At the start of 2010, the particle physics community was abuzz with hopes and excitement. Just a few weeks later, the experiments at the Large Hadron Collider (LHC) would venture beyond the energy frontier, where physicists hoped to find exotic particles that would pave the way for a more complete theory of the infinitely small: to physics beyond the Standard Model.

The Standard Model of particles and forces was developed in the second half of the 20th century to explain the discovery of a host of new particles, and to describe – within the framework of a single theory – their behaviour and the forces that link them. This model has been hugely successful and accurately summarises the various phenomena that have been observed. However, it leaves a number of questions unanswered, about subjects such as the nature of dark matter or the absence of antimatter in the universe.

Indeed, when the huge collider was on the verge of starting up, theories about “Beyond the Standard Model” physics were igniting passionate debates and the acronym BSM was cropping up in everyone’s presentations. Claude Duhr had just defended his thesis at the Catholic University of Leuven (Belgium) and was wondering which direction to take. “I had a choice of focusing on precision calculations of the Standard Model or studying physics beyond the Standard Model. Lots of my colleagues couldn’t see any future in precision calculations and advised me to pursue research into BSM theories,” he recalls, ten years later. But Claude Duhr’s hunch was right.

Standard Model,Higgs boson,Diagrams and Charts
The Standard Model of particles and forces describes three of the four forces of nature that act on 12 particles of matter through the exchange of messenger particles. (Image: Daniel Dominguez/CERN)


Two years later, ATLAS and CMS discovered the Higgs boson, confirming the validity of the Brout-Englert-Higgs mechanism. A fabulous discovery that has left physicists hungry for more. But the Higgs was a giant tree hiding a meadow full of well-known flowers. No exotic plants were to be found in these high-energy plains. No unknown particle has made its presence felt by producing a bump on the physicists’ charts since. Month after month, the Standard Model has revealed itself to be more solid than ever.

On the road to precision

But our explorers weren’t discouraged. As no hitherto unknown particle had emerged, they would study, with ever more precision, known phenomena at all new energies. They scrutinised every blade of grass and every flower in this beautiful meadow, looking for a curiosity, an anomaly that would lead them to something new.

“To begin with, scientists were looking for spectacular phenomena that have now mostly been ruled out. The approach now is to carry out precision measurements,” explains Paolo Azzurri, co-leader of the Standard Model group in the CMS experiment.

Over the years, the LHC has therefore been used for increasingly precise studies, which represent a real challenge for a hadron collider (we’ll see later why this is the case). This was the road that Claude Duhr, who today is a theorist at CERN, ultimately decided to take. “More and more of the work of theorists focused on precision calculations to test the Standard Model as thoroughly as possible,” he explains. In the CERN Courier article in March 2020 on the same theme as this series of features, Michelangelo Mangano, a theorist at CERN, reminded readers that 1600 of the 2700 articles on the LHC in peer-reviewed publications report measurements of Standard Model particles.

The Standard Model of particles and forces describes three of the four forces of nature that act through the exchange of messenger particles, known as bosons. The strong force, which binds quarks in protons and neutrons, is carried by gluons. The electromagnetic force is transmitted by photons, and the weak force, which is responsible for radioactive decay,  is carried by the W and Z bosons. There are also 12 particles of matter, grouped into two families: quarks, like those that form protons and neutrons, which feel the strong and weak forces; and leptons, such as electrons, on which the electromagnetic and weak forces act. Each of the two families comprises six particles (see table above).

In reality, the Standard Model is built on two quantum theories : the electroweak theory, which describes the electromagnetic and the weak forces, and  quantum chromodynamics, which describes the strong force. So, here we have the basics.

Determining the free parameters

Proton Collisions,Event Displays,Physics,ATLAS,W bosons,7 TeV,muons,neutrinos
A candidate event for a W boson decaying into one muon and one neutrino recorded by the ATLAS experiment in 2011. Such events were used for the measurement of the W boson’s mass. (Image: ATLAS/CERN) (Image: CERN)

One advantage of the Standard Model is that it is predictive: it predicts all possible interactions between particles with a precise probability (which physicists call the “cross section”). However, it doesn’t predict the masses of the fundamental particles: these are among the parameters measured by the experiments. Moreover, these masses vary greatly: for example, the mass of the heaviest quark, the top quark, is almost 90 000 greater than the up quark, the lightest.

In total, there are 19 free parameters (aside from the parameters relating to neutrinos). Measuring them precisely is crucial to be able to calculate the interaction cross sections and test the consistency of the Standard Model. Although the Standard Model doesn’t predict their values, it ties some parameters together. And, as the measurements still have a degree of uncertainty, “if the measured mass of the W boson changes while the measured mass of the top quark remains unchanged, then the predicted mass of the Higgs should also change,” explains Andrew Pilkington, a physicist with the ATLAS experiment. “By measuring all of these parameters independently, we test the relationships predicted by the Standard Model and impose constraints on physics beyond the Standard Model.

One of the success stories of the LHC is how it has improved the measurements of these free parameters, starting, of course, by determining the mass of the Higgs boson. ATLAS has also increased the precision of the mass of the W boson. “This was a remarkable achievement that no one had anticipated,” says Jonathan Butterworth, a physicist with the ATLAS experiment who was co-leader of the Standard Model group in 2010.

Using a hadron collider to make precise measurements is far from easy. The LHC collides composite particles, protons, formed of three quarks that interact via gluons. The starting energy is not known – we don’t know which components of the proton are colliding – and the background (all the simultaneous minor interactions that interfere with the result we’re looking for) is very significant. But, armed with ten years’ worth of simulations of their proposed detector and drawing on the outstanding work of hundreds of physicists to understand and reconstruct the events (physics jargon for the collisions and the particles emerging from them), the LHC experiments managed to deliver precise results after just two years.

Real Events,For Press,CMS ,Top quark,Single Top,Event Display,collision,CMS event display,tZq
A collision event from 2016 in which a top quark is produced in association with a Z boson at CMS. (Image: CMS/CERN)

The LHC has also chalked up one of the best measurements of the mass of the top quark, which was discovered in 1995 at the Tevatron collider in the United States. “The value combining the results of the Tevatron was already very precise,” remarks Nadjieh Jafari, co-leader of the top-quark physics group of the CMS experiment. “But at the LHC we are able to measure the mass of the top quark using additional channels of production of top quarks, and for some we got equal or better accuracy.”

Other free parameters enter into the calculation of interactions. The precise measurement of the electroweak mixing angle is one of the key results from the LHC experiments. This result serves to constrain the masses of the W and Z bosons.

Beauty particles and flavour physics

The LHCb experiment specialises in the study of B hadrons, particles that contain a bottom quark or its antiparticle, and has developed expertise in measuring the parameters that can be used to determine the probability that a quark will transform into another via the weak interaction. These transformation processes were first described by Nicola Cabibbo, Makoto Kobayashi and Toshihide Maskawa, and can be calculated using a matrix that bears their initials. The CKM matrix is made up of four free parameters – like the masses of particles – that are measured in experiments. Measurements via different processes can be used to test the robustness of the Standard Model. The structure of the CKM matrix can be represented graphically by triangles, with the parameters represented by the lengths of the sides and the angles. For example, LHCb has obtained the best measurement of one of these angles, γ. This work is linked to work on the phenomenon of charge-parity (CP) violation, which is at the origin of a difference in behaviour between matter and antimatter. The experiment has also obtained excellent results relating to CP violation, including proof of the phenomenon occurring with particles containing a charm quark, whereas before it had been observed only with particles containing a strange or a bottom quark. 

But B mesons have opened up an even wider field of study for LHCb.

“The LHCb programme has evolved not only to confirm CP violation with B mesons, but also to understand the phenomena of flavour physics in general,” explains Tatsuya Nakada, a pioneer of LHCb and its first spokesperson. “The study of these phenomena is an extremely useful way of measuring the coherence of the Standard Model.”

The smallest of the LHC’s main experiments has become a gold standard in the field of flavour physics. A great success considering that its capabilities were considered to be limited to begin with. “The start-up of LHCb wasn’t easy,” recalls Giovanni Passaleva, another former spokesperson of the experiment. “Our objectives were considered far too ambitious for a hadron collider with so much background. The B factories (the BaBar experiment in the United States and the Belle experiment in Japan – Ed.) already covered the research we were planning. We were worried, but today we are proud and happy.”

LHCb experiment has become a gold standard in the field of flavour physics, achieving crucial results studies of the weak interaction, and in the field of CP violation. (Image: Maximilien Brice/CERN)

Among other phenomena, the experiment is interested in decays that the Standard Model predicts to be very rare. The comparison of their measurements with the predictions allows it to test the robustness of the Standard Model. “If you discover a deviation, you might have come across a sign of new physics,” explains Tatsuya Nakada. LHCb and CMS have thus measured the cross section of the decay of the B0s meson into two muons, a process that, according to the theory, is produced in only three of every billion decays of this meson (the image at the top shows such an event, recorded by LHCb in 2016. The two muon tracks from the B0s decay are seen as two green tracks running through the whole detector). LHCb has studied other very rare interactions of B mesons. The results are in agreement with the Standard Model but the possibilities for new measurements are far from being exhausted, covering many other phenomena.

“Precision is a fantastic tool for understanding the world of particles,” says Gian Giudice, head of CERN’s Theory department. “The LHC has moved from discovery to precision and there is lots to learn.”

Next up: The surprises of the Standard Model at high energies