One Higgs, three discoveries

18 September 2020

The ATLAS and CMS collaborations have not only discovered a new particle, argues Yosef Nir, but also laid bare the underpinnings of electroweak interactions and uncovered the first evidence for a new type of fundamental interaction – one not related to a known symmetry of nature.

The discovery of the Higgs boson in 2012 was the culmination of almost five decades of research, beginning in 1964 with the theoretical proposal of the Brout–Englert–Higgs (BEH) mechanism. This discovery was monumental, but was itself just a beginning, and research into the properties of the Higgs boson and the BEH mechanism, which has unique significance for the dynamics of the Standard Model, stretches the horizons of even the most ambitious future-collider proposal. Despite this, the ATLAS and CMS collaborations have already made three major discoveries relating to the Higgs boson. These are the jewels in the crown of LHC research so far: an elementary spin-zero particle, the mechanism that makes the weak interaction short range, and the mechanism that gives the third-generation fermions their masses. They can be related to three distinct classes of measurements: the decay of the Higgs boson into two photons, and its production from and decays into the weak force carriers and third-generation fermions, respectively.

Until 2012, the list of elementary particles could be divided into just two broad classes: spin-1/2 matter particles (fermions) and spin-1 force carriers (vector bosons), with a spin-2 force carrier (the graviton) pencilled in by most theorists to mediate the gravitational force. The first jewel in the LHC’s crown is the discovery of an elementary spin-0 particle – the first and only particle of this type to have been discovered. The question of the spin of the Higgs boson is intrinsically linked to the dominant discovery mode in 2012: the decay into two photons. Conservation laws insist that only a spin-0 or spin-2 particle can decay into two photons.

A Higgs candidate event

To decide between the two spin options, a more complex study than just measuring decay rates was needed. The spin of the parent particle affects the angular distributions of the daughter particles of Higgs-boson decays. Studies began immediately within ATLAS and CMS, showing unambiguously that the newly discovered particle was spin-0. The ways in which this particle is produced and the ways in which it decays call for its identification with the only particle that was predicted by the Standard Model of particle physics that had not been observed by 2012 – the Higgs boson. The field related to this particle is the BEH field.

The next question was whether this new particle is elementary or composite. If the Higgs boson is actually a composite spin-0 particle, then there should be a whole series of new composite particles with different quantum numbers – in particular, spin-1 particles whose mass scale is roughly inversely proportional to the distance scale that characterises their internal structure.

One can test the question of whether the Higgs boson is elementary or composite in three ways. Firstly: indirectly. The virtual effects of these heavy spin-1 particles would modify the properties of the W and Z bosons. Part of the legacy of the LEP experiments, which operated at CERN between 1989 and 2000, and the SLD experiment, which operated in SLAC between 1992 and 1998, is a large class of precision measurements of these properties. The other two ways are pursued by the LHC experiments: the direct search for the new spin-1 particles, and precision measurements of properties of the Higgs boson itself, such as its couplings to electroweak vector-boson pairs, which would differ if it were composite. No such composite excitations have been discovered to date, and the Higgs boson shows no signs of internal structure down to a scale of 10–19 m – some four orders of magnitude smaller than the proton.

The energy stored in the Higgs field

A second jewel

The electromagnetic and strong interactions are mediated by massless mediators – the photon and the gluon. Consequently, they are long-range, though colour confinement – the phenomenon that quarks and gluons cannot be isolated – renders the long-range effects of the strong interaction unobservable. By contrast, weak interactions are mediated by massive mediators – the W and Z bosons – with masses of the order of 100 times larger than that of the proton. As a result, the weak force is exponentially suppressed at distances larger than 10–18 m.

A common feature of the electromagnetic, strong and weak forces is that their mediators are all spin-1. This type of interaction is very special. By assuming that nature has certain gauge symmetries, our current quantum field theories can predict the existence of these types of interactions, and many of their features. There are numerous predictions stemming from these symmetries that have been successfully tested by experiments, such as the identical couplings between gluons and quarks of all flavours, the fact that photons don’t interact with each other, and the structure of higher-order corrections, for example the running of coupling constants and the anomalous magnetic moment of the electron and the muon. Yet, as the mass term in the Lagrangian isn’t invariant under gauge transformations, gauge symmetry predicts, at least naively, that the spin-1 force carriers should be massless. So, while the symmetries that predict the electromagnetic and strong interactions also explain why their force carriers are massless, the symmetry principle that predicts the weak interaction is challenged by the experimental fact that its force carriers are massive.

This conundrum has a possible solution if a symmetry is respected by the quantum field theory but not by the ground state of the universe (see “Broken symmetry” image). The theory’s predictions will then be different from those that would follow if the ground state were also symmetric. One way in which the symmetry can be broken is if there is a scalar field that does not vanish in the ground state. This is the case for the Higgs potential, which, unlike a purely parabolic potential, does not have rotational symmetry around its ground state. The weak-force carriers are affected by their interaction with the BEH field, and this interaction slows them down. Moving at speeds slower than the speed of light – the consequence of interacting with the BEH field in the ground state – is equivalent to having non-zero masses, making weak interactions short range. These insights also transformed our understanding of the early universe. Following the Glashow–Weinberg–Salam breakthrough shortly after the BEH proposal, the Standard Model presents a universe in which the ground state transitioned from zero to non-zero due to the spontaneous breaking of electroweak symmetry – a cosmological event that took place when the universe was about 10-11 seconds old.

A 2016 ATLAS candidate

A BEH field different from zero in the ground state of the universe has important observational and experimental consequences. For example, if the symmetry were unbroken, a process where a single Higgs particle decays into a pair of Z bosons would be forbidden. But, once the ground state of the universe breaks the symmetry – the BEH field is non-zero – this process is allowed to occur. (Strictly speaking, the Higgs boson cannot decay into two Z bosons because the sum of their masses is larger than the mass of the Higgs boson, however, the Higgs boson can decay into a real Z boson and a virtual one that produces a pair of fermions.) Similarly, the symmetry would not allow a single Higgs-boson production from Z-boson fusion. But, once the ground state of the universe breaks the symmetry, the latter process is also allowed to occur.

An asymmetric ground state costs the theory none of its predictive power. The strength of the interaction of the Z boson with the BEH field, measured by the mass it gains from this interaction, is closely related to the strength of the interaction of the Z boson with the Higgs particle, measured by the rate at which the Higgs boson decays into two Z bosons, or by the rate at which it is produced by Z-boson fusion. This relation is commonly expressed as the ratio μZZ* between the measured and the predicted rates: if the field related to the newly discovered spin-0 particle is indeed responsible for the mass of the Z boson, then μZZ* = 1.

ATLAS and CMS have established a new law of nature

The rate of the Higgs decay into two Z bosons was first measured with 5σ significance by the ATLAS and CMS experiments in 2016. Its current value is μZZ* ≈ 1.2 ± 0.1. The rate at which the Higgs boson decays into a pair of W bosons was measured in the same year. Its current value of μWW* ≈1.2 ± 0.1 also corresponds to the strength of interaction that would give the W boson its mass. Finally, the experiments measured the rate at which a single Higgs boson is produced in vector-boson fusion to be μVBF ≈ 1.2 ± 0.2. Thus, ATLAS and CMS have established a new law of nature: the force carriers of the weak interaction gain their masses via their interactions with the everywhere-present BEH field. The strength of this interaction is precisely the right size to limit the effects of the weak interaction to distances shorter than 10–18 metres.

Third generation, third jewel

The third jewel in the crown of the LHC is the explanation for how the tau-lepton and the top and bottom quarks – members of the third, heaviest fermion family – gain their masses. The same electroweak symmetry that predicts that the weak-force carriers should be massless also predicts that all 12 spin-1/2 matter particles known to us should also be massless. Experiments have shown, however, that all the matter particles are massive, with the one possible exception of the lightest neutrino. The fact that this symmetry is broken in the ground state of the universe also opens the door to the possibility that matter particles gain masses. But via what mechanism? For the ground state of the BEH field to slow down the fermions as well as the W and Z bosons, a new type of interaction has to exist: an interaction with a spin-0 mediator – the Higgs boson itself. Discovering a Higgs-boson decay into a pair of fermions would mean the discovery of this new type of spin-0 mediated interaction, which was first proposed in a different context by Hideki Yukawa in the 1930s.

Yukawa interactions are fundamentally different from the interactions through which the W and Z bosons get their mass because they are not deduced from a symmetry principle. Another difference, in contrast not only to weak, but also to strong and electromagnetic interactions, is that the interaction strength is not quantised. However, the strength of the interaction of a matter particle with the BEH field, measured by the mass it gains from this interaction, is still closely related to the strength of the Yukawa interaction of that matter particle with the Higgs boson, measured by the rate at which the Higgs boson decays into two such fermions. Once again, if the field that gives the matter particles their masses is indeed the one related to the newly discovered spin-0 particle, then the measured decay rate of the Higgs particle to fermion pairs should give a value of unity to the corresponding μ-ratio.

A candidate event for the production of a Higgs boson

The three heaviest spin-1/2 particles – the top quark, the bottom quark and the tau lepton – are expected to have the strongest couplings to the Higgs boson, and consequently the largest rates of Yukawa interactions with it. The first Yukawa interaction to be measured, with the significance in both the ATLAS and CMS analyses rising to 5σ in 2015, concerned the decay of a Higgs boson into a tau lepton–antilepton pair. The current decay rate is μτ+τ ≈ 1.15 ± 0.15, which, within present experimental accuracy, corresponds to the strength of interaction that would give the tau lepton its mass. The rate of Higgs-boson decays into the bottom quark–antiquark pair was measured by ATLAS and CMS three years later. The current value is μbb ≈ 1.04 ± 0.13. Within present experimental accuracy, this corresponds to the strength of interaction that would give the bottom quark its mass.

The potential of the LHC to discover new facts about nature and the universe is far from saturated

In the case of the top quark, the Higgs boson has a vanishingly tiny decay rate into a top–antitop pair, because the mass of each is individually larger than that of a Higgs boson, and both would have to be produced virtually. To extract the strength of the Higgs–top interaction, experiments instead measure the rate at which this trio of particles is produced. The rate of the production of a Higgs boson together with a top quark–antiquark pair was measured by the ATLAS and CMS experiments in 2018. The current value is μtth ≈ 1.3 ± 0.2. Within present experimental accuracy, this value corresponds to the strength of interaction that would give the top quark its mass. (The remaining third-generation particle, a neutrino, is at least 12 orders of magnitude lighter than the top quark, and is suspected to derive its mass via a different mechanism, which is unlikely to be tested experimentally in the near future.)

ATLAS and CMS have therefore discovered a new fact about nature: the third-generation charged particles – the tau lepton, the bottom quark and the top quark – also gain their masses via their interaction with the everywhere-present BEH field. This is also the discovery of the new and rather special Yukawa interactions among elementary particles, which are mediated by a spin-0 force carrier, the Higgs boson.

The path forward

Answering questions about nature’s fundamental workings almost always leads to new questions. The discovery of the Higgs boson has already been the source of at least two. Firstly, the value of the Higgs boson’s mass suggests the possibility that our universe is likely in an unstable state. In the extremely distant future, a transition to an entirely different universe with a different ground state could occur. Should this remain true as precision improves, not only is there nothing special about Earth, nor the solar system, nor even Milky Way galaxy, but the fundamental structure of the universe is itself only temporary. What’s more, the lightness of the mass of the Higgs boson compared to both the Planck scale (above which quantum-gravity effects become significant) and the “seesaw scale” (below which new particles, beyond those of the Standard Model, are predicted to exist), poses a challenge to the basic framework that we use to formulate the laws of nature. In quantum field theory, cancellations between tree-level and higher order loop-diagram contributions to the mass of the Standard Model Higgs boson are huge, and require extreme fine-tuning, perhaps by as many as 32 orders of magnitude, between seemingly unrelated constants of nature. Various ideas of how to restore “naturalness”, such as supersymmetry and Higgs compositeness, have been suggested, but the LHC experiments have not uncovered any of the TeV-scale particles predicted by these models and are ruling out ever-increasing swathes of parameter space for the models.

Evidence for the production of a Higgs boson

The potential of the LHC to discover new facts about nature and the universe is far from saturated. There are at least two additional, big open questions that are guaranteed to be answered, at least in part, by the LHC experiments. First is the understanding of the mechanism that gives second-generation particles – in particular the muon and the charm quark – their masses. That may be the same mechanism as the one that has been shown to give the third-generation fermions masses, or it may be different (for the latest progress, see Turning the screw on H → μμ). Second is the question of what happened at the electroweak phase transition in the early universe? It may have been a smooth crossover, where the value of the BEH field changed from zero to its present value continuously and uniformly in space, as predicted by the combination of the Standard Model of particle physics and the Big Bang model, or it may have been a first-order phase transition, where bubbles with a finite value of the BEH field nucleated within the surrounding plasma. A first-order phase transition could open the door to a new mechanism to explain the matter–antimatter imbalance in the universe. These deep questions depend on a new chapter of Higgs research concerning the self-interaction of the Higgs boson, which will be carried forward by a future collider.

Beyond constituting amazing intellectual and technological achievements, the LHC experiments have already made a series of profound discoveries about nature. The existence of a spin-0 particle whose non-zero force field is responsible for both the short range of weak interactions and, in a distinct way, the masses of spin-1/2 particles, represents three major discoveries. That theorists have long speculated on these new laws of nature ideas must not diminish the significance of establishing them experimentally. These three jewels in the crown of LHC research, the first steps in the exploration of Higgs physics, begin a trek to some of the most significant open questions in particle physics and cosmology.

Further reading

ATLAS Collab. 2012 Phys. Lett. B 716 1.

CMS Collab. 2012 Phys. Lett. B 716 30.

F Englert and R Brout 1964 Phys. Rev. Lett. 13 321.

B Heinemann and Y Nir 2019 Phys. Usp. 62 920.

P W Higgs 1964 Phys. Rev. Lett. 13 508.

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