"Robust” is what scientists working on the Large Hadron Collider (LHC) like to use to describe the Standard Model. By stubbornly probing it for weaknesses over the past 10 years, they have run up against the extreme solidity of this theory, which describes particles and forces. However, particle physicists are well aware that this model, finalised in the 1970s, has a few shortcomings. They are therefore searching for a wider theory that could resolve certain mysteries, and are banking on the LHC to help them find it. But apart from the triumphant discovery of the Higgs boson, no other new fundamental particle has been discovered, nor any extraordinary phenomenon that might lead to a more comprehensive theory.

Has all this deterred them from their quest? “Quite the opposite,” smiles Nadjieh Jafari, co-leader of the top-quark group at the CMS experiment. “There are many different territories for us to explore with the LHC: it’s an exciting period.” By venturing to the highest energies ever reached, physicists are observing many phenomena that were previously out of their reach.

“We are measuring the behaviour of nature at new energies,” says Jonathan Butterworth, a physicist with the ATLAS experiment. “Even though they fit with the Standard Model, these phenomena are totally new to us.” 

New energies bring new phenomena

The physicists at ATLAS are interested, for example, in the high-energy transverse jets of quarks and gluons. These jets can contain massive particles such as the W and Z bosons, the messenger particles of the weak force. “These new observations open up fields of research on the structure of such jets, to help us understand the strong interaction, as well as the electroweak interaction when a W or Z boson is emitted,” says Butterworth. The image above shows an ATLAS experiment event with two such jets (yellow and green cones).

The experiments are therefore examining every square centimetre of this new territory, looking for processes that have been predicted but are either extremely rare, have never been observed before, or even better, are completely unexpected. These experiments include ATLAS and CMS, which observe the fusion and diffusion of electroweak bosons – very rare interactions. These events produce W and Z bosons, which either fuse together to produce another particle (fusion) or bounce away from each other (diffusion). “It’s as if the LHC had become a collider of weak bosons; these phenomena are completely new at these energies,” says Paolo Azzurri, co-leader of the Standard Model group at CMS.

On the left, a CMS event display of a candidate event in which two W bosons and one Z boson are produced. On the right, an ATLAS event display of a candidate event in which two Z bosons are produced. (Image: CMS and ATLAS, CERN)

Another observation in this region, which is around 50 times rarer than the production of the Higgs boson, is the simultaneous production of three weak bosons. This phenomenon is seen only once in approximately every 100 billion proton collisions. These interactions also provide a new tool with which to probe the Standard Model and the weak interaction carried by the W and Z bosons. “The programme of boson fusion and diffusion started recently,” says Andrew Pilkington, a physicist with the ATLAS experiment. “There is still a long way to go before we can move from observation to the precision measurements that could allow us to detect deviations.”

The promise of virtual particles

Physicists measure the frequency of these phenomena (their cross section) as precisely as possible and compare it with theoretical predictions. Any difference could indicate the presence of new particles. If unknown particles exist, they may be too massive to be produced at the LHC, but their quantum behaviour could help spot them.“In quantum field theory, anything that isn’t forbidden can happen,” explains Claude Duhr, a theoretical physicist at CERN. “Particles that are too massive to be produced in reality may appear and disappear fleetingly during an interaction.” These particles are known as virtual particles: they are involved in the interaction, but they are not directly detected. “We can deduce their presence because they have an impact on the interaction. For example, we could observe an excess of events during an interaction, which would indicate the presence of virtual particles,” continues Duhr. This is why it is necessary to measure interactions very precisely, in order to be able to compare the results with the theoretical predictions.

However, one big difficulty is obtaining precise theoretical predictions. Due to the virtual particles, there are not just one but many ways in which the particles can be produced during a proton collision. Physicists have to take into account not only the direct processes (leading order or LO), in which these particles are directly produced without any contribution from virtual particles, but also the processes that result from the appearance of a virtual particle (next-to-leading order or NLO) or even two virtual particles (next-to-next-to-leading order or NNLO) and so on.

These processes with the appearance of virtual particles occur more frequently when the strong interaction is involved (which is the case for proton collisions) and when the energy level is high. It is crucial to take them into account for certain interactions, such as the production of the Higgs boson. However, these “perturbative” theoretical calculations are very complex and have required physicists to develop new mathematical tools, spurred on by the results from the LHC experiments. “It took four people four years to calculate the production of the Higgs boson at the next-to-next-to-leading order NNLO,” explains Duhr, a specialist in this field. And physicists are studying numerous interactions at the LHC, which pushes theorists to carry out many perturbative calculations to allow a comparison with the theory.

To make things even more challenging, the theoretical predictions also rely on solid knowledge of the proton. Paradoxically, the proton, which makes up all the matter around us, is a complex system and its structure is poorly understood. Its three quarks are bound by the strong force, which acts through the exchange of gluons, the messenger particles of the strong interaction. Determining the distribution of a given proton energy among the components of the proton (which we also refer to as partons) is anything but simple. This information is important to understand the initial conditions or, in other words, the energy available during the collision. “The huge amounts of data from the LHC have allowed us to considerably improve our understanding of the structure of the proton,” says Giorgio Passaleva, a physicist with the LHCb experiment.

The top quark: a massive effect

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Event recorded by the CMS experiment in 2016 in which four top quarks were produced simultaneously (Image: CMS/CERN)

Among the many studies of the Standard Model, those relating to the top quark are particularly special. The top quark is the heaviest of the quarks and is almost 90 000 heavier than the lightest, the up quark. It has a very strong coupling with the Higgs boson, which is to be expected since the mechanism associated with this boson that gives elementary particles their mass. As the top quark is also sensitive to the strong, weak and electromagnetic forces, it can be produced by a myriad of processes. It is therefore an ideal candidate for exploring the new energy territories made accessible by the LHC. Florencia Canelli, co-leader of the top-quark physics group at the CMS experiment, started working on the topic at Fermilab in the US in 1998, three years after the laboratory discovered the quark. Pioneering studies were carried out at the Tevatron to define the top quark’s characteristics but, for the past 10 years, the LHC has provided an excellent observation ground for this particle. In the space of just a few years, ATLAS and CMS have been able to measure the mass of the top quark with excellent precision.

“With the LHC, we have access to unexplored regions and huge amounts of data, which allow us to gain a more complete and precise understanding of the top quark. These measurements also allow us to constrain new physics processes,” explains Florencia Canelli, CMS physicist.
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Event recorded in 2018 by the ATLAS experiment in which four top quarks are produced. (Image: ATLAS/CERN)

The high energies at the LHC also provide an opportunity to study the production of top quarks with massive particles such as the W and Z bosons. “Or the simultaneous production of four top quarks, a quite extraordinary phenomenon,” confirms her colleague Nadjieh Jafari, who has been working on the subject since 2008 and is now co-leader of the CMS top-quark analysis group.

The study of the top quark is one of the main focuses of the search for physics beyond the Standard Model. It is thought that unknown particles with a higher mass could decay into top quarks. “The top quark opens a door to theories beyond the Standard Model. Many predict new particles would decay into top quarks or into the same final states as those of the top quark,” confirms Francesco Spano, co-leader of the ATLAS top-quark analysis group.

The study of the interactions involving this special particle is far from complete. Wolfgang Wagner, a physicist with the ATLAS experiment, displays a table indicating the different processes producing the top quark at the LHC and the analyses carried out for each of them. 19 of the 48 boxes in his table are marked with a cross, indicating that the process in question has been studied. “Ten years ago, we were just starting the study of the production of top-antitop pairs, the most accessible of the processes. Today, we have exceeded the precision of the theory for this process, but we still have many other processes to examine,” he explains.

Strange assemblies

Illustration of the possible layout of quarks in a pentaquark particle, such as those discovered at LHCb. (Image: Daniel Dominguez/CERN)

In its exploration of these new energy territories, LHCb has unearthed exotic assemblies of quarks in which four or even five quarks are bound by the strong interaction. According to the model of hadrons, there are two categories of composite particles: mesons, composed of pairs containing a quark and an antiquark, and baryons, such as protons, containing three quarks. In the quark model proposed in 1964, Murray Gell-Mann and George Zweig also predicted the possible existence of exotic hadrons such as tetraquarks and pentaquarks.

In 2010, LHCb spotted its first tetraquark, followed by several others over the course of the last 10 years. In 2015, the experiment created a stir by announcing the first discovery of a pentaquark. In 2019, a second pentaquark was identified. “These exotic systems are so extreme and strange that they have aroused the interest of theoretical physicists,” explains Giovanni Passaleva, a physicist and former LHCb spokesperson. In fact, the appearance of these exotic hadrons has inspired new research in order to understand their internal mechanisms.

“The study of these exotic assemblies is another tool for testing the hadron model and quantum chromodynamics, the theory of the strong interaction,” adds Tatsuya Nakada, the first spokesperson of LHCb.The experimental data on exotic hadrons will allow physicists to improve their understanding of quantum chromodynamics at low energies, which describes the bound states of quarks.

LHCb physicists are pursuing their examination of this small corner of the Standard Model, just like all the other thousands of LHC scientists studying the new areas opened up by the LHC. Even though the number of events produced by the LHC is already phenomenal, large quantities of data are still required to understand these new phenomena in detail. The Standard Model is robust, so scientists need patience and precision to find its limits.

“We explore nature by getting close to the conditions at the very beginning of time, on the smallest scales ever achieved, and we look for deviations from our expectations. It’s in these minuscule regions of space and time that we will be able to detect the limits of the Standard Model,” concludes Francesco Spano, ATLAS physicist.