Lessons from a decade with the Higgs boson

The standard model (SM) of particle physics, the theoretical framework that describes the electromagnetic, weak, and strong interactions between particles, is one of the most tested theories in physics. Yet the theory would never have come together if not for a crucial insight regarding symmetries.

Half a century ago, theoretical physicists faced a problem: The symmetries that play a critical role in particle physics due to their link to conservation laws through Noether’s theorem also predict that the mass of all known particles must be zero . In three separate papers published in 1964, six physicists independently proposed a solution. They suggested that the universe is permeated by a field with a radially symmetric potential, featuring a local maximum at zero and a set of minima displaced from zero. As the universe cooled, that field—which came to be called the Higgs field—spontaneously settled to a nonzero minimum value. Known as electroweak symmetry breaking (EWSB), the proposed process would allow particles to gain mass through their interaction with the Higgs field while preserving all the other symmetries related to the known conservation laws.

Another prediction of EWSB was the existence of a new particle, the Higgs boson. The particle has very particular quantum properties: a spin of 0, a wavefunction that does not change under a reversal of charge and parity (CP), and an interaction with itself through self-coupling. That combination of properties makes it unlike any other known fundamental particle.

The mass of the Higgs boson was not predicted. But upon determination of the mass, the couplings of other particles with the Higgs boson are given by the SM. Therefore, measurements of the Higgs boson’s mass, its coupling strengths to other particles, and its self-coupling would help establish if EWSB is the mechanism through which particles gain mass.

In 2012, almost half a century after the Higgs boson was first postulated, a new particle consistent with the predictions was finally discovered by the ATLAS and CMS collaborations at CERN’s Large Hadron Collider (LHC), the world’s largest proton–proton collider.

In the decade since, experimentalists have focused on making precise measurements of this new particle, investigating each of its properties, and using it to probe new physics. To enable this, the LHC has delivered a wealth of data, with researchers sifting through a small fraction of the almost 7 million proton–proton collision events that exposed each of the detectors to Higgs bosons. All the measurements performed to date have shown that the properties of the particle are consistent with the predictions of the SM Higgs boson.

Properties of the new particle

Mass. One of the first properties to be precisely measured was the Higgs boson’s mass. Because the particle decays in roughly 10^–22 seconds, only its decay products are observed in the detectors. The two decay modes that the ATLAS and CMS detectors can most precisely measure are the Higgs boson decaying to two photons and the Higgs boson decaying to two Z bosons, which then decay to two pairs of electrons or muons. Figure 1 below shows a candidate two-photon event. The most precise measurement of the mass, obtained by the CMS team in 2020, is 125.38 ± 0.14 GeV, which corresponds to a precision of roughly 0.2%. That is approximately the same precision as that of the mass measurement of the top quark, a particle discovered 27 years ago.

Spin/CP. The next critical properties to establish are the spin and CP, which are measured through the angular distributions of the Higgs boson decay products. Observation of the Higgs boson decaying to two photons ruled out a spin of 1, because that would violate the conservation of quantum spin. Various exotic hypotheses, such as different decay modes originating from a Higgs boson with different spin, have been tested. All results indicate that this boson, no matter how it is produced or how it decays, has a spin/CP of 0+, as predicted by the SM.

Coupling to other particles. The Higgs boson production and decay rates are a function of the particle’s coupling strength to other particles. Figure 2 shows current experimental constraints on the Higgs boson coupling to various other particles. Due to the high resolution for measurements of leptons and W and Z bosons decaying to leptons, the Higgs boson couplings to the W and Z bosons have been measured to within 6% uncertainty. Due to the large production and decay rates, the couplings to top and bottom quarks and to tau leptons (third-generation quarks and leptons) have been constrained to the SM prediction to within 7–11% uncertainty.

Self-coupling. The rate of events containing two Higgs bosons depends on the strength of the particle’s self-coupling. However, due to the quantum interference of the self-coupling processes with similar SM processes, events containing two Higgs bosons are extremely rare.

For measurements of events producing two Higgs bosons, at least one of the Higgs bosons is typically required to decay to a pair of bottom quarks to ensure that sufficient events are selected, as this is the most probable Higgs decay. For the second Higgs boson, decays to a pair of photons or a pair of tau leptons are used because the better resolution and smaller backgrounds make these the most sensitive channels. Although the Higgs self-coupling process has not yet been observed experimentally, recent results combining these channels limit the self-coupling strength to be within a factor of 3.1 of the SM prediction.

Width. Improvements to theoretical predictions have been critical in increasing experimental precision and enabling new measurements. One insight permitted the attainment of a measurement previously thought to be impossible. The width of the Higgs boson is a critical parameter that is tied to the sum of all the various ways it can decay. Any deviations from the SM prediction would be strong evidence for new physics beyond the SM (BSM). However, there is a problem: The width is expected to be a thousandth of the experimental resolution.

Recent theoretical developments have highlighted that the level of quantum interference of the Higgs boson with other processes observed in proton–proton collisions depends on the boson’s width. By measuring the rate of the other processes (and making some theoretical assumptions), researchers can derive indirect constraints on the Higgs boson width. Using that insight, the best experimental constraints have placed a limit on the width at twice the SM prediction .

Looking beyond the SM

Particle physicists usually interpret Higgs measurement results within the context of the SM due to the theory’s success and wide applicability. However, other theories can also describe known particles and their interactions. Just as the EWSB mechanism of the SM predicted a new boson and new interactions, alternative models and BSM theories also predict new particles and interactions. The question therefore becomes: Do Higgs measurements support the plausibility of the SM? Or do other theories, such as the popular supersymmetry , better fit the data?

A partial answer comes from the Higgs boson mass. In the SM the mass of the Higgs boson is determined by the Higgs quartic coupling, which is a free parameter that must be determined experimentally, whereas in supersymmetry an SM-like Higgs boson’s mass would be closely linked to the characteristics of the particles and forces predicted by the theory. The mass measurement at approximately 125 GeV rules out several supersymmetric models and complements direct searches for supersymmetric particles that are also undertaken at the LHC.

The presence of additional Higgs bosons is another prediction of supersymmetric models. In those theories, there are various possibilities for how the extra Higgs bosons would interact. For example, one boson could couple only to quarks and leptons, while a second would couple only to bosons. Another possibility is that the multiple Higgs-like bosons would couple with different strengths to the quarks and leptons from different generations. In this context, it is important to establish if the ATLAS and CMS collaborations are observing the effects of only one Higgs boson.

Experimentalists can search for additional Higgs bosons directly, and they can search indirectly through Higgs coupling measurements. Within the SM, the strength of the couplings is proportional to the particle’s mass, as shown in figure 2. Current results show excellent agreement with the SM and tip the scale in the direction of a single Higgs boson. However, little is known regarding the coupling of second-generation leptons (muons) and quarks (charm). That important piece of the puzzle is one of the many factors driving the LHC’s next run, during which observation of the coupling to muons is expected to be within reach.

The properties of this new boson and their agreement with SM expectations have even more profound implications. In the SM, the shape of the Higgs potential is determined to first order by the masses of the Higgs boson and of the heaviest SM particle, the top quark . As shown in figure 3, when combined with the top quark mass measurement, the measurement of the Higgs boson mass reveals that the minimum the universe settled into billions of years ago may not be the global minimum of the Higgs field’s potential. If it is not, a phase transition could eventually take the universe to a different minimum, with fatal consequences due to the resulting changes to the constants of nature. The discovery of additional particles or interactions, such as those predicted by BSM theories, would significantly alter the predicted shape of the Higgs potential and could potentially reveal that we reside in a stable universe.

BSM theories are motivated by the fact that the SM is known to be incomplete. Certain phenomena such as the nature of dark matter (DM) cannot be explained within the SM. Commonly proposed DM candidates, including those offered by theories with extra dimensions, typically interact only through the weak or gravitational forces due to cosmological constraints, and they remain extremely challenging to detect despite many direct and indirect searches.

At the LHC, the Higgs boson presents an additional avenue for this search: DM candidates are massive, and their mass could originate from the Higgs mechanism. DM particles do not interact through the electromagnetic or strong forces, so they are invisible to the ATLAS and CMS detectors. However, if DM particles are light enough, Higgs couplings to DM would increase the Higgs boson width. The current result of 3.2 –1.7 +2.4 MeV agrees with the SM prediction of 4.1 MeV, and therefore no evidence of Higgs couplings to DM particles currently exists. Dedicated searches for Higgs decays to particles that are invisible to the detectors additionally aim to set independent limits on the strength of potential Higgs couplings to such particles.

Higgs measurements in the future

The third data-taking run of the LHC has just begun, and it is expected to double the size of the LHC data set by the end of 2025. The larger data set should improve the precision of Higgs boson measurements and include tricky observations such as the coupling of the Higgs boson to muons.

The upgrade to the LHC, the High-Luminosity LHC (HL-LHC), is expected to begin data-taking in 2029. Thanks to upgrades of the accelerator to higher luminosity and of the detectors, by the end of the program it is expected to provide an order of magnitude more data than the existing data set. This will allow many properties of the Higgs boson to be measured more precisely , which will increase the sensitivity to deviations that could provide evidence for BSM physics. For example, the production cross section, which currently has an uncertainty of 7%, could be measured to a precision of 1.6% using the combined data sets from ATLAS and CMS. Many of the couplings of the Higgs boson could be measured to a precision of 1.5–4%, including the Higgs–top quark to a precision of 3% (currently known to 11%). The Higgs self-coupling is expected to be measured with an uncertainty of 50%, which will provide experimental evidence for this key component of EWSB.

Despite the success of the LHC and the exciting results expected from the HL-LHC, given the significant time scales for particle physics, preparations for the collider or colliders to follow have already begun. Candidate colliders are under consideration at CERN and in China and Japan. Electron–positron colliders have low background rates and precise control of the collision energy. They offer the possibility to make extremely precise absolute measurements of Higgs boson couplings by measuring the width to percent-level accuracy. Extremely precise measurements of Higgs couplings could be used to detect new physics indirectly at high energy scales—a constraint on a coupling of 0.3%, for example, probes new physics at energy scales of 10–30 TeV. Proton–proton colliders have larger backgrounds but can access higher energies. They are projected to measure the Higgs–top coupling to 1% and the Higgs self-coupling to 5%. Should any hints of new physics be obtained at the HL-LHC or one of the electron–positron colliders, the proton–proton colliders would likely be able to observe any new particles directly.

A deeper understanding of EWSB will provide not only a better understanding of fundamental particles and their interactions but also an invaluable window into the early development of our universe—and a powerful probe in the search for physics beyond the SM. Perhaps the measurements from runs of the LHC, HL-LHC, or a future collider will reveal new secrets about the physics of our universe.

Haider Abidi is a Goldhaber fellow at Brookhaven National Laboratory. He studies the interactions of the Higgs boson with vector bosons using the ATLAS detector and develops tracking algorithms at trigger level for the HL-LHC. Heather Gray is an assistant professor at the University of California, Berkeley, and a faculty scientist at Lawrence Berkeley National Laboratory. She is a member of the ATLAS experiment. Her research focuses on the interaction of the Higgs boson with fermions and on the development of software algorithms. Martina Ojeda is a postdoctoral fellow at DESY in Hamburg, Germany. She is working on various measurements of Higgs boson interactions and on the upgrade of the ATLAS detector for the HL-LHC.