁰ T. IXPE’s first ever measurement of polarised emission from a magnetar in the X-ray region shows this extreme object to have an energy-integrated polarisation degree of 12%, while in the thermal (2–4 keV) range this is about 12%, and as high as 41% for emission at higher energies (5.5–8 keV). The polarisation angles of the two emission components are orthogonal.

The results appear to agree best with a model where the thermal emission stems from a condensed iron atmosphere: the higher energy emission would be a result of some thermal photons being up-scattered to higher energies when interacting with charged particles following the magnetic field lines. However, since other models link the emission to a gaseous atmosphere heated by a constant bombardment of particles, measurements of additional magnetars are needed.

Fundamental physics

Apart from providing novel insights into neutron-star properties, time-resolved studies of the emission during the rotation period hints at more fundamental physics at play. The spectral profile of 4U 0142+61 was found to be rather constant during the rotation, indicating that the emission does not come from hot-spots, such as the poles, but rather from a large area on the surface. As the magnetic field over such a large area would, however, be expected to vary significantly, so would the polarisation angle of the emitted X-rays. As a result, the net polarisation seen on Earth would largely be blurred out, resulting in a much lower polarisation degree than is observed.

An intriguing explanation for this, note the authors, is vacuum birefringence – an effect predicted to be important in the presence of extreme magnetic fields, but which has never been observed. While for the magnetar the polarisation angle of the emission varies with the emission location, it gets altered as the photons travel through the strong magnetic field in which continuous electron–positron pairs affect their propagation. Only when the magnetic field is weak enough, at around 100 times the radius of the star, does the polarisation angle get frozen. Since this angle is aligned with the magnetic field, which at this point is smoother, the emission will realign the emission travelling towards Earth and allow for a net polarisation.

Although the polarisation degrees measured by IXPE are not high enough to definitively prove vacuum birefringence, the results give a clear hint. Furthermore, the measurements of 4U 0142+61 are only the first of many performed by the IXPE team. Throughout the coming months, detailed measurements of galactic objects such as the Crab Nebula, as well as extra-galactic sources, are predicted to be released. Among these objects there will be other magnetars, the X-ray emission from which will soon bring further understanding of these extreme objects and potentially confirm the existence of vacuum birefringence.

Higgs Hunting

The origin of electroweak symmetry breaking is one of the central topics of research in fundamental physics. The discovery of a Higgs boson at CERN on 4 July 2012, following a hunt that spanned several decades and multiple colliders, changed the landscape of these investigations and provided key evidence for the Brout–Englert–Higgs mechanism of mass generation through the spontaneous breaking of Electroweak symmetry.

Almost ten years later, the hunt goes on several fronts, in particular for:

New physics through precision studies of the properties of the Higgs boson: in particular its mass, spin and couplings to other Standard Model particles.
New production and decay modes, in particular in processes involving multiple Higgs bosons which provide key insight into the shape of the Higgs potential.
New Higgs-like states and signals for physics beyond the Standard Model.

The 12^th workshop of the Higgs Hunting series organised on 12–14 September 2022 will present an overview of these topics, focusing in particular on new developments in the LHC Run-2 analyses, detailed studies of Higgs boson properties and possible deviations from Standard Model predictions. Highlights will also include a first look at LHC Run-3 analyses, prospects from studies at future colliders, and recent theoretical developments.

Thermonuclear explosions fuel cosmic rays

The RS Ophiuchi outburst — **Shocking** An artist’s impression of the RS Ophiuchi outburst. Credit: DESY/H.E.S.S.

Normally, RS Ophiuchi is a faint astronomical object at a distance of about 5000 light years from Earth. Once every 15 years or so, however, it brightens dramatically to the point it becomes visible to the naked eye, only to disappear again within several days. This object, classified as a recurrent nova, is not a single star but rather a binary system consisting of a white dwarf and a red giant. Due to the proximity of the white dwarf to its massive companion, it slowly accumulates matter from which it forms a thin atmospheric-like layer on its surface. Over time, this atmosphere becomes denser and heats up until it reaches a critical temperature of around 20 million K. The thermonuclear explosion initiated at this temperature rapidly spreads across the dwarf’s surface, causing all the remaining material to be blown away. This process, which in the case of RS Ophiuchi occurs between every 9 to 26 years, makes the object visible in the optical region. However, the process has also been theorised to be capable of producing cosmic rays.

Bipolar shape

The first recorded explosion on RS Ophiuchi was in 1898 after it was discovered in optical images by Williamina Fleming in 1905. A more recent explosion in 2006 was observed in detail by Hubble, while the last one occurred in August 2021. Hubble’s 2006 images show a shock wave propagating from the object. The shock, which is originally radially symmetric, gets distorted by the gas present in the orbital plane of the binary system. This gas slows down the shock in the orbital plane, leading to a final bipolar shape capable of accelerating electrons and hadrons to high energies. These accelerated charged particles can reach Earth in the form of cosmic rays, but due to the influence of magnetic fields it is not possible to directly trace these back to the source. The high-energy gamma rays produced by some of these cosmic rays, on the other hand, do point directly to the source. Gamma rays formed in this way during the 2021 explosion have recently been used by the H.E.S.S. collaboration to test cosmic-ray acceleration models.

After the initial detection of the brightening of the source in optical wavelengths, the ground-based H.E.S.S. facility in Namibia pointed its five telescopes (which are sensitive to the Cherenkov light emitted as TeV gamma rays induce showers in the atmosphere) to the source. In parallel, the space-based Fermi–LAT telescope, which directly detects gamma rays in the ~100 MeV to ~500 GeV energy range, observed the target for a duration of several weeks. The emission measured by both telescopes as a function of time shows the maximum energy flux as measured by Fermi–LAT peaking about one day after the peak in optical brightness. For H.E.S.S., which covered the 250 GeV to 2.5 TeV energy range, the peak only occurred three days after the optical peak, indicating a significant hardening of the emission spectrum with time.

Hadronic origin

These results match what would be expected from a hadronic origin of these gamma rays. The shock wave produced by the thermonuclear explosion is capable of accelerating charged particles every time they traverse the shock. Magnetic fields, which are in part induced by some of the accelerated hadrons themselves, trap the charged particles in the region, thereby allowing these to traverse the shock many times. Some of the hadrons collide with gas in the surrounding medium to produce showers in which neutral pions are produced, which in turn produce the gamma rays detected on Earth. The maximum energy of these gamma rays is about an order of magnitude lower than the hadrons that induced the showers. This implies that one day after the explosion, hadrons had been accelerated up to 1 TeV, producing the photons detected by Fermi–LAT, while it took an additional two days for the source to further accelerate such hadrons up to the 10 TeV required to produce the emission visible to H.E.S.S. These timescales, as well as the measured energies, match with the theoretical predictions for sources with the same size and energy as RS Ophiuchi.

The results show a clear correlation between the theoretical predictions of hadronic production of gamma rays by recurring novae

The results, published in Science by the H.E.S.S. collaboration, show a clear correlation between the theoretical predictions of hadronic production of gamma rays by recurring novae. The alternative theory of a leptonic origin of the gamma rays is more difficult to fit due to the relatively large fraction of the shock energy that would need to be converted into electron acceleration. The measurements form an almost direct way to test models of the origin of cosmic rays and thereby add several important pieces to the puzzle of cosmic-ray origins.

The search for new physics: take three

**Striking out** An ATLAS mono-jet event containing a single energetic jet and large missing transverse energy. Credit: ATLAS

Aside from the discovery of the Higgs boson, the absence of additional elementary-particle discoveries is the LHC’s main result so far. For many physicists, it is also the more surprising one. Such further discoveries are suggested by the properties of the Higgs boson, which are now established experimentally to a large extent. The Higgs boson’s low mass, despite its susceptibility to quantum corrections from heavy particles that should push it orders-of-magnitude higher, and its hierarchy of coupling strengths to fermions present extreme, “unnatural” values that so far lack an explanation. Therefore, searches for new physics at the TeV energy scale remain strongly motivated, irrespective of the no-show so far.

Naturalness has triggered the development of many new-physics models, but the large extent of their parameter space allows them to evade exclusion again and again. Whereas the discoveries of the past decades, including that of the Higgs boson, were driven by precise quantitative predictions, the search for physics beyond the Standard Model (SM) simply requires more perseverance.

LHC Run 3 will bring long-awaited new insights to the question of naturalness with respect to Higgs physics, as well as to many other SM puzzles such as the nature of dark matter or the cosmological matter–antimatter asymmetry. With considerably more data and a slightly higher centre-of-mass energy than at Run 2, in addition to new triggers and improved event reconstruction and physics-analysis techniques, a significant increase in sensitivity compared to the current results will be achieved. Searches for new phenomena with Run 3 data will also benefit from a much improved definition of the physics targets, thanks to information gathered during Run 2 and the various anomalies observed at lower energies.

The story so far

During the past 12 years, a broad search programme has emerged at the LHC in parallel with precision measurements (see “Pushing the precision frontier”). Initially, the most favoured new-physics scenario was supersymmetry (SUSY), a new fermion–boson symmetry that gives rise to supersymmetric partners of SM particles and naturally leads to a light Higgs boson close to the masses of the W and Z bosons. SUSY is expected to produce events containing jets and missing transverse energy (MET), the study of which at Run 2 placed exclusion limits on gluino masses as high as 2.3 TeV. More challenging searches for stop quarks, with background processes up to a million times more frequent than the predicted signal, were also performed thanks to the excellent performance of the ATLAS and CMS detectors. Yet, no signs of stops have been found up to a mass of 1.3 TeV, excluding a sizeable fraction of the SUSY parameter space suggested by naturalness arguments. Further SUSY searches were performed, including those for only weakly interacting SUSY particles (“electroweakinos”), where the Run 2 data allowed the experiments to surpass the sensitivity achieved by LEP in some scenarios. Half a century since SUSY was first proposed, ATLAS and CMS have demonstrated that the simplest models containing TeV-scale sparticle masses are not realised in nature (see “Stop quarks and electroweakinos” figure).

**Stop quarks and electroweakinos** Mass exclusion limits on supersymmetric top-quark partners and neutralino particles determined by ATLAS from a variety of final states (left) and on supersymmetric partners of the gauge and Higgs bosons (right), showing that a large fraction of the parameter space suggested by naturalness is excluded. Source: ATL-PHYS-PUB-2022-013

In fact, a large number of new-physics searches during LHC Run 1 and Run 2 targeted models other than SUSY, many of which also address the question of naturalness. Signs of extra spatial dimensions have been searched for in “mono-jet” events containing a single energetic jet and large MET, which could be caused by excited gravitons propagating in a higher dimensional space. Searches for vector-like quarks, as suggested by models with a composite Higgs boson, covered numerous complex final states with decays into all of the heavier known elementary particles. In these and other searches, the Higgs boson has entered the experimental toolkit, for example via the identification of high-momentum Higgs-boson decays reconstructed as large-radius jets.

The Higgs sector itself has been the subject of new-physics searches. These target additional Higgs bosons that would arise from an extended Higgs sector and exotic decays of the known Higgs boson, for instance into weakly interacting massive particles (WIMPs), which are candidates for dark matter. Improvements in both theoretical and data-driven background determinations have also allowed searches for Higgs-boson decays into invisible particles, with the Run 2 dataset setting an upper limit of 10% on their rate.

Searches for dark matter also continued to be performed in traditional channels, for example via the mono-jet signature. To increase the accuracy of this search using the full Run 2 statistics, theorists contributed differential background predictions that go beyond the next-to-leading order in perturbation theory to achieve an unprecedented background uncertainty of only 3% at MET values above 1 TeV. The resulting constraints on WIMP dark matter are complementary to those achieved with ultrasensitive detectors deep underground as well as astroparticle experiments. The absence of dark-matter signals in such established search channels led to the development of new models that predict a number of relevant but previously unexplored signatures.

LHC Run 3 will allow searches to go significantly beyond the sensitivity achieved with the Run 2 data

In several respects, searches for new physics at the LHC experiments have gone well beyond what was foreseen at the time of their design. “Scouting” data streams were introduced to store small-size event records suitable for di-jet and di-muon resonance searches such that recording rates could be increased by up to two orders of magnitude within the available bandwidth. Consequently, the mass reach of these searches was extended to lower values whereas previously this was impossible due to the high background rates at low masses. Long-lived particle searches also opened a new frontier, motivating proposals for new LHC detectors.

Overall, LHC Run 1 and Run 2 led to an enormous diversification of new-physics searches at the energy frontier by ATLAS and CMS, with complementary searches conducted by LHCb targeting lower invariant masses. The absence of new-physics signals despite the exploration of a multitude of signatures with unforeseen precision is a strong experimental result that feeds back to the phenomenology community to shape this programme further. While the analysis of Run 2 data is still ongoing, the experience gained so far in terms of experimental techniques and investigated signatures puts the experimental collaborations in a better position to search for new physics at Run 3.

Experimental improvements

LHC Run 3 will allow searches to go significantly beyond the sensitivity achieved with the Run 2 data. ATLAS and CMS are expected to collect datasets with an integrated luminosity of up to 300 fb^–1, adding to the 140 fb^–1 collected in Run 2. Taking into account the additional, smaller benefit provided by the increase in the centre-of-mass energy from 13 to 13.6 TeV, new-physics search sensitivities will generally increase by a factor of two in terms of cross sections. Additional gains in sensitivity will result from the exploration of new territory in several respects.

Already at the level of data acquisition, significant improvements will increase the sensitivity of searches. The CMS higher level trigger system has been reinforced using graphics processing units to increase the recording rate in the data scouting stream from 9 to 30 kHz. ATLAS has extended this technique to encompass more final states, including photons and b-jets. These techniques extend the sensitivity to hadronic resonances with low masses and weak coupling strengths to a domain that has never been probed before.

**Leptoquarks** Mass exclusions for spin-1 leptoquarks depending on the coupling strength to fermions, gU, as determined by CMS using Run 2 events containing pairs of tau leptons. The green band indicates the 95% confidence region which fits the low-energy data. Run 3 data will increase the sensitivity to test a significant fraction of this parameter space. Source: CMS-PAS-HIG-21-001

The particularly challenging searches for new long-lived particles will also benefit from experimental advances. ATLAS has improved the reconstruction of displaced tracks, reducing the amount of fake tracks by a factor of 20 at similar efficiencies compared to the current data analysis. New, dedicated triggers have been developed by ATLAS and CMS to identify electrons, muons and tau-leptons displaced from the primary interaction vertex. These trigger developments will allow the collection of signal candidate events at unprecedented rates, for example to test exotic Higgs-boson decays into long-lived particles with branching ratios far below the current experimental limits.

Likewise, ongoing developments in machine learning will contribute to the Run 3 search programme. While Run 1 physics analyses used generic, simple algorithms to distinguish between hypotheses, in Run 2 more powerful approaches of deep learning were introduced. For Run 3 their development continues, using a multitude of different algorithms tailored to the needs of event reconstruction and physics analysis to increase the reach of new-physics searches further.

New signatures

The Run 3 data will also be scrutinised in view of final states that either have been proposed more recently or that require a particularly large dataset. Examples of the latter are searches for electroweakinos, which have a production cross-section at the LHC at least two orders of magnitude smaller than strongly interacting SUSY particles. First results based on Run 2 data surpassed the sensitivity of the LEP experiments, including tests of unconventional “R-parity violating” scenarios in which electroweakinos can decay into only SM particles. This results in complicated final states containing electrons, muons and many jets but relatively low MET. Here, the challenging background determination could only be achieved thanks to machine-learning techniques, which lay the ground for further searches for particularly rare and challenging SUSY signals at Run 3.

If R-parity is not a symmetry, SUSY does not provide a WIMP dark-matter candidate. Among alternative explanations of the nature of this substance, models with bound-state dark matter are gaining increasing attention. In this new approach, strong interactions similar to quantum chromodynamics determine the particle spectrum in a dark sector that includes stable dark-matter candidate particles such as dark pions. At the LHC, coupling between such dark-sector particles and known ones would result in “semi-visible” jets comprising both types of particle (traditional dark-matter searches at the LHC have avoided such events to reduce background contributions). With the Run 2 data, CMS has already provided the very first collider constraints on these dark sectors, and more results from both ATLAS and CMS will follow in this and other proposed dark-sector scenarios.

Multiple deviations from the SM observed at lower energies are starting to shape the search programme at the energy frontier. The long-standing anomaly in the magnetic moment of the muon has recently reached a significance of 4.2σ, motivating increased efforts in searching for possible causes. One is the pair-production of a supersymmetric partner of the muon, for which models fit the low-energy data if the mass of this “smuon” is below 1 TeV and hence within the reach of the LHC. Another is to look for vector-like leptons, which are suggested by consistent extensions of the SM apart from SUSY, using final states containing a large number of leptons.

Multiple deviations from the SM observed at lower energies are starting to shape the search programme at the energy frontier

Moreover, the anomalies in B-meson decays consistently reported by BaBar, Belle and LHCb (see “A flavour of Run 3 physics”) have a strong and growing impact on the Run 3 search programme. Explanations for these anomalies require new particles with TeV-scale masses to fit the size of the observed effects and a hierarchy of fermion couplings to fit the deviations from lepton-flavour universality. Intriguingly these two requirements happen to coincide with the two peculiarities of the Higgs boson. Particular attention is now given to leptoquark searches investigating several production and decay modes. ATLAS and CMS have already started to probe leptoquark models suggested by the B-meson anomalies using Run 2 data (see “Leptoquarks” figure). While the analysis of key channels is ongoing, Run 3 will allow the experiments to probe a large fraction of the relevant parameter space. Furthermore, consistent models of leptoquarks include more new particles, namely colour-charged and colour-neutral bosons, vector-like quarks and vector-like leptons. These predict a variety of new-physics signatures that will further shape the Run 3 search programme.

In summary, searches for new physics at Run 3 will bring significant gains in sensitivity beyond the benefit provided by the increased amount of data. In particular, potential explanations of the anomalies observed at lower energies will be tested. Assuming that these anomalies point to new physics, the relevant searches with Run 3 data have a good chance of finding the first deviations from the SM at the TeV energy scale. Such an outcome would be of the utmost importance for particle physics, strengthening the case for the proposed Future Circular Collider at CERN.

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