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Introduction to the Standard Model and Beyond

Stuart Raby has written a modern, comprehensive textbook on quantum field theory, the Standard Model (SM) and its possible extensions. The focus of the book is on symmetries, and it contains a wealth of recent experimental results on Higgs and neutrino physics, which sets it apart from other textbooks addressing the same audience. It is published at a time when the incredible success story of the SM has come to a close with the discovery of the Higgs boson, and when the upcoming neutrino experiments promise to probe beyond-the-SM physics.

Raby is the author of some of the most important papers on supersymmetric grand unified theories and the book reflects that. It is no easy task to cover such a wide range of topics, from the basics of group theory to very advanced concepts such as gauge and gravity-mediated supersymmetry breaking, in one book. Raby devotes 120 pages to the basics of group theory, representations of the Poincaré group and the construction of the S matrix to provide the necessary foundations for the introduction to quantum electrodynamics in part III. Parts IV–VI introduce the reader to discrete symmetries, flavour symmetries and spontaneous symmetry breaking. Next, Raby describes two “Roads to the Standard Model” following the development of quantum chromodynamics and of electroweak theory, before arriving at the SM in part IX. The remaining parts deal with neutrino physics, grand unified theories and the minimal supersymmetric SM.

There are no omissions topic-wise, which makes the book very comprehensive. This comes at a price, however. In several places, complicated topics are discussed with only the most minimal of context, reading like a collection of equations rather than a textbook. Two examples of this are the discussion of causality for fermionic fields or the step from global to local supersymmetry, to which the author devotes only half a page each. In other places, more cross-referencing would improve legibility. For example, the chapter on SU(5) grand unified theory does not mention the automatic cancellation of gauge anomalies, a topic previously introduced in the context of the SM.

The use of materials is very distinctive. I doubt there is another book on the market that presents the reader with such a wealth of plots, figures and sketches, including recent experimental results on all the important topics discussed. The most important plots are reproduced in 12 pages of colour tables in the centre. There are exercises for the first five parts and a single Mathematica notebook is printed for Wigner rotations. Another distinguishing feature are the detailed suggested projects to use during a two-term course based on the book.

A very useful resource for designing a lecture of quantum field theory and beyond-the-SM physics

Although advertised as useful for both theorists and experimentalists, it is undeniably a book written from a theorist’s perspective. This becomes most clear in the latter parts, where relevant sections of the plots presenting experimental results remain unexplained. That being said, other very important experimental topics are explained, which you will not find in other textbooks about the SM. Raby explains how the anomalous magnetic moments of the electron and the muon are measured, and goes into quite some detail on neutrino experiments.

The book would benefit from improved editing. For example, the units are sometimes in italics, sometimes not, some equations are double tagged, some plots do not have axes labels, and there is inconsistent use of wavy and curly lines in the Feynman diagrams. Raby does make good use of references though, and points the reader to other textbooks and original literature; although the index needs to be extended significantly to be useful.

I recommend this book for advanced undergraduates, graduate students and lecturers. It provides a very useful resource for designing a lecture of quantum field theory and beyond-the-SM physics, and the amount of material covered is impressive and comprehensive. Beginners might be overwhelmed by Raby’s compact style , so I would recommend those who are new to quantum field theory to read a more accessible textbook in parallel.

The A-to-Z of CERN: Universe Unlocked

This book by CERN’s Archana Sharma and her two students Robin Mathews and Ben Richardson merges the classic A-to-Z formula with CERN concepts, making it suitable for all audiences. Each letter is divided into four categories: physics, accelerator, computing and experiments, allowing the reader to get a good understanding of each area.

All concepts are described in a simple and understandable way, such as antimatter being the same particles of matter with opposite charge. More complex concepts are explained with fun facts to help the reader: the temperature of the quark–gluon plasma is 100,000 times hotter than the centre of the Sun, and the time it takes to record a video call of 1 exabyte is 237,823 years. Each description is accompanied by a photograph, logo or simulation representing the described concept, which makes the book visually attractive for the reader.

Born at the start of the global pandemic, the A-to-Z of CERN arose from the need to tell science and technology stories at CERN when internships and summer lectures were either limited or cancelled. Overall, it provides an informative and entertaining glossary of CERN and particle physics in general, peppered with some general physics and technology concepts, such as the SI-unit system and even some non-CERN experiments, such as the former ZEUS experiment at DESY.

Marie-Noëlle Minard 1947–2022

Marie-Noëlle Minard passed away on 15 May 2022. She began her career as a physicist in 1969, with a postgraduate thesis at the Institute of Nuclear Physics (IPN) in Orsay under the direction of Louis Massonnet, on the subject of high-energy neutron detectors. She joined the CNRS as a research associate, while still at the IPN, in 1972 and began her PhD studies exploring ways to detect exotic particles under the supervision of Michel Yvert. Minard defended her thesis in 1976 and joined the newly created Annecy particle-physics laboratory (LAPP). She then spent two years at SLAC, where she worked on the rapid-cycling bubble chamber. Back at LAPP in 1979, she joined the group of physicists involved in the UA1 collaboration at the CERN SppS proton–antiproton collider. The group participated in the construction of the electromagnetic calorimeter, analysis tools, data taking and physics analyses.

With her colleagues at LAPP and CERN, Marie-Noëlle created an analysis to search for Z bosons, exploiting the UA1 data extracted online by the 168E emulators – the so-called “express line”. It was by analysing these events that Marie-Noëlle spotted the first Z boson on the night of 4 May 1983 – a source of immense pleasure in her career.

In 1987 Marie-Noëlle turned to LEP physics. She created, with Daniel Décamp, the ALEPH group at LAPP. This idea came up against obstacles: there was already an L3 group, and the rule at the time was that each IN2P3 laboratory could only participate in one experiment at LEP (with one exception). This occasion demonstrated the measure of Marie-Noëlle’s determination: when she was convinced of the merits of a project, her enthusiasm and energy were such that she was able to convince even the most reluctant. She finally obtained the green light for an ALEPH team at LAPP, which, under her direction, made many contributions to the experiment. She herself was run coordinator, responsible for calibration, and a pillar of the di-fermion analysis group (measuring the Z lineshape).

In the early 2000s Jacques Lefrançois invited Marie-Noëlle to join the LHCb collaboration. The team at LAPP, under her direction, made a major contribution to the experiment, particularly in the construction and operation of calorimetric systems as well as in numerous physics analyses. Project manager of the calorimeter group during its start-up between 2008 and 2011, then assistant to the project manager until 2013, Marie-Noëlle participated in the commissioning and definition of control and calibration procedures for the calorimeters and ensured the continuous monitoring of the gains and of the aging of the cells of the electromagnetic calorimeter throughout the first period of data taking (2011–2013).

Between 2000 and 2006 Marie-Noëlle was deputy director of LAPP, during which she strongly contributed to the definition and implementation of its scientific strategy. Very careful to communicate our science to the public, her creativity enabled her to organise several original and appreciated events. Marie-Noëlle supervised nine theses. For services rendered to research, she received one of the highest awards in France (de chevalier de la Légion d’honneur).

She was certainly demanding, much more of herself than of others, but always convinced that in a group everyone makes a positive contribution. A physicist and communicator of immense talent, she was above all a woman of limitless generosity, with a sometimes caustic sense of humour. She was brave and couldn’t stand injustice, often expressing aloud what others were quietly thinking. Marie-Noëlle loved swimming, sailing, cooking, reading and welcoming her many friends and family to her table. Those who, like us, have had the chance to work with her will miss her boundless commitment, the relevance of her advice and her humanity. We are thinking of Claude, her husband of 50 years, and of her large family.

LHCb digs deeper in CP-violating charm decays

LHCb figure 1 — **Fig. 1.** Preliminary plot of the contours showing the measurement of the direct CP asymmetry for the decays D⁰ → π⁺π^– versus D⁰ → K⁺K^–. The new measurement of a_d(D⁰ → K⁺K^–) improves the precision significantly and leads to evidence that a_d(D⁰ → π⁺π^–) is different from zero. The inner (outer) ellipse shows the 1 (2) sigma contours. Source: LHCb-PAPER-2022-024

To explain the large matter–antimatter asymmetry in the universe, the laws of nature need to be asymmetric under a combination of charge-conjugation (C) and parity (P) transformations. The Standard Model (SM) provides a mechanism for CP violation, but it is insufficient to explain the observed baryon asymmetry in the universe. Thus, searching for new sources of CP violation is important.

The non-invariance of the fundamental forces under CP can lead to different rates between a particle and an antiparticle decay. The CP violation in the decay of a particle is quantified through the parameter A_CP, equal to the relative difference between the decay rate of the process and the decay rate of the CP-conjugated process. Three years ago, the LHCb collaboration reported the first observation of CP violation in the decay of charmed hadrons by measuring the difference between the time-integrated A_CPin D⁰→K^–K⁺ and D⁰→π^– π⁺ decays, ΔA_CP. This difference was found to lie at the upper end of the SM expectation, prompting renewed interest in the charm-physics community. There is now an ongoing effort to understand whether this signal is consistent with the SM or a sign of new physics.

At the 41^st ICHEP conference in Bologna on 7 July, the LHCb collaboration announced a new measurement of the individual time-integrated CP asymmetry in the D⁰→K^–K⁺ decay using the data sample collected during LHC Run 2. The measured value, A_CP(K^–K⁺)=[6.8±5.4(stat)±1.6(syst)]×10^–⁴, is almost three times more precise than the previous LHCb determination obtained with Run 1 data. This was thanks not only to a larger data sample but also the inclusion of additional control channels D_s⁺→K^–K⁺π⁺ and D_s⁺→K_s⁰K⁺. Together with the previous control channels, D⁺→K^–π⁺π⁺ and D⁺→K_s⁰π⁺, these decays allow the separation between tiny signals of CP asymmetries from the much larger bias due to the asymmetric meson production and instrumental effects.

The combination of the measured values with the previously obtained ones of A_CP(K^–K⁺) and ΔA_CP by LHCb allowed the determination of the direct CP asymmetries in the D⁰→π^– π⁺ and D⁰→K^–K⁺ decays: [23.2±6.1]×10^–⁴ and [7.7±5.7]×10^–⁴, respectively, with correlated uncertainties (ρ=0.88). This is the first evidence of direct CP violation in an individual charm–hadron decay (D⁰→π^–π⁺), with a significance of 3.8σ.

The sum of the two direct asymmetries, which is expected to be equal to 0 in the limit of s–d quark symmetry (called U-spin symmetry), is equal to [30.8±11.4]×10^–⁴. This corresponds to a departure from U-spin symmetry of 2.7σ. In addition, this result is essential to the theory community in the quest to clarify the theoretical picture of CP-violation in the charm system. Since the measurement is statistically limited, its precision will improve with the larger dataset collected during Run 3.

The LHC cryogenics and its adaptation to the operational parameters for beams, related physics and energy preservation

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The cryogenic infrastructure of the Large Hadron Collider (LHC) at CERN is the most complex helium refrigeration system of all the world’s research facilities.

The operation of the LHC’s cryogenic system was initiated in 2008 after reception testing and a first cool down to 1.9 K. This webinar will cover information on the design, operational experiences and main challenges linked to the accelerator, along with the physics requirements.

During the first stage, the operation team had to learn about the responsivity and limitations of the system. They then had to manage stable operation by maintaining the necessary conditions for the superconducting magnets, RF cavities, electrical feed boxes, power links and detector devices, thus contributing to the physics programme and the discovery of the Higgs boson in 2012.

One of the most challenging parameters impacting the cryogenics was the beam-induced heat load that was taken up, beginning during the second operation period (Run 2) of the LHC in 2015 with increased beam parameters. A complicated optimisation of the configuration of the cryogenic system was successfully applied to cope with these requirements.

Run 3 (preparation for which started in 2020) required the handling of several hundred magnet training quenches towards the nominal beam energy for physics production.

Now, after several years of operational experience with steady state and transient handling, the cryogenic system is being optimised to provide the necessary refrigeration, whilst incorporating the all-important aspect of energy preservation.

In conclusion, there will be a brief discussion of the next four years of operation.

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Krzysztof Brodzinski is a senior staff member in the cryogenics group at the technology department at CERN. He is a mechanical engineer with a specialisation in refrigeration equipment, and graduated from Cracow University of Technology in Poland. Krzysztof joined the LHC cryogenic design team in 2001, has been a member of the cryogenic operation team since 2009 and in 2019 was mandated as a section leader of the cryogenic operation team for the LHC, ATLAS and CMS. He is also involved in the engineering of the cryogenic system for the HiLumi LHC RF deflecting cavities project, as well as participating in the ongoing FCC cryogenics study.

Why not watch our other related Higgs boson anniversary webinars?

• Superconducting magnets: an enabling technology for the discovery of the Higgs boson

• RF technology for LHC and HL-LHC

CERN Courier’s Higgstory

higgstory_collage — **Through the years** *CERN Courier* issues covering famous milestones of the Higgs discovery throughout the decades. Credit: K Bernhard-Novotny

It was March 1977 when the hypothetical Higgs boson first made its way onto the pages of this magazine. Reporting on a talk by Steven Weinberg at the Chicago Meeting of the American Physical Society, the editors noted the dramatic success of gauge theories in explaining recent discoveries at the time — beginning with the observation of the neutral current at CERN in 1973 and the “new physics” following the J/ψ discovery at Brookhaven and Stanford the following year, observing: “The theories also postulate a set of scalar particles in a similar mass range… If Higgs bosons exist, they will affect particle behaviour at all energies. However, their postulated interactions are even weaker than the normal weak interactions. The effects would only be observable on a very small scale and would usually be drowned out by the stronger interactions.”

vol19-issue9-p395figa — Harvard professors Sheldon Glashow (left) and Steven Weinberg at a news conference at Harvard after it was announced that they would share the 1979 Physics Nobel Prize with Abdus Salam. Credit: Photopress. Source: *CERN Courier* December 1979.

The topic clearly drew the attention of readers, as just a few issues later, in September 1977, the editors delved deeper into the origins of the Higgs boson and its role in spontaneous symmetry breaking, offering Abdus Salam’s “personal picture” to communicate this abstruse concept: “Imagine a banquet where guests sit at round tables. A bird’s eye view of the scene presents total symmetry, with serviettes alternating with people around each table. A person could equally well take a serviette from his right or from his left. The symmetry is spontaneously broken when one guest decides to pick up from his left and everyone else follows suit.”

Within a year, CERN Courier was on the trail of how the Higgs boson might show itself experimentally. Reporting on a “Workshop on Producing High Luminosity Proton–Antiproton Storage Rings” held at Berkeley, the April 1978 issue stated: “As well as the intermediate boson, the proton–antiproton colliders could give the first signs of the Higgs particles or of other unexpected states. While the discovery of weak neutral currents and charm provided impressive evidence for the gauge-theory picture that unifies electromagnetic and weak interactions, one prediction of this picture is the existence of spinless Higgs bosons. If these are not found at higher energies, some re-thinking might be required.” In the December 1978 issue, with apologies to Neil Armstrong, the Courier ran a piece titled “A giant LEP for mankind”. The hope was that with LEP, physicists had the tool to explore in depth the details of the symmetry breaking mechanism at the heart of weak interaction dynamics.

vol18-issue12-p434fig — A drawing of the LEP tunnel cross-section at the location of a bending magnet. The tunnel itself could be built using similar techniques to those used in the construction of the CERN SPS. Source: *CERN Courier* December 1978.

The award of the 1979 Nobel Prize in Physics to Weinberg, Glashow and Salam for the electroweak theory received full coverage in December that year, with the Courier expressing confidence in the Higgs: “Another vital ingredient of the theory which remains to be tested are the Higgs particles of the spontaneous symmetry breaking mechanism. Here the theory is still in a volatile state and no firm predictions are possible. But this mechanism is crucial to the theory, and something has to turn up.”

A Higgs for the masses

To many people, wrote US theorist Sam Treiman in November 1981, the Higgs particle looks somewhat artificial — “a kind of provisional stand-in for deeper effects at a more fundamental level”. Four years later, “with several experiments embarking on fresh Higgs searches”, Richard Dalitz and Louis Lyons organised a neatly titled workshop “Higgs for the masses” to review the theoretical and experimental status. Another oddity of the Higgs, wrote Lyons, is that unless it is very light (less than 10^–17 eV), the Higgs should make the universe curved, “contributing more to the cosmological constant than the known limit permits”. Lower limits (from spontaneous symmetry breaking) and higher limits (from the unitarity requirement) open up a wide range of masses for the Higgs to manoeuvre — between 7 and 1000 GeV, he noted. “From time to time, new ‘bumps’ and effects are tentatively put forward as candidate Higgs, but so far none are convincing.”

LEP’s electroweak adventure reached a dramatic climax in the summer of 2000, with hints that a light Higgs boson was showing itself. In October, the machine was granted a stay of Higgs execution. Alas, the signal faded, and the final curtain fell on LEP in November — a “LEPilogue” heralding the beginning of a new era: the LHC.

Discussions about a high-energy hadron collider were ongoing long before: ICFA’s Future Perspectives meeting at Brookhaven in October 1987 noted two major hadron collider projects on the market: “the US Superconducting Supercollider, with collision energies of 40 TeV in an 84 kilometre ring, and the CERN Large Hadron Collider, with up to 17 TeV collision energies”. In December 1994, shortly after CERN turned 40, Council provided the lab with “The ultimate birthday present“: the unanimous approval of the LHC. A quarter of a century later, the LHC started up and brought particle physics to the world.

vol35-issue1-p001fig — Pride, happiness and relief at LHC approval – left to right: CERN’s research director Lorenzo Foa, LHC project Leader Lyn Evans and Director-General Chris Llewellyn Smith (1995).

Together with LEP data, Fermilab’s CDF and DØ experiments and the LHC 2011 measurement campaign narrowed down the possible mass range for the Higgs boson to be between 115 and 127 GeV. First tantalising hints of the Higgs boson were presented on 13 December 2011. The quest remained open for another half a year, until Director-General Rolf Heuer, following the famous talks by ATLAS and CMS spokespersons Fabiola Gianotti and Joe Incandela, concluded: “As a layman I would say: I think we have it” on 4 July 2012. It was a day to remember: a breakthrough discovery rooted in decades of work by thousands of individuals that rocked the CERN auditorium and reverberated around the world. A new chapter in particle physics had begun…

To mark the 10^th anniversary of this momentous event, from Monday 4 July the Courier will be exploring the theoretical and experimental effort behind the Higgs-boson discovery, the immense progress made by ATLAS and CMS in our understanding of this enigmatic particle, and the deep connections between the Higgs boson and some of the most profound open questions in fundamental physics.

Wherever the Higgs boson leads, CERN Courier will be there to report!

The Higgs enigma: celebrating 10 years of discovery

Artistic impression of the Brout–Englert–Higgs field — An artistic impression of the Brout–Englert–Higgs field. Credit: D Dominguez/CERN

Ten years ago, a few small bumps in ATLAS and CMS data confirmed a 48 year-old theoretical prediction, and particle physics hasn’t been the same since. Behind those sigmas was the hard work, dedication, competence and team spirit of thousands of experimentalists and accelerator physicists worldwide. Naturally it was a triumph for theory, too. Peter Higgs, François Englert, Carl Hagen and Gerald Guralnik received a standing ovation in the CERN auditorium on 4 July 2012, although Higgs insisted it was a day to celebrate experiment, not theory. The Nobel prize for Englert and Higgs came a year later. Straying from tradition for elementary-particle discoveries, the citation explicitly acknowledged the experimental effort of ATLAS and CMS, the LHC and CERN.

The implications of the Higgs-boson discovery are still being understood. Ten years of precision measurements have shown the particle to be consistent with the minimal version required by the Standard Model. Combined with the no-show of non-Standard Model particles that were expected to accompany the Higgs, theorists are left scratching their heads. As we celebrate the collective effort of high-energy physicists in discovering the Higgs boson and determining its properties, another intriguing journey has opened up.

Marvelously mysterious

As “a fragment of vacuum” with the barest of quantum numbers, the Higgs boson is potentially connected to many open questions in fundamental physics. The field from which it hails governs the nature of the electroweak phase transition in the early universe, which might be connected with the observed matter–antimatter asymmetry; as the only known elementary scalar particle, it could serve as a portal to other, hidden sectors relevant to dark matter; its couplings to matter particles — representing a new interaction in nature — may hold clues to the puzzling hierarchy of fermion masses; and its interactions with itself have implications for the ultimate stability of the universe.

Nobody knows what the Higgs boson has in store

With the LHC and its high-luminosity upgrade, physicists have 20 years of Higgs exploration to look forward to. But to fully understand the shape of the Brout–Englert–Higgs potential, the couplings of the Higgs boson to Standard Model particles and its possible connections to new physics, a successor collider will be needed. It is fascinating to picture future generations of particle physicists working as one with astroparticle physicists, cosmologists, quantum technologists and others to fill out the details of this potential new vista, with colliders driving progress alongside astrophysical, cosmological and gravitational-wave observatories. Future colliders aren’t just about generating knowledge, argues Anna Panagopoulou of the European Commission, but are “moonshots” delivering a competitive edge in technology, innovation, education and training — opening adventures that inspire young people to enter science in the first place.

Nobody knows what the Higgs boson has in store. Perhaps further studies will confirm the scenario of a Standard-Model Higgs and nothing else. The sheer number and profundity of known unknowns in the universe would suggest otherwise, think theorists. The good news is that, in the Higgs boson, physicists have clear measurement targets – and in principle the necessary theoretical and experimental machinery – to explore such mysteries, building upon the events of 4 July 2012 to reach the next level of understanding in fundamental physics.

Engines of knowledge and innovation

**One of a kind** As a large research infrastructure, CERN has a key role in shaping a globally competitive European research and innovation system. Credit: CERN-201808-226-1

The search for the Higgs boson is the kind of adventure that draws many young people to science, even if they go on to work in more applied areas. I first set out to become a nuclear physicist, and even applied for a position at CERN, before deciding to specialise in electrical engineering and then moving into science policy. Today, my job at the European Commission (EC) is to co-create policies with member states and stakeholders to shape a globally competitive European research and innovation system.

Large research infrastructures (RIs) such as CERN have a key role to play here. Having visited CERN for the first time last year, I was impressed not just by the basic research but also by the services that CERN provides the collaborations, its relationships with industry, and its work in training and educating young people. It is truly an example of what it means to collaborate on an international level, and it helped me understand better the role of RIs in research and innovation.

Innovation is one of three pillars of the EC’s €95.5 billion Horizon Europe programme for the period 2021–2027. The first pillar is basic science, and the second concerns applied research and knowledge diffusion. Much of the programme’s focus is “missions” geared to societal challenges such as soil, climate and cancer, driven by the UN’s 2030 Sustainable Development Goals. So where does a laboratory like CERN fit in? Pillar one is the natural home of particle physics, where there is well established support via European Research Council grants, Marie Skłodowska-Curie fellowships and RI funding. On the other hand, the success of the Horizon Europe missions relies on the knowledge and new technologies generated by the RIs.

**Anna Panagopoulou** is director of European Research Area and Innovation at the European Commission. Credit: CERN-202110-161-4

We view the role of RIs as driving knowledge and technology, and ensuring it is transferred in Europe – acting as engines in a local ecosystem involving other laboratories and institutes, hospitals and schools, attracting the best people and generating new labour forces. COVID-19 is a huge social challenge that we also managed to address using basic research, RIs and opening access to data. This is a clear socioeconomic impact of current research and also data collected in the past.

Open science is a backbone of Horizon Europe, and an area where particle physics and CERN in particular are well advanced. I chair the governance board of the European Open Science Cloud, a multi-disciplinary environment where researchers can publish, find and re-use data, tools and services, in which CERN has a long-standing involvement.

Indeed, the EC has established a very strong collaboration with CERN across several areas. Recently we have been meeting to discuss the proposed Future Circular Collider (FCC). The FCC is worthwhile not just to be discussed but supported, and we are already doing so via significant projects. We are now discussing possibilities in Horizon Europe to support more technological aspects, but clearly EU money is not enough. We need commitment from member states, so there needs to be a political decision. And to achieve that we need a very good business plan that turns the long-term FCC vision into clearly defined short-term goals and demonstrates its stability and sustainability.

Societal impact

Long-term projects are not new to the EC: we have ITER, for example, while even the neutrality targets for the green-deal and climate missions are for 2050. The key is to demonstrate their relevance. There is sometimes a perception that people doing basic research are closed in their bubble and don’t realise what’s going on in the “real” world. The space programme has managed to demonstrate over the years that there are sufficient applications providing value beyond its core purpose. Nowadays, with issues of defence, security and connectivity rising up political agendas, researchers can always bring to the table that their work can help society address its needs. For big RIs such as the FCC we need to demonstrate first: what is the added value, even if it’s not available today? Why is it important for Europe? And what is the business plan? The FCC is not a typical project. To attract and convince politicians and finance ministers of its merits, it has to be presented in terms of its uniqueness.

The FCC brings to mind the Moon landings

The FCC brings to mind the Moon landings. Contrary to popular depictions, this was a long-term project that built on decades of competitive research from different countries. Yes, it was a period during the Cold War, but it was also the basis of fruitful collaboration. If we don’t dare to spend money on projects that bring us to the future then we lose, as Europe, a competitive advantage.

The Higgs after LHC

Many of the most arbitrary aspects of the Standard Model of particle physics (SM) are intimately connected to the scalar sector of the theory. The SM comprises just one scalar particle, the Higgs boson, and assumes a specific scalar potential (the famous “Mexican hat”) to define the dynamics of electroweak (EW) interactions. But the fact that the Higgs boson acquires a non-zero vacuum expectation value that defines the mass scale of EW interactions (around 100–200 GeV) is assumed, not explained, by the SM. Indeed, why the Higgs-boson mass is constrained to be at the EW scale, while quantum corrections should push it to much higher values (the so-called naturalness problem, see Naturalness after the Higgs), is not justified by any symmetry of the SM. At the same time, the SM assumes that fermion masses are generated via arbitrary Yukawa-type interactions with the scalar field but it does not explain the hierarchy of couplings or masses that we observe, nor the specific flavour structure that arises from the presence of just one scalar field.

Future colliders are vital to push the precision Higgs programme to the next level

The scalar sector of the SM may therefore be seen as a messenger of a more fundamental theory that replaces the SM at energies beyond the EW scale and turns apparent arbitrariness into logical consequences. After all, the mechanism of EW symmetry breaking as realised in the SM via the Brout–Englert–Higgs (BEH) field is just the simplest possible way to generate massive EW gauge bosons and fermions while preserving gauge symmetry. The scalar potential could be more complicated, for example involving multiple scalar fields, as is common in many beyond-the-SM (BSM) theories. This would result in a richer pattern of stable and metastable minima and influence the nature of the EW phase transition. A first-order phase transition, together with extra sources of CP violation beyond what is implied by the SM, could explain the origin of the matter–antimatter asymmetry of the universe via EW baryogenesis (see Electroweak baryogenesis). Understanding the origin of the EW scale is thus key to connecting very different realms of particle physics and cosmology, and the question we face while we look into the future of collider physics.

Game changer

The discovery of the Higgs boson during Run 1 of the LHC has been a game changer in the exploration of new physics beyond the EW scale. The measurement of the Higgs-boson mass has added the last missing input parameter to precision global fits of the SM, which now provide a very powerful tool to constrain BSM scenarios. Thanks to an unprecedented level of precision reached in both theory and experiment, the measurement of Higgs-boson couplings to EW gauge bosons (W, Z) and to the first two generations of quarks and leptons (t, b, τ, µ) from Run 2 data has already constrained their deviations from SM expectations to within 5–20%, with the best accuracy reached for the couplings to the gauge bosons. Based on these results, the High-Luminosity LHC (HL-LHC) is projected to constrain the effects of new physics on Higgs-boson couplings to EW gauge bosons to 1–2%, and to heavy quarks and fermions to 3–5%. If no anomalies are found, this level of accuracy will push the lower bound on the scale of new physics into the TeV ballpark. Vice versa, the detection of possible anomalies may point to the presence of new physics at the TeV scale, possibly just around the corner.

An ATLAS di-Higgs event — **Going further** Di-Higgs events, such as this candidate from ATLAS (original colour scheme modified), probe the Brout–Englert–Higgs potential, but future colliders will be needed to access the cubic and quartic Higgs self-couplings that govern the potential’s shape. Credit: ATLAS

On the other hand, testing the SM scalar potential will still be challenging even during the HL-LHC era. The shape of the BEH potential can be tested by measuring the Higgs-boson self-interactions corresponding to its cubic and quartic terms. In the SM, these interactions are strictly proportional to the Higgs-boson mass via the vacuum expectation value of the BEH field. Deviations from the SM are searched for via Higgs pair production and radiative corrections to single-Higgs measurements. Although the LHC and HL-LHC promise to provide evidence for di-Higgs production, the extraction of the Higgs self-coupling from such measurements will be statistically limited.

Future colliders are vital to push the precision Higgs programme to the next level. While the type and concept of the next collider is yet to be decided, all proposed facilities would deliver a huge number of Higgs bosons over their lifetime, operating at different and well targeted centre-of-mass energies (see “At a glance” figure). They can complement one another and, staggered over a period of the next few decades, provide the missing elements of the EW puzzle.

Among future lepton colliders under study, circular e⁺e^– colliders (CEPC, FCC-ee) are expected to operate at lower energies between 90–350 GeV with very high luminosities, while linear e⁺e^– colliders (ILC, C³, CLIC) offer both low- and high-energy phases generally with slightly lower luminosities. Combined with data from the HL-LHC, these “Higgs factories” would enable the SM, including most Higgs couplings, to be stress-tested below the per-cent level and in cases at or below the per-mille level. In particular, FCC-ee operating at the s-channel Higgs resonance (125 GeV) has the capability to provide bounds on couplings as small as the electron Yukawa coupling, while linear e⁺e^– colliders operating at 550–600 GeV and above could substantially improve on the top-quark Yukawa coupling with respect to the HL-LHC. A possible muon collider, operated either as a Higgs factory at 125 GeV or as a high-energy discovery machine at 3–10 TeV, is estimated to reach similar precisions on Higgs couplings to other particles as e⁺e^– machines.

**Self-coupling** Uncertainties on the Higgs self-coupling (presented in terms of the “κ factor” of the cubic self-coupling) projected for the HL-LHC and for the various stages of proposed future colliders, with the solid and shaded bars representing di-Higgs and single-Higgs results, respectively. Source: arXiv:1910.00012

Finally, high-energy lepton colliders (ILC 1000, CLIC 3000 and a 3–30 TeV muon collider) and very high-energy hadron colliders (FCC-hh at 100 TeV) would reach enough statistics and energy to measure the Higgs self-coupling and investigate the nature of the BEH potential, either via di-Higgs or single-Higgs production (see “Self-coupling” figure). With an aggressive Higgs physics programme they may also reach enough sensitivity to probe the cubic and quartic terms in the BEH potential separately.

Almost half a century after it was predicted, the LHC delivered the Higgs boson in spectacular style on 4 July 2012. Over the next 15–20 years, the machine and its luminosity upgrade will continue to enable ATLAS and CMS to make great strides in understanding the Higgs boson’s properties. But to fully exploit the discovery of the Higgs boson and explore its mysterious relation to new physics beyond the EW scale, we will need a successor collider.

Through the Higgs portal

Referring to the ﬁeld equation of general relativity R_μ_ν – ½ Rg_μ_ν = κT_μ_ν , Einstein is reported to have said that the left-hand side, constructed from space–time curvature, is “a palace of gold”; while the right-hand side, which parameterises the energy and momentum of matter, is by comparison “a hovel of wood”. Present-day physics has arrived at much more concrete ideas about the right-hand side than were available to Einstein. It is fair to say that some of it has come to look quite palatial, and fully worthy to stand alongside the left-hand side. These are the terms that involve field kinetic energy and gauge bosons, as described by the Standard Model (SM). Their form follows logically, within the framework of relativistic quantum ﬁeld theory, directly from the principles of local gauge symmetry and relativity. Mathematically, they also speak the same geometric language as the right-hand side. The gauge bosons are avatars of curvature in “internal spaces”, similar to how gravitons are the avatars of space–time curvature. Internal spaces parameterise ways in which fields can vary – and thus, in effect, move – independently of ordinary motion in space–time. In this picture, the strong, weak and electromagnetic interactions arise from the influence of internal space curvature on internal space motion, similar to how gravity arises from the influence of space–time curvature on space–time motion.

The Higgs particle is the only portal connecting normal matter to such phantom ﬁelds

The other contributions to T_μ_ν, all of which involve the Higgs particle, do not yet reach that standard. We can aspire to do better! They are of three kinds. First, there are the many Yukawa-like terms from which quark and lepton masses and mixings arise. Then there is the Higgs self-coupling and ﬁnally a term representing its mass. These contributions to T_μ_ν contain almost two dozen dimensionless coupling parameters that present-day theory does not enable us to calculate or even much constrain. It is therefore important to investigate experimentally, through quantitative studies of Higgs-particle properties and interactions, whether this ramshackle structure describes nature accurately.

Higgs potential

The Higgs boson is special among the elementary particles. As the quantum of a condensate that fills all space, it is metaphorically “a fragment of vacuum”. Speaking more precisely, the Higgs particle has no spin, no electric or colour charge and, at the level of strong and electromagnetic interactions, normal charge conjugation and parity. Thus, it can be emitted singly and without angular momentum barriers, and it can decay directly into channels free of colour and electromagnetically charged particles, which might otherwise be difficult to access. For these and other, more technical, reasons, the Higgs particle has the potential to reveal new physical phenomena of several kinds.

A unique aspect of the Higgs mass term is especially promising for revealing possible shortcomings in the SM. In quantum field theory, an important property of an interaction is the “mass dimension” of the operator that implements it – a number that in an important sense indicates its complexity. Scalar and gauge fields have mass dimension 1 as do space–time derivatives, whereas fermion fields have mass dimension 3/2. More complicated operators are built up by multiplying these, and the mass dimension of a product is the sum of the mass dimensions of its factors. Interactions associated with operators whose mass dimension is greater than 4 are problematic because they lead to violent quantum fluctuations and mathematical divergences. Whereas all the other terms in the SM Lagrangian arise from operators of mass dimension 4, the Higgs mass term has mass dimension 2. Thus it is uniquely open to augmentation by couplings to hypothetical new SU(3) × SU(2) × U(1) singlet scalar ﬁelds, because the mass dimension of the augmented interaction can be 3 or 4 – i.e. still “safe”. The Higgs particle is the only portal connecting normal matter to such phantom ﬁelds.

Dark matter map — **Phantom fields** The Higgs boson could connect normal matter to a hidden sector that does not participate in strong or electroweak interactions, as has been proposed to explain dark matter – the most detailed map of which so far (by the Dark Energy Survey) is shown for a patch of sky in the southern hemisphere. Credit: DES

Why is this an interesting observation? There are three main reasons: two broadly theoretical, one pragmatic. First of all, the particles that are generally considered part of the SM carry a variety of charge assignments under the gauge groups SU(3) × SU(2) × U(1) that govern the strong and electroweak interactions. For example, the left-handed up quark is charged under all three groups, while the right-handed electron carries only U(1) hypercharge. Thus it is not only logically possible, but reasonably plausible, that there could be particles that are neutral under all three groups. Such phantom particles might easily escape detection, since they do not participate in the strong or electroweak interactions. Indeed, there are several examples of well-motivated candidate particles of that kind. Axions are one. Since they are automatically “dark” in the appropriate sense, phantom particles could contribute to the astronomical dark matter, and might even dominate it, as model-builders have not failed to notice. Also, many models of uniﬁcation bring in scalar ﬁelds belonging to representations of a unifying gauge group that contains SU(3) × SU(2) × U(1) singlets, as do models with supersymmetry. Only phantom scalars are directly accessible through the Higgs portal, but phantoms of higher spin, including right-handed neutrinos, could cascade from real or virtual scalars.

Mysterious values

Second, the empirical value of the Higgs mass term is somewhat mysterious and even problematic, given that quantum corrections should push it to a value many orders of magnitude higher. This is the notorious “hierarchy problem” (see Naturalness after the Higgs). Given this situation, it seems appropriate to explore the possibility that part (or all) of the effective mass-term of the SM Higgs particle arises from more fundamental couplings upon condensation of SU(3) × SU(2) × U(1) singlet scalar ﬁelds, i.e. the emergence of a non-zero space-filling field, as occurs in the Brout–Englert–Higgs mechanism.

The portal idea leads to concrete proposals for directions of experimental exploration

Third, the portal idea leads to concrete proposals for directions of experimental exploration. These are of two basic kinds: one involves the observed strength of conventional Higgs couplings, the other the kinematics of Higgs production and decay. Couplings of the Higgs field to singlets that condense will lead to mixing, altering numerical relationships among Higgs-particle couplings and masses of gauge bosons, and of fermions from their minimal SM values. Also, the Higgs-ﬁeld couplings to gauge bosons and fermions will be divided among two or more mass eigenstates. Since existing data indicates that deviations from the minimal model are small, the coupling of normal matter to the “mostly but not entirely” singlet pieces could be quite small, perhaps leading to very long lifetimes (as well as small production rates) for those particles. Whether or not the phantom particles contribute signiﬁcantly to cosmological dark matter, they will appear as missing energy or momentum accompanying Higgs particle decay or, through Bremsstrahlung-like processes, when they are produced.

We introduced the term “Higgs portal” to describe this circle of ideas in 2006, triggering a ﬂurry of theoretical discussion. Now that the portal is open for business, and with larger data samples in store at the LHC, we can think more concretely about exploring it experimentally.

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