The Discovery of the Higgs Boson

Physicists have been hunting for the Higgs boson ever since the mid-1970s, when the SM gained widespread acceptance. The search for the elusive particle was among the highest priorities for several generations of experiments, but it appeared to be extremely challenging. The theory does not predict the mass of the H, whereas the production cross-section, width and branching fractions in the various decay modes strongly depend on it. To make things even more complicated, many interesting decay modes are imitated by different, numerous sources of reducible and irreducible background.

The task was successfully accomplished only with the construction of the Large Hadron Collider (LHC) and the two general-purpose detectors, ATLAS and CMS.

The LHC is the most powerful collider ever built. It is a gigantic accelerator equipped with thousands of superconducting magnets and accelerating cavities distributed along a 27 km tunnel, 100 m underground, near Geneva, Switzerland. It started producing collisions of squeezed packets of protons at an unprecedented centre of mass energy of 7–8 TeV in the first years of operation, and later raised its energy to 13 TeV. ATLAS and CMS are very sophisticated experiments, based on a complex set of detectors, built and operated by thousands of physicists and engineers.

Thanks to the excellent performance of these outstanding experiments, at the end of 2011 the two collaborations presented to the public the first evidence of a new, neutral particle, with a mass near 125 GeV. Subsequently, the two experiments collected more data and improved the precision of their analysis such that, on 4 July 2012, both of them formally announced the long-awaited discovery. ^{1 – 4} Thanks to these results, the 2013 Nobel Prize in physics was jointly assigned to François Englert and Peter Higgs.

A Real Breakthrough in our Understanding of Matter and the Universe

The Higgs boson is an unstable particle, living for only the tiniest fraction of a second. But it plays a major role in shaping the cosmos. The H can be seen as a manifestation of an invisible field that fills every corner of our universe, assigning a distinctive mass to each elementary particle, through its interaction with the field.

With its discovery we can reconstruct what happened at about 10^–11 s after the Big Bang. When the average temperature of the universe was about 100 GeV, the electroweak symmetry-breaking mechanism suddenly entered into action. In that instant, the H field suddenly changed the properties of the vacuum, and particles propagating through it were differentiated forever.

The W and Z bosons, interacting heavily with the new medium, become so massive that the weak force cannot propagate anymore beyond the tiny sub-nuclear distances. Photons on the other hand, which do not interact with the H field, remain massless; they therefore fly at the speed of light to bring electromagnetism to the farthest corners of the universe.

Lastly, a similar mechanism affected the other elementary particles. Some quarks, i.e. the top, experience such a strong coupling to the Higgs field that they become very massive particles. They are so heavy that they can form neither bound states nor stable forms of matter. Other quarks interact only slightly with the new vacuum and get a small mass. This is the case of the up and down quarks that are light enough to group themselves into triplets which are held together by gluons carrying the strong force. Through this mechanism, at around 10⁻⁶ s after the Big Bang, the first protons were formed: a positively charged, very stable form of matter, whose lifetime exceeds the current age of the universe. Some special leptons, the electrons, interact very softly with the H field and get a tiny mass, just the right value to allow the negatively charged particles to permanently orbit around a proton and form the first stable atoms.

In the blink of an eye, everything changed forever.

The current shape of everything, including us, was somehow determined in those moments. As a consequence of this mechanism the chaotic ingredients of the early universe collapsed into persistent material structures that later led to the formation of stars, galaxies and planets, including a very special one located in a comfortable corner of a solar system, where several forms of life became possible.

Thanks to the electroweak vacuum, this thin scaffolding holding together the enormous structure that we call the universe, matter has acquired the characteristics that are so familiar to us.

The Problematic Triumph of the Standard Model

The discovery of the H boson marks another success of particle physics. The last missing piece has been found and the Standard Model of fundamental interactions is now complete. Still, while we celebrate the most recent triumph of this theory, we are left with a long list of open questions, whose answer would probably require the emergence of new paradigms.

It is well known that the SM does not account for many important phenomena. For example, it does not contain particles or forces responsible for dark matter and dark energy; neither does it provide a mechanism explaining the puzzling asymmetry between matter and antimatter. Last but not least, gravity is not included in it.

We already know that, sooner or later, we shall be forced to abandon it. The appearance of new particles or new interactions will bring about a more general description of nature, generically called New Physics (NP). We expect it will explain matter to a much higher energy scale, while the SM will be considered as a particular, low-energy case of the new theory.

The beauty of our field is that this could occur any time. It might be tomorrow, if new states of matter emerge from LHC data; or it could take decades and even the need to build a new generation of powerful accelerators.

As of today we do not know at which energy scale we shall find answers to some of these questions. However, from now on, any theory of NP will be further constrained by the need to include the Higgs boson itself; and the newly discovered particle will be exploited as an additional tool to explore any uncharted territory.

We are just in the midst of a scientific revolution whose contours will perhaps become clearer in a few decades’ time. In the following, we shall discuss some of the implications of the discovery and their impact on a few NP scenarios.

Looking for Higgs Bosons Decaying into Dark Matter Particles

The existence of dark matter in the universe is well established experimentally. The most recent data confirm that its amount is about five times that of ordinary matter and, since the SM contains no mechanism accounting for it, the discovery of dark matter particles would immediately open the door to NP.

Many extensions of the SM, such as models with weakly interacting massive particles could explain the puzzling issue. The most popular examples are the lightest stable particles in Supersymmetry (SUSY), or the lightest Kaluza–Klein particle in extra dimensions. Of course, the extremely light axion is also a good candidate.

Several experiments are ongoing to detect any possible signal that could shed light on the question. Sophisticated detectors are used in underground laboratories to look for the direct scattering of dark-matter particles with the nucleons of ordinary matter. A somehow complementary approach is used at high-energy accelerators such as LHC, where ATLAS and CMS are searching for invisible decays of the Higgs boson.

In general, the interactions of the H with the unknown dark matter sector may introduce invisible decay modes. In the so-called ‘Higgs-portal’ models, the H takes the role of mediator between the SM particles and the dark particles. Recent theories proposing that the Higgs boson played a central role in the evolution of the early universe provide further motivation to understanding the relationship between it and dark matter.

The typical signature for invisible H decays at LHC is a large missing transverse momentum recoiling against a distinctive visible system, usually a high-energy jet or a photon. ATLAS and CMS have explored many different topologies, including the ones in which the H is produced in association with a vector boson, W or Z or with a pair of jets, signalling therefore the production through the fusion of vector bosons. Since no excess of events has been detected so far, it was only possible to produce upper limits. The current results exclude a branching ratio of the Higgs boson decaying into invisible particles higher than 25–30%, meaning that there is still plenty of room for surprises.

With additional data, these limits will be significantly improved but, even with the full statistics available at the end of LHC, it will be very difficult to go below 5%. At a hadron collider, such as LHC, it will be practically impossible to really exclude the decay of the H into invisible particles. A much better job could be done if we can build a new lepton collider. High-energy collisions of elementary, point-like particles, like electrons and positrons, characterised by a complete knowledge of the initial state, are the ideal environment for this kind of studies. An e ⁺–e ⁻ linear or circular collider, powerful enough to produce Higgs bosons in association with a Z (i.e. running at an energy around 250 GeV) would allow placing very stringent limits, <1%, on the H branching ratio for invisible decays or to simply discover some of these new decay modes.

Could the H be the Inflaton?

If confirmed to be an elementary object, this particle would be the only fundamental scalar ever observed in nature. Many consider this a puzzle in itself that could open the door to other discoveries. In particular, it could shed light on one of the hottest issues of modern cosmology.

Whether the primordial universe has passed through a stage of cosmic inflation is still a matter of heated discussions. The assumption of a dramatic exponential growth, quickly transforming a tiny fluctuation of the vacuum into an immense object, solves many contradictions that afflicted previous theories. In particular, it explains why the universe is so homogeneous and uniform in any direction, and why we live in a world in which there are no magnetic monopoles; those north or south poles isolated from their partners, which would make the equations of electromagnetism perfectly symmetric and which the traditional Big Bang model predicted.

The theory of cosmic inflation was proposed in the early 1980s and, as of today, nobody has been able to find the ‘smoking gun’, an extraordinary piece of evidence that will close all discussions on its correctness. It is amazing, however, to note that all data collected over the last 30 years, in particular the most precise measurements on the cosmic microwave background (CMB), are an astonishing reproduction of the predictions of the theory. Nevertheless, finding the inflaton, the particle responsible of the explosive growth, will definitely constitute a major breakthrough.

It has been known for many years that inflation could be driven by a negative-pressure vacuum energy density. A slowly rolling scalar field, with a potential very similar to the one predicted for a 125 GeV Higgs boson at high energy, could do the job. In other words, the fundamental scalar of the SM could also have played a role in inflation. Scientists have split opinions on this subject and the situation will be clarified only through new measurements. Everything could suddenly change if additional scalar particles are discovered at LHC, or if new precise measurements of the CMB identify the tiny signals due to the interactions of its photons with the primordial gravitational waves emerging from the inflationary period. The recent discovery of gravitational waves by LIGO opens the fantastic possibility of a direct detection of inflationary gravitational waves embedded in the so-called stochastic background.

New measurements or new experiments will settle, one way or another, in the near future, the issue of cosmic inflation and the role of the H boson in it.

The Stability of the Electroweak Vacuum

The question of the stability of the electroweak vacuum has been discussed at length for many years. Now that the mass of the new boson has been measured with great accuracy, the evolution of the H potential with energy can be computed with simple assumptions. The current value of the Higgs mass is close to the minimum value that ensures absolute stability of the electroweak vacuum within the Standard Model; this in turn implies a vanishing Higgs quartic coupling λ at the Planck scale. It is intriguing to note that, with the current central values of the H and top mass, λ seems to be very small at energies corresponding to the Planck mass, while a fully vanishing Higgs self-coupling is not favoured.

With a heavy top quark and a 125 GeV H, the electroweak vacuum in our Universe appears to be in a meta-stable state. The Higgs potential could somehow develop an instability for energies in the range 10¹⁰–10¹² GeV with a lifetime, however, much longer than the age of our universe. Nevertheless, taking into account theoretical and experimental errors, a stability up to the Planck scale cannot be excluded. We expect further refinements in the computations coming from more precise measurements of a few key parameters, namely the strong coupling constant α _s, the H mass itself and, mostly, the top quark mass.

It must be noted, however, that the extrapolation of the SM up to the Planck scale requires very strong assumptions that will be severely challenged in case of any NP discovery.

It would be extremely important to test the hypothesis that a light H boson could, in principle, rule its self-interactions, and the Yukawa interactions with fermions, in such a way that the theory could remain weakly coupled up to the Planck scale, without any dynamics appearing beyond the electroweak scale. If we could prove this assumption, it would in itself be an outstanding discovery: for the first time we would have a theory describing matter across 15 orders of magnitude in energy. Although possible, this scenario would, however, be severely constrained by the need for the couplings of the H boson to be finely tuned to very well predicted values.

SUSY and a Light Higgs Boson

While in the SM the H is unique, and its mass is essentially a free parameter, the most popular models of SUSY contain an entire family of Higgs bosons. Among its members the lightest CP-even Higgs super-particle has a mass that is strongly bounded from above. The discovery of a 125 GeV H has therefore killed all SUSY models predicting a lighter Higgs and has imposed strong constraints on all surviving ones. By tuning the many parameters of the theory it is still possible to accommodate a heavier-than-expected scalar boson, but this in turn introduces further constraints.

From the point of view of quantum mechanics, a 125 GeV scalar particle is a very strange object. Because it interacts preferably with heavier particles, it has a special relationship with the top quark. More precisely, quantum corrections would tend to push its mass towards absurd values, enormously higher than the 125 GeV we have measured. Since this is not the case, there is an unknown mechanism, built ad hoc, that protects it; or, for every contribution that tends to make it heavier, there is another one that cancels it out.

This last possibility is exactly what would happen if SUSY were true. Fermions and bosons yield opposite-sign contributions to the quantum corrections to the mass; therefore, for every positive contribution due to the top quark, there would be a negative one from the stop squark.

The presence of supersymmetric particles, in short, would explain in a natural way why the Higgs is so light, and this is also the reason why SUSY continues to maintain its fascination. However, for this ingenious mechanism to work, the stop squark should not have a mass too much greater than that of the top, which is about 172 GeV. And here we have a problem, because if the stops were so light we would have discovered them already at the LHC. All searches carried out so far have not yielded any signal, and the stops, if they exist, must have a mass greater than 400–500 GeV.

Here is the point: SUSY appears as a wonderful theory, able to solve, in a single stroke, some of the deepest questions of modern physics including dark matter, but has a very weak side. ATLAS and CMS have conducted hundreds of independent searches, but none of them has detected, so far, any of the many particles that the theory predicts.

If SUSY exists, its particles must be very heavy, and, since there is no sign of them for now, some scientists think that it is time to abandon this beautiful conjecture. Probably it is still early to do so, especially because in the coming years we will have the opportunity to systematically explore new regions in which many surprises could still be hidden.

However, if no sign of SUSY appears in the next few years, it will be definitely time to review in depth some of its paradigms.

Probing the Intimate Nature of the New Boson

All measurements of the new boson until now indicate full compatibility with the properties of the SM Higgs scalar, but the associated uncertainties are large, and the possibility for non-standard properties remains. Moreover, although other SM-like Higgs bosons have been excluded over a wide range of masses, additional Higgses, with exotic production and decay modes, remain a possibility.

Many open questions on the H itself are still on the table. Are the strengths of its interactions with all other particles and with itself precisely the ones predicted by the SM? Is it alone or accompanied? Is it elementary or composite? Answering some of these questions might open unexpected paths toward new physics.

The discovery of new, fundamental particles or forces can happen through direct detection of new states of matter, but can also proceed indirectly through precision measurements. Ultra-massive particles, far too heavy to be produced at LHC, can float like ghosts around known particles, producing virtual effects that interfere with the known mechanisms of the SM. This results in subtle anomalies that might yield an indirect discovery of NP. Being so sensitive to any such particle, the H boson is a natural candidate to act as a portal for physics beyond the SM.

This is the reason why the LHC experiments are now performing precision measurements of the H properties, in particular of its couplings. The strength of the interaction of the Higgs boson with known particles can be extracted from the signal strength, σ/σ _SM, expressed as a ratio with respect to the SM expectations, for different production and decay modes.

The discovery of the Higgs has been driven by decay modes of the H into pairs of bosons: photons, W and Z. Much more difficult to handle are the decays into pairs of fermions. We have just recently achieved the first observation of the H decaying into tau leptons, while we are still struggling to reach a 5σ signal for the decay into b quarks. Similar efforts are made trying to identify H produced in association with a pair of top quarks. This latter is an extremely challenging production mechanism, with tiny cross-sections at LHC, and directly sensitive to the top Yukawa coupling.

Meanwhile, detailed studies are looking for potential anomalies in the H differential cross-sections and in the searches for rare decays of the H, with the secret hope that some of those could lead to surprises.

One example of these is the search for H decaying into Zγ, for which the SM predicts a branching ratio of 1.54×10⁻³; the channel is particularly interesting since it is very sensitive to possible contributions from NP via decay loops of new, heavy charged particles.

Establishing the coupling with muons will be an extremely tough job, since the SM predicts a branching ratio of 2.2×10⁻⁴ for this decay mode. Along the same lines, it will be practically impossible, unless there are huge enhancements induced by NP processes, to address the decay of the Higgs into pairs of electrons, where we expect a SM branching ratio of 5×10⁻⁹.

Statistics matters a lot for all these studies. We need to produce tens of millions of Higgs bosons to improve the accuracy on the couplings and to study the rare decays that could hide anomalies. This will happen with LHC running another ≈20 years, while significantly improving its instantaneous luminosity. With the phase of High Luminosity LHC – expected to start in the mid-2020s – CMS and ATLAS plan to collect a total luminosity of more than 3000 fb⁻¹, a total statistics more than 30 times higher compared with today.

The projections that have been produced by extrapolating the ongoing studies tell us that it will be possible to measure the H mass with an accuracy better than 50 MeV. The H total width could be estimated down to the SM level (4.2±2 MeV). Furthermore, it will be possible to perform detailed studies of difficult production modes like ttH, while rare decays such as Zγ and μμ could be thoroughly investigated.

For what concerns the couplings, the projections estimate an ultimate precision in the range 2–10%. To put this result into the right context, it must be noted that the heavier the unknown particle interacting with the H, the smaller the effect on its couplings. To define the scale, objects as heavy as a few TeV will modify the couplings at the percent level or below. This means that at the end of the LHC lifetime, if nothing new appears in data, the challenge to discover new physics through precision measurements will still be open.

Lastly, it will be very difficult at LHC to measure the H self-coupling λ, a crucial parameter of the SM that probes the H sector to its full extent, including the detailed structure of the electroweak phase transition. It could be extracted from the very rare events in which Higgs bosons are produced in pairs, but they are extremely difficult to reconstruct in the LHC environment. It is clear, therefore, that to fully explore these issues we need to start looking into new accelerators beyond the LHC.

Future Colliders?

Many different alternatives are under evaluation in considering future colliders. There are projects to build e ⁺ –e ⁻ colliders, to be used as precision Higgs factories, and studies to prepare a new powerful p–p accelerator aiming at a centre-of-mass energy of 100 TeV.

The two approaches are fully complementary. In a lepton collider we could perform the most precise measurements of all parameters of the SM, stressing it to the extreme limit, while in a 100 TeV p–p collider we could directly discover new states of matter up to masses of tens of TeV. In addition, a high-energy hadron machine would definitely allow measuring the Higgs self-coupling and studying its potential away from equilibrium, thus accessing all details of the electroweak phase transition.

Among the different options, scientists are also investigating the possibility to increase the energy of LHC to 28 TeV by equipping the existing tunnel with more powerful magnets.

These are all very ambitious projects that require the effort of hundreds of scientists, to address the most important physics cases and to find solutions to the many technological challenges.

It is urgent to start thinking forward to the next generation of colliders. The very first discussions on the LHC started in the mid-1980s and the accelerator was completed in 2008. If we want a new machine at the end of the high luminosity phase of the LHC, the time to act is now.