Higgs boson

Introduction

Standard Model

Physicists explain the fundamental particles and forces of the universe in terms of the Standard Model – a widely accepted framework based on quantum field theory that predicts almost all known particles and forces aside from gravity with great accuracy. (A separate theory, general relativity, is used for gravity.) In the Standard Model, the particles and forces in nature (aside from gravity) arise from properties of quantum fields known as gauge invariance and symmetries. Forces in the Standard Model are transmitted by particles known as gauge bosons.

Gauge-invariant theories and symmetries

"It is only slightly overstating the case to say that physics is the study of symmetry" – Philip Anderson, Nobel Prize Physics

Gauge-invariant theories are theories with a useful feature, namely that changes to certain quantities make no difference to experimental outcomes. For example, increasing the electric potential of an electromagnet by 100 volts does not itself cause any change to the magnetic field that it produces. Similarly, the measured speed of light in vacuum remains unchanged, whatever the location in time and space, and whatever the local gravitational field.

In these theories, the gauge is a quantity that can be changed with no resultant effect. This independence of the results from some changes is called gauge invariance, and these changes reflect symmetries of the underlying physics. These symmetries provide constraints on the fundamental forces and particles of the physical world. Gauge invariance is therefore an important property within particle physics theory. The gauge symmetries are closely connected to conservation laws and are described mathematically using group theory. Quantum field theory and the Standard Model are both gauge-invariant theories – meaning that the gauge symmetries allow theoretical derivation of properties of the universe.

Gauge boson rest mass problem

Quantum field theories based on gauge invariance had been used with great success in understanding the electromagnetic and strong forces, but by around 1960, all attempts to create a gauge invariant theory for the weak force (and its combination with the electromagnetic force, known together as the electroweak interaction) had consistently failed. As a result of these failures, gauge theories began to fall into disrepute. The problem was that symmetry requirements for these two forces incorrectly predicted that the weak force's gauge bosons (W and Z) would have zero mass (in the specialized terminology of particle physics, "mass" refers specifically to a particle's rest mass). But experiments showed the W and Z gauge bosons had non-zero (rest) mass.

Further, many promising solutions seemed to require the existence of extra particles known as Goldstone bosons, but evidence suggested these did not exist. This meant that either gauge invariance was an incorrect approach, or something unknown was giving the weak force's W and Z bosons their mass, and doing it in a way that did not imply the existence of Goldstone bosons. By the late 1950s and early 1960s, physicists were at a loss as to how to resolve these issues, or how to create a comprehensive theory for particle physics.

Symmetry breaking

In the late 1950s, Yoichiro Nambu recognised that spontaneous symmetry breaking, a process whereby a symmetric system becomes asymmetric, could occur under certain conditions. Symmetry breaking is when some variable takes on a value that does not reflect the symmetries that the underlying laws have, such as when the space of all stable configurations possesses a given symmetry but the stable configurations do not individually possess that symmetry. In 1962, physicist Philip Anderson, an expert in condensed matter physics, observed that symmetry breaking plays a role in superconductivity, and suggested that it could also be part of the answer to the problem of gauge invariance in particle physics.

Specifically, Anderson suggested that the Goldstone bosons that would result from symmetry breaking might instead, in some circumstances, be "absorbed" by the massless W and Z bosons. If so, perhaps the Goldstone bosons would not exist, and the W and Z bosons could gain mass, solving both problems at once. Similar behaviour was already theorised in superconductivity. In 1964, this was shown to be theoretically possible by physicists Abraham Klein and Benjamin Lee, at least for some limited (non-relativistic) cases.

Higgs mechanism

Following the 1963 and early 1964 papers, three groups of researchers independently developed these theories more completely, in what became known as the 1964 PRL symmetry breaking papers. All three groups reached similar conclusions and for all cases, not just some limited cases. They showed that the conditions for electroweak symmetry would be "broken" if an unusual type of field existed throughout the universe, and indeed, there would be no Goldstone bosons and some existing bosons would acquire mass.

The field required for this to happen (which was purely hypothetical at the time) became known as the Higgs field (after Peter Higgs, one of the researchers) and the mechanism by which it led to symmetry breaking became known as the Higgs mechanism. A key feature of the necessary field is that the field would have less energy when it had a non-zero value than when it was zero, unlike every other known field; therefore, the Higgs field has a non-zero value (or vacuum expectation) everywhere. This non-zero value could in theory break electroweak symmetry. It was the first proposal that was able to show, within a gauge invariant theory, how the weak force gauge bosons could have mass despite their governing symmetry.

Although these ideas did not gain much initial support or attention, by 1972 they had been developed into a comprehensive theory and gave "sensible" results that accurately described particles known at the time, and which, with exceptional accuracy, predicted several other particles, which were discovered during the following years. During the 1970s, these theories rapidly became the Standard Model of particle physics.

Higgs field

To allow symmetry breaking, the Standard Model includes a field of the kind needed to "break" electroweak symmetry and give particles their correct mass. This field, which became known as the Higgs field, was hypothesized to exist throughout space, and to break some symmetry laws of the electroweak interaction, triggering the Higgs mechanism. It would therefore cause the W and Z gauge bosons of the weak force to be massive at all temperatures below an extremely high value. When the weak force bosons acquire mass, this affects the distance they can freely travel, which becomes very small, also matching experimental findings. Furthermore, it was later realised that the same field would also explain, in a different way, why other fundamental constituents of matter (including electrons and quarks) have mass.

Unlike all other known fields, such as the electromagnetic field, the Higgs field is a scalar field, and has a non-zero average value in vacuum.

The "central problem"

Prior to the discovery of the Higgs Boson, there was no direct evidence that the Higgs field exists, but even without direct evidence, the accuracy of predictions within the Standard Model led scientists to believe the theory might be correct. By the 1980s, the question of whether the Higgs field exists, and whether the entire Standard Model is correct, had come to be regarded as one of the most important unanswered questions in particle physics. The existence of the Higgs field became the last unverified part of the Standard Model of particle physics, and for several decades was considered "the central problem in particle physics".

For many decades, scientists had no way to determine whether the Higgs field exists because the technology needed for its detection did not exist at that time. If the Higgs field did exist, then it would be unlike any other known fundamental field, but it also was possible that these key ideas, or even the entire Standard Model, were somehow incorrect.

The hypothesised Higgs theory made several key predictions. One crucial prediction was that a matching particle, called the Higgs boson, should also exist. Proving the existence of the Higgs boson would prove the existence of the Higgs field, and therefore finally prove the Standard Model. Therefore, there was an extensive search for the Higgs boson as a way to prove the Higgs field itself exists.

Search and discovery

Although the Higgs field would exist and be nonzero everywhere, proving its existence was far from easy. In principle, it can be proved to exist by detecting its excitations, which manifest as Higgs particles (Higgs bosons), but these are extremely difficult to produce and detect due to the energy required to produce them and their very rare production even if there is sufficient energy available. It was, therefore, several decades before the first evidence of the Higgs boson would be found. Particle colliders, detectors, and computers capable of looking for Higgs bosons took more than 30 years (c. 1980–2010) to develop. The importance of this fundamental question led to a 40-year search, and the construction of one of the world's most expensive and complex experimental facility to date, CERN's Large Hadron Collider (LHC), in an attempt to create Higgs bosons and other particles for observation and study.

On 4 July 2012, the discovery of a new particle with a mass between 125 and 127 GeV/c2 was announced; physicists suspected that it was the Higgs boson. Since then, the particle has been shown to behave, interact, and decay in many of the ways predicted for Higgs particles by the Standard Model, including having even parity and zero spin, two fundamental attributes of a Higgs boson. This also means it is the first elementary scalar particle discovered in nature.

By March 2013, the existence of the Higgs boson was confirmed, and therefore the concept of some type of Higgs field throughout space is strongly supported. The presence of the field, confirmed by experiment, explains why some fundamental particles have (a rest) mass, despite the symmetries controlling their interactions implying that they should be "massless". It also resolves several other long-standing problems, such as the reason for the extremely short distance travelled by the weak force bosons, and therefore the weak force's extremely short range. As of 2018, in-depth research shows the particle continuing to behave in line with predictions for the Standard Model's Higgs boson. More studies are needed to verify with higher precision that the discovered particle has all of the properties predicted or whether, as described by some theories, multiple Higgs bosons exist.

The nature and properties of this field are being investigated further, using more data collected at the LHC.

Interpretation

Various analogies have been used to describe the Higgs field and boson, including analogies with well-known symmetry-breaking effects such as the rainbow and prism, electric fields, and ripples on the surface of water.

Other analogies based on the resistance of macroscopic objects moving through media (such as people moving through crowds, or some objects moving through syrup or molasses) are commonly used but misleading, since the Higgs field does not actually resist particles, and the effect of mass is not caused by resistance.

Overview of Higgs boson and field properties

In the Standard Model, the Higgs boson is a massive scalar boson whose mass must be found experimentally. Its mass has been determined to be 125.35±0.15 GeV/c2 by CMS (2022) and 125.11±0.11 GeV/c2 by ATLAS (2023). It is the only particle that remains massive even at very high energies. It has zero spin, even (positive) parity, no electric charge, no colour charge, and it couples to (interacts with) mass. It is also very unstable, decaying into other particles almost immediately via several possible pathways.

The Higgs field is a scalar field, with two neutral and two electrically charged components that form a complex doublet of the weak isospin SU(2) symmetry. Unlike any other known quantum field, it has a sombrero potential. This shape means that below extremely high cross-over temperature of 159.5±1.5 GeV/kB such as those seen during the first picosecond (10−12 s) of the Big Bang, the Higgs field in its ground state has less energy when it is nonzero, resulting in a nonzero vacuum expectation value. Therefore, in today's universe the Higgs field has a nonzero value everywhere (including in otherwise empty space). This nonzero value in turn breaks the weak isospin SU(2) symmetry of the electroweak interaction everywhere. (Technically the non-zero expectation value converts the Lagrangian's Yukawa coupling terms into mass terms.) When this happens, three components of the Higgs field are "absorbed" by the SU(2) and U(1) gauge bosons (the Higgs mechanism) to become the longitudinal components of the now-massive W and Z bosons of the weak force. The remaining electrically neutral component either manifests as a Higgs boson, or may couple separately to other particles known as fermions (via Yukawa couplings), causing these to acquire mass as well.

Even though the knowledge of many of the Higgs boson properties has advanced significantly since its discovery, the Higgs boson's self-coupling remains unmeasured. The shape of the Higgs potential in the Standard Model includes both trilinear and quartic self-couplings, which are key to understanding the complete shape of the potential and the nature of the Higgs field and EWSB. Higgs boson pair production offers a direct experimental probe of the self-coupling λ at the electroweak scale.

Significance

Evidence for the Higgs field and its properties has been extremely significant for many reasons. The primary importance of the Higgs boson is that it completes the mechanism by which the heavy electroweak bosons acquire mass, and it is fortunate that the mass is such that it is able to be examined using existing experimental technology, as a way to confirm and study the entire Higgs field theory. Conversely, evidence that the Higgs field and boson did not exist within the expected mass range would have also been significant.

Particle physics

The Higgs boson validates the Standard Model mechanism of mass generation for the weak bosons, and can provide masses to the fermions. As more precise measurements of its properties are made, more advanced extensions may be suggested or excluded. As experimental means to measure the Higgs field behaviour and interactions are developed, this fundamental field may be better understood. If the Higgs boson had not been discovered, the Standard Model would have needed to be modified or superseded.

Related to this, it is a widely held belief among many physicists that there is likely to be "new" physics beyond the Standard Model, and the Standard Model will at some point be extended or superseded. The discovery of the Higgs boson, as well as the many measured collisions occurring at the LHC, provide physicists with a sensitive tool to search their data for any evidence of the failure of the Standard Model, and might provide considerable evidence to guide researchers into future theoretical developments.

Below an extremely high temperature, electroweak symmetry breaking causes the electroweak interaction to manifest in part as the short-ranged weak force, which is carried by massive gauge bosons. In the history of the universe, electroweak symmetry breaking is believed to have happened at about 1 picosecond (10−12 s) after the Big Bang, when the universe was at a temperature 159.5±1.5 GeV/kB. This symmetry breaking is required for atoms and other structures to form, as well as for nuclear reactions in stars, such as the Sun. The Higgs field is responsible for this symmetry breaking.

The Higgs field is pivotal in generating the masses of quarks and charged leptons (through Yukawa coupling) and the W and Z gauge bosons (through the Higgs mechanism), although it was the generation of mass for the weak bosons which is the most significant factor – providing terms in the Standard Model Lagrangian that allow for the generation of fermion masses, was a useful, but less significant by product. The fermion masses must be entered by hand, essentially determining the relative strength of the coupling of the fermion to the Higgs field.

The Higgs field does not "create" mass out of nothing, nor is the Higgs field responsible for the mass of all particles. For example, approximately 99% of the mass of baryons (composite particles such as the proton and neutron) is due instead to quantum chromodynamic binding energy, which is the sum of the kinetic energies of quarks and the energies of the massless gluons mediating the strong interaction inside the baryons. In Higgs-based theories, the property of "mass" is a manifestation of potential energy transferred to fundamental particles when they interact ("couple") with the Higgs field.

Cosmology

There has been considerable scientific research on possible links between the Higgs field and the inflaton – a hypothetical field suggested as the explanation for the expansion of space during the first fraction of a second of the universe (known as the "inflationary epoch"). Some theories suggest that a fundamental scalar field might be responsible for this phenomenon; the Higgs field is such a field, and its existence has led to papers analysing whether it could also be the inflaton responsible for this exponential expansion of the universe during the Big Bang. Such theories are highly tentative and face significant problems related to unitarity, but may be viable if combined with additional features such as large non-minimal coupling, a Brans–Dicke scalar, or other "new" physics, and they have received treatments suggesting that Higgs inflation models are still of interest theoretically.

In the Standard Model, there exists the possibility that the underlying state of our universe – known as the "vacuum" – is long-lived, but not completely stable. In this scenario, the universe as we know it could effectively be destroyed by collapsing into a more stable vacuum state. This was sometimes misreported as the Higgs boson "ending" the universe. If the masses of the Higgs boson and top quark are known more precisely, and the Standard Model provides an accurate description of particle physics up to extreme energies of the Planck scale, then it is possible to calculate whether the vacuum is stable or merely long-lived. A Higgs mass of 125–127 GeV/c2 seems to be extremely close to the boundary for stability, but a definitive answer requires much more precise measurements of the pole mass of the top quark. New physics can change this picture.

If measurements of the Higgs boson suggest that our universe lies within a false vacuum of this kind, then it would imply – more than likely in many billions of years – that the universe's forces, particles, and structures could cease to exist as we know them (and be replaced by different ones), if a true vacuum happened to nucleate. It also suggests that the Higgs self-coupling λ and its βλ function could be very close to zero at the Planck scale, with "intriguing" implications, including theories of gravity and Higgs-based inflation. A future electron–positron collider would be able to provide the precise measurements of the top quark needed for such calculations.

More speculatively, the Higgs field has also been proposed as the energy of the vacuum, which at the extreme energies of the first moments of the Big Bang caused the universe to be a kind of featureless symmetry of undifferentiated, extremely high energy. In this kind of speculation, the single unified field of a Grand Unified Theory is identified as (or modelled upon) the Higgs field, and it is through successive symmetry breakings of the Higgs field, or some similar field, at phase transitions that the presently known forces and fields of the universe arise.

History

Theorisation

Particle physicists study matter made from fundamental particles whose interactions are mediated by exchange particles – gauge bosons – acting as force carriers. At the beginning of the 1960s a number of these particles had been discovered or proposed, along with theories suggesting how they relate to each other, some of which had already been reformulated as field theories in which the objects of study are not particles and forces, but quantum fields and their symmetries. However, attempts to produce quantum field models for two of the four known fundamental forces – the electromagnetic force and the weak nuclear force – and then to unify these interactions, were still unsuccessful.

One known problem was that gauge invariant approaches, including non-abelian models such as Yang–Mills theory (1954), which held great promise for unified theories, also seemed to predict known massive particles as massless. Goldstone's theorem, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions, since it appeared to show that zero-mass particles known as Goldstone bosons would also have to exist that simply were "not seen". According to Guralnik, physicists had "no understanding" how these problems could be overcome.

Particle physicist and mathematician Peter Woit summarised the state of research at the time:Yang and Mills work on non-abelian gauge theory had one huge problem: in perturbation theory it has massless particles which don't correspond to anything we see. One way of getting rid of this problem is now fairly well understood, the phenomenon of confinement realized in QCD, where the strong interactions get rid of the massless "gluon" states at long distances. By the very early sixties, people had begun to understand another source of massless particles: spontaneous symmetry breaking of a continuous symmetry. What Philip Anderson realized and worked out in the summer of 1962 was that, when you have both gauge symmetry and spontaneous symmetry breaking, the massless Nambu–Goldstone mode [which gives rise to Goldstone bosons] can combine with the massless gauge field modes [which give rise to massless gauge bosons] to produce a physical massive vector field [gauge bosons with mass]. This is what happens in superconductivity, a subject about which Anderson was (and is) one of the leading experts. [text condensed]

The Higgs mechanism is a process by which vector bosons can acquire rest mass without explicitly breaking gauge invariance, as a byproduct of spontaneous symmetry breaking. Initially, the mathematical theory behind spontaneous symmetry breaking was conceived and published within particle physics by Yoichiro Nambu in 1960 (and somewhat anticipated by Ernst Stueckelberg in 1938), and the concept that such a mechanism could offer a possible solution for the "mass problem" was originally suggested in 1962 by Philip Anderson, who had previously written papers on broken symmetry and its outcomes in superconductivity. Anderson concluded in his 1963 paper on the Yang–Mills theory, that "considering the superconducting analog ... [t]hese two types of bosons seem capable of canceling each other out ... leaving finite mass bosons"), and in March 1964, Abraham Klein and Benjamin Lee showed that Goldstone's theorem could be avoided this way in at least some non-relativistic cases, and speculated it might be possible in truly relativistic cases.

Experimental search

To produce Higgs bosons, two beams of particles are accelerated to very high energies and allowed to collide within a particle detector. Occasionally, although rarely, a Higgs boson will be created fleetingly as part of the collision byproducts. Because the Higgs boson decays very quickly, particle detectors cannot detect it directly. Instead the detectors register all the decay products (the decay signature) and from the data the decay process is reconstructed. If the observed decay products match a possible decay process (known as a decay channel) of a Higgs boson, this indicates that a Higgs boson may have been created. In practice, many processes may produce similar decay signatures. Fortunately, the Standard Model precisely predicts the likelihood of each of these, and each known process, occurring. So, if the detector detects more decay signatures consistently matching a Higgs boson than would otherwise be expected if Higgs bosons did not exist, then this would be strong evidence that the Higgs boson exists.

Because Higgs boson production in a particle collision is likely to be very rare (1 in 10 billion at the LHC),

and many other possible collision events can have similar decay signatures, the data of hundreds of trillions of collisions needs to be analysed and must "show the same picture" before a conclusion about the existence of the Higgs boson can be reached. To conclude that a new particle has been found, particle physicists require that the statistical analysis of two independent particle detectors each indicate that there is less than a one-in-a-million chance that the observed decay signatures are due to just background random Standard Model events – i.e., that the observed number of events is more than five standard deviations (sigma) different from that expected if there was no new particle. More collision data allows better confirmation of the physical properties of any new particle observed, and allows physicists to decide whether it is indeed a Higgs boson as described by the Standard Model or some other hypothetical new particle.

To find the Higgs boson, a powerful particle accelerator was needed, because Higgs bosons might not be seen in lower-energy experiments. The collider needed to have a high luminosity in order to ensure enough collisions were seen for conclusions to be drawn. Finally, advanced computing facilities were needed to process the vast amount of data (25 petabytes per year as of 2012) produced by the collisions. For the announcement of 4 July 2012, a new collider known as the Large Hadron Collider was constructed at CERN with a planned eventual collision energy of 14 TeV – over seven times any previous collider – and over 300 trillion (3×1014) LHC proton–proton collisions were analysed by the LHC Computing Grid, the world's largest computing grid (as of 2012), comprising over 170 computing facilities in a worldwide network across 36 countries.

Theoretical issues

Theoretical need for the Higgs

Gauge invariance is an important property of modern particle theories such as the Standard Model, partly due to its success in other areas of fundamental physics such as electromagnetism and the strong interaction (quantum chromodynamics). However, before Sheldon Glashow extended the electroweak unification models in 1961, there were great difficulties in developing gauge theories for the weak nuclear force or a possible unified electroweak interaction. Fermions with a mass term would violate gauge symmetry and therefore cannot be gauge invariant. (This can be seen by examining the Dirac Lagrangian for a fermion in terms of left and right handed components; we find none of the spin-half particles could ever flip helicity as required for mass, so they must be massless.)

W and Z bosons are observed to have mass, but a boson mass term contains terms which clearly depend on the choice of gauge, and therefore these masses too cannot be gauge invariant. Therefore, it seems that none of the standard model fermions or bosons could "begin" with mass as an inbuilt property except by abandoning gauge invariance. If gauge invariance were to be retained, then these particles had to be acquiring their mass by some other mechanism or interaction.

Additionally, solutions based on spontaneous symmetry breaking appeared to fail, seemingly an inevitable result of Goldstone's theorem. Because there is no potential energy cost to moving around the complex plane's "circular valley" responsible for spontaneous symmetry breaking, the resulting quantum excitation is pure kinetic energy, and therefore a massless boson ("Goldstone boson"), which in turn implies a new long range force. But no new long range forces or massless particles were detected either. So whatever was giving these particles their mass had to not "break" gauge invariance as the basis for other parts of the theories where it worked well, and had to not require or predict unexpected massless particles or long-range forces which did not actually seem to exist in nature.

A solution to all of these overlapping problems came from the discovery of a previously unnoticed borderline case hidden in the mathematics of Goldstone's theorem,

that under certain conditions it might theoretically be possible for a symmetry to be broken without disrupting gauge invariance and without any new massless particles or forces, and having "sensible" (renormalisable) results mathematically. This became known as the Higgs mechanism.

Simple explanation of the theory, from its origins in superconductivity

The proposed Higgs mechanism arose as a result of theories proposed to explain observations in superconductivity. A superconductor does not allow penetration by external magnetic fields (the Meissner effect). This strange observation implies that somehow, the electromagnetic field becomes short ranged during this phenomenon. Successful theories arose to explain this during the 1950s, first for fermions (Ginzburg–Landau theory, 1950), and then for bosons (BCS theory, 1957).

In these theories, superconductivity is interpreted as arising from a charged condensate field. Initially, the condensate value does not have any preferred direction, implying it is scalar, but its phase is capable of defining a gauge, in gauge based field theories. To do this, the field must be charged. A charged scalar field must also be complex (or described another way, it contains at least two components, and a symmetry capable of rotating each into the other(s)). In naïve gauge theory, a gauge transformation of a condensate usually rotates the phase. But in these circumstances, it instead fixes a preferred choice of phase. However, it turns out that fixing the choice of gauge so that the condensate has the same phase everywhere also causes the electromagnetic field to gain an extra term. This extra term causes the electromagnetic field to become short range.

Once attention was drawn to this theory within particle physics, the parallels were clear. A change of the usually long range electromagnetic field to become short ranged, within a gauge invariant theory, was exactly the needed effect sought for the weak force bosons (because a long range force has massless gauge bosons, and a short ranged force implies massive gauge bosons, suggesting that a result of this interaction is that the field's gauge bosons acquired mass, or a similar and equivalent effect). The features of a field required to do this were also quite well defined – it would have to be a charged scalar field, with at least two components, and complex in order to support a symmetry able to rotate these into each other.

Alternative models

The Minimal Standard Model as described above is the simplest known model for the Higgs mechanism with just one Higgs field. However, an extended Higgs sector with additional Higgs particle doublets or triplets is also possible, and many extensions of the Standard Model have this feature. The non-minimal Higgs sector favoured by theory are the two-Higgs-doublet models (2HDM), which predict the existence of a quintet of scalar particles: two CP-even neutral Higgs bosons h0 and H0, a CP-odd neutral Higgs boson A0, and two charged Higgs particles H±. Supersymmetry ("SUSY") also predicts relations between the Higgs-boson masses and the masses of the gauge bosons, and could accommodate a 125 GeV/c2 neutral Higgs boson.

The key method to distinguish between these different models involves study of the particles' interactions ("coupling") and exact decay processes ("branching ratios"), which can be measured and tested experimentally in particle collisions. In the Type-I 2HDM model one Higgs doublet couples to up and down quarks, while the second doublet does not couple to quarks. This model has two interesting limits, in which the lightest Higgs couples to just fermions ("gauge-phobic") or just gauge bosons ("fermiophobic"), but not both. In the Type-II 2HDM model, one Higgs doublet only couples to up-type quarks, the other only couples to down-type quarks. The heavily researched Minimal Supersymmetric Standard Model (MSSM) includes a Type-II 2HDM Higgs sector, so it could be disproven by evidence of a Type-I 2HDM Higgs.

In other models the Higgs scalar is a composite particle. For example, in technicolour the role of the Higgs field is played by strongly bound pairs of fermions called techniquarks. Other models feature pairs of top quarks (see top quark condensate). In yet other models, there is no Higgs field at all and the electroweak symmetry is broken using extra dimensions.

Further theoretical issues and hierarchy problem

The Standard Model leaves the mass of the Higgs boson as a parameter to be measured, rather than a value to be calculated. This is seen as theoretically unsatisfactory, particularly as quantum corrections (related to interactions with virtual particles) should apparently cause the Higgs particle to have a mass immensely higher than that observed, but at the same time the Standard Model requires a mass of the order of 100 to 1000 GeV/c2 to ensure unitarity (in this case, to unitarise longitudinal vector boson scattering). Reconciling these points appears to require explaining why there is an almost-perfect cancellation resulting in the visible mass of ~ 125 GeV/c2, and it is not clear how to do this. Because the weak force is about 1032 times stronger than gravity, and (linked to this) the Higgs boson's mass is so much less than the Planck mass or the grand unification energy, it appears that either there is some underlying connection or reason for these observations which is unknown and not described by the Standard Model, or some unexplained and extremely precise fine-tuning of parameters – however at present neither of these explanations is proven. This is known as a hierarchy problem. More broadly, the hierarchy problem amounts to the worry that a future theory of fundamental particles and interactions should not have excessive fine-tunings or unduly delicate cancellations, and should allow masses of particles such as the Higgs boson to be calculable. The problem is in some ways unique to spin-0 particles (such as the Higgs boson), which can give rise to issues related to quantum corrections that do not affect particles with spin. A number of solutions have been proposed, including supersymmetry, conformal solutions and solutions via extra dimensions such as braneworld models.

There are also issues of quantum triviality, which suggests that it may not be possible to create a consistent quantum field theory involving elementary scalar particles. This can also lead to a predictable Higgs mass in asymptotic safety scenarios.

Properties

Properties of the Higgs field

In the Standard Model, the Higgs field is a scalar tachyonic field – scalar meaning it does not transform under Lorentz transformations, and tachyonic meaning the field (but not the particle) has imaginary mass, and in certain configurations must undergo symmetry breaking. It consists of four components: Two neutral ones and two charged component fields. Both of the charged components and one of the neutral fields are Goldstone bosons, which act as the longitudinal third-polarisation components of the massive W+, W−, and Z bosons. The quantum of the remaining neutral component corresponds to (and is theoretically realised as) the massive Higgs boson. This component can interact with fermions via Yukawa coupling to give them mass as well.

Mathematically, the Higgs field has imaginary mass and is therefore a tachyonic field. While tachyons (particles that move faster than light) are a purely hypothetical concept, fields with imaginary mass have come to play an important role in modern physics. Under no circumstances do any excitations ever propagate faster than light in such theories – the presence or absence of a tachyonic mass has no effect whatsoever on the maximum velocity of signals (there is no violation of causality). Instead of faster-than-light particles, the imaginary mass creates an instability: Any configuration in which one or more field excitations are tachyonic must spontaneously decay, and the resulting configuration contains no physical tachyons. This process is known as tachyon condensation, and is now believed to be the explanation for how the Higgs mechanism itself arises in nature, and therefore the reason behind electroweak symmetry breaking.

Although the notion of imaginary mass might seem troubling, it is only the field, and not the mass itself, that is quantised. Therefore, the field operators at spacelike separated points still commute (or anticommute), and information and particles still do not propagate faster than light. Tachyon condensation drives a physical system that has reached a local limit – and might naively be expected to produce physical tachyons – to an alternate stable state where no physical tachyons exist. Once a tachyonic field such as the Higgs field reaches the minimum of the potential, its quanta are not tachyons any more but rather are ordinary particles such as the Higgs boson.

Properties of the Higgs boson

Since the Higgs field is scalar, the Higgs boson has no spin. The Higgs boson is also its own antiparticle, is CP-even, and has zero electric and colour charge.

The Standard Model does not predict the mass of the Higgs boson. If that mass is between 115 and 180 GeV/c2 (consistent with empirical observations of 125 GeV/c2), then the Standard Model can be valid at energy scales all the way up to the Planck scale (1019 GeV/c2). It should be the only particle in the Standard Model that remains massive even at high energies. Many theorists expect new physics beyond the Standard Model to emerge at the TeV-scale, based on unsatisfactory properties of the Standard Model.

The highest possible mass scale allowed for the Higgs boson (or some other electroweak symmetry breaking mechanism) is 1.4 TeV; beyond this point, the Standard Model becomes inconsistent without such a mechanism, because unitarity is violated in certain scattering processes.

It is also possible, although experimentally difficult, to estimate the mass of the Higgs boson indirectly: In the Standard Model, the Higgs boson has a number of indirect effects; most notably, Higgs loops result in tiny corrections to masses of the W and Z bosons. Precision measurements of electroweak parameters, such as the Fermi constant and masses of the W and Z bosons, can be used to calculate constraints on the mass of the Higgs. As of July 2011, the precision electroweak measurements tell us that the mass of the Higgs boson is likely to be less than about 161 GeV/c2 at 95% confidence level. These indirect constraints rely on the assumption that the Standard Model is correct. It may still be possible to discover a Higgs boson above these masses, if it is accompanied by other particles beyond those accommodated by the Standard Model.

The LHC cannot directly measure the Higgs boson's lifetime, due to its extreme brevity. It is predicted as 1.56×10−22 s based on the predicted decay width of 4.07×10−3 GeV. However it can be measured indirectly, based upon comparing masses measured from quantum phenomena occurring in the on shell production pathways and in the, much rarer, off shell production pathways, derived from Dalitz decay via a virtual photon (H → γ*γ → ℓℓγ). Using this technique, the lifetime of the Higgs boson was tentatively measured in 2021 as 1.2 – 4.6×10−22 s, at sigma 3.2 (1 in 1000) significance.

Production

If Higgs particle theories are valid, then a Higgs particle can be produced much like other particles that are studied, in a particle collider. This involves accelerating a large number of particles to extremely high energies and extremely close to the speed of light, then allowing them to smash together. Protons and lead ions (the bare nuclei of lead atoms) are used at the LHC. In the extreme energies of these collisions, the desired esoteric particles will occasionally be produced and this can be detected and studied; any absence or difference from theoretical expectations can also be used to improve the theory. The relevant particle theory (in this case the Standard Model) will determine the necessary kinds of collisions and detectors. The Standard Model predicts that Higgs bosons could be formed in a number of ways, although the probability of producing a Higgs boson in any collision is always expected to be very small – for example, only one Higgs boson per 10 billion collisions in the Large Hadron Collider. The most common expected processes for Higgs boson production are:

Gluon fusion

If the collided particles are hadrons such as the proton or antiproton – as is the case in the LHC and Tevatron – then it is most likely that two of the gluons binding the hadron together collide. The easiest way to produce a Higgs particle is if the two gluons combine to form a loop of virtual quarks (see Feynman diagram). Since the coupling of particles to the Higgs boson is proportional to their mass, this process is more likely for heavy particles. In practice it is enough to consider the contributions of virtual top and bottom quarks (the heaviest quarks). This process is the dominant contribution at the LHC and Tevatron being about ten times more likely than any of the other processes.

Higgs Strahlung

If an elementary fermion collides with an anti-fermion – e.g., a quark with an anti-quark or an electron with a positron – the two can merge to form a virtual W or Z boson which, if it carries sufficient energy, can then emit a Higgs boson. This process was the dominant production mode at the LEP, where an electron and a positron collided to form a virtual Z boson, and it was the second largest contribution for Higgs production at the Tevatron. At the LHC this process is only the third largest, because the LHC collides protons with protons, making a quark-antiquark collision less likely than at the Tevatron. Higgs Strahlung is also known as associated production.

Decay

Quantum mechanics predicts that if it is possible for a particle to decay into a set of lighter particles, then it will eventually do so. This is also true for the Higgs boson. The likelihood with which this happens depends on a variety of factors including: the difference in mass, the strength of the interactions, etc. Most of these factors are fixed by the Standard Model (SM), except for the mass of the Higgs boson itself. Given that the Higgs boson has a mass of 125 GeV/c2, the SM then predicts a mean life time of about 1.6×10−22 s.

Since it interacts with all the massive elementary particles of the SM, the Higgs boson has many different processes through which it can decay. Each of these possible processes has its own probability, expressed as the branching ratio; the fraction of the total number decays that follows that process. The SM predicts these branching ratios as a function of the Higgs mass (see plot, right).

One way that the Higgs can decay is by splitting into a fermion–antifermion pair. As general rule, the Higgs is more likely to decay into heavy fermions than light fermions, because the mass of a fermion is proportional to the strength of its interaction with the Higgs. By this logic the most common decay should be into a top–antitop quark pair. However, such a decay would only be possible if the Higgs were heavier than ~346 GeV/c2, twice the mass of the top quark. Given a Higgs mass of 125 GeV/c2, the SM predicts that the most common decay is into a bottom–antibottom quark pair, which happens 57.7% of the time. The second most common fermion decay at that mass is a tau–antitau pair, which happens only about 6.3% of the time.

Another possibility is for the Higgs to split into a pair of massive gauge bosons. The most likely possibility is for the Higgs to decay into a pair of W bosons (the light blue line in the plot), which happens about 21.5% of the time for a Higgs boson with a mass of 125 GeV/c2. The W bosons can subsequently decay either into a quark and an antiquark or into a charged lepton and a neutrino. The decays of W bosons into quarks are difficult to distinguish from the background, and the decays into leptons cannot be fully reconstructed (because neutrinos are impossible to detect in particle collision experiments). A cleaner signal is given by decay into a pair of Z bosons (which happens about 2.6% of the time for a Higgs with a mass of 125 GeV/c2), if each of the bosons subsequently decays into a pair of easy-to-detect charged leptons (electrons or muons).

Pair production

At the Large Hadron Collider (LHC), Higgs boson pair production occurs through several distinct mechanisms, similarly as single Higgs production:

Gluon–gluon fusion (ggF) is the dominant production mode. It proceeds via loop diagrams involving heavy quarks, primarily the top quark, and includes both box and triangle topologies. The triangle diagram explicitly depends on the Higgs trilinear self-coupling, and its interference with the box diagram significantly affects the total cross section.

Vector boson fusion (VBF) involves the radiation of Higgs bosons from virtual W or Z bosons exchanged between incoming quarks. Although subdominant in rate, VBF offers distinctive event topologies and complementary sensitivity to new physics.

Associated production channels, such as ttHH (with top quark pairs) and VHH (with vector bosons), become increasingly important at higher center-of-mass energies and provide unique sensitivity to the Higgs-top and Higgs-gauge boson interactions.

Each of these production mechanisms offers different levels of sensitivity to the Higgs self-coupling λ, making them essential components in a comprehensive search for deviations from the Standard Model prediction.

Higgs boson pairs can decay through various channels. The most studied final states include:

HH → bb̄bb̄: Has the highest branching fraction (~34%) but suffers from large QCD background.

HH → bb̄γγ: Low branching fraction (~0.3%) but excellent mass resolution due to clean photon identification.

HH → bb̄τ⁺τ⁻: Offers a good compromise between signal rate and background contamination (~7.3% branching ratio).

The choice of decay mode affects the sensitivity of LHC experiments to the HH signal.

Public discussion

Naming

The name most strongly associated with the particle and field is the Higgs boson and Higgs field. For some time the particle was known by a combination of its PRL author names (including at times Anderson), for example the Brout–Englert–Higgs particle, the Anderson–Higgs particle, or the Englert–Brout–Higgs–Guralnik–Hagen–Kibble mechanism, and these are still used at times. Fuelled in part by the issue of recognition and a potential shared Nobel Prize,

the most appropriate name was still occasionally a topic of debate until 2013.

Higgs himself preferred to call the particle either by an acronym of all those involved, or "the scalar boson", or "the so-called Higgs particle".

A considerable amount has been written on how Higgs's name came to be exclusively used. Two main explanations are offered. The first is that Higgs undertook a step which was either unique, clearer or more explicit in his paper in formally predicting and examining the particle. Of the PRL papers' authors, only the paper by Higgs explicitly offered as a prediction that a massive particle would exist and calculated some of its properties;

he was therefore "the first to postulate the existence of a massive particle" according to Nature.

Physicist and author Frank Close and physicist-blogger Peter Woit both comment that the paper by GHK was also completed after Higgs and Brout–Englert were submitted to Physical Review Letters,

and that Higgs alone had drawn attention to a predicted massive scalar boson, while all others had focused on the massive vector bosons.

In this way, Higgs's contribution also provided experimentalists with a crucial "concrete target" needed to test the theory.

However, in Higgs's view, Brout and Englert did not explicitly mention the boson since its existence is plainly obvious in their work, while according to Guralnik the GHK paper was a complete analysis of the entire symmetry breaking mechanism whose mathematical rigour is absent from the other two papers, and a massive particle may exist in some solutions. Higgs's paper also provided an "especially sharp" statement of the challenge and its solution according to science historian David Kaiser.

Educational explanations and analogies

There has been considerable public discussion of analogies and explanations for the Higgs particle and how the field creates mass,

including coverage of explanatory attempts in their own right and a competition in 1993 for the best popular explanation by then-UK Minister for Science Sir William Waldegrave

and articles in newspapers worldwide.

Matt Strassler explains (summarised):

Most of the universe’s quantum fields have characteristic resonant frequencies at which they most readily vibrate. The more rapidly its particles vibrate (the higher its resonant frequency), the greater their mass. If the field does not have a resonant frequency, its particles can only travel, not vibrate, and have no mass.

Quantum fields do not by themselves have a resonant frequency, so initially all particles are massless. They can only vibrate if an external influence interacts with ('stiffens') them, in a way that gives them a resonant frequency, similar to how a pendulum will only swing back and forth if it is pulled in a specific direction by gravity, and its swing will then have a resonant frequency.

The pendulum swings because under the influence of gravity, it tends to return to a specific equilibrium state, known as a 'restoring effect'. Without adding that restoring effect, the pendulum could not swing. The stronger the gravitational field, the more powerful the restoring effect and the higher the pendulum’s resonant frequency.

This was the core insight of the PRL symmetry breaking papers: that an unusual kind of field could stiffen other fields, creating a restoring effect and a resonant frequency for those fields. This could explain how their particles can vibrate in place, which we know as 'mass'.

Initially none of the universe's quantum fields had resonant frequencies. So particles could not vibrate, they could only travel (they were massless). As the universe expanded and cooled, the Higgs field suddenly developed a nonzero strength everywhere. When this happened, it stiffened certain quantum fields, and they acquired a restoring effect. This gave the fields resonant frequencies, so now their particles could vibrate in place with a resonant frequency (acquired a mass), where they had only been able to travel (be massless) before.

Recognition and awards

There was considerable discussion prior to late 2013 of how to allocate the credit if the Higgs boson is proven, made more pointed as a Nobel Prize had been expected, and the very wide basis of people entitled to consideration. These include a range of theoreticians who made the Higgs mechanism theory possible, the theoreticians of the 1964 PRL papers (including Higgs himself), the theoreticians who derived from these a working electroweak theory and the Standard Model itself, and also the experimentalists at CERN and other institutions who made possible the proof of the Higgs field and boson in reality. The Nobel Prize has a limit of three persons to share an award, and some possible winners are already prize holders for other work, or are deceased (the prize is only awarded to persons in their lifetime). Existing prizes for works relating to the Higgs field, boson, or mechanism include:

Nobel Prize in Physics (1979) – Glashow, Salam, and Weinberg, for contributions to the theory of the unified weak and electromagnetic interaction between elementary particles

Nobel Prize in Physics (1999) – 't Hooft and Veltman, for elucidating the quantum structure of electroweak interactions in physics

J. J. Sakurai Prize for Theoretical Particle Physics (2010) – Hagen, Englert, Guralnik, Higgs, Brout, and Kibble, for elucidation of the properties of spontaneous symmetry breaking in four-dimensional relativistic gauge theory and of the mechanism for the consistent generation of vector boson masses (for the 1964 papers described above)

Wolf Prize (2004) – Englert, Brout, and Higgs

Special Breakthrough Prize in Fundamental Physics (2013) – Fabiola Gianotti and Peter Jenni, spokespersons of the ATLAS Collaboration and Michel Della Negra, Tejinder Singh Virdee, Guido Tonelli, and Joseph Incandela spokespersons, past and present, of the CMS collaboration, "For [their] leadership role in the scientific endeavour that led to the discovery of the new Higgs-like particle by the ATLAS and CMS collaborations at CERN's Large Hadron Collider".

Nobel Prize in Physics (2013) – Peter Higgs and François Englert, for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider(Englert's co-researcher Robert Brout had died in 2011 and the Nobel Prize is not ordinarily given posthumously.)

Technical aspects and mathematical formulation

In the Standard Model, the Higgs field is a four-component scalar field that forms a complex doublet of the weak isospin SU(2) symmetry:

ϕ

=

1

2

(

ϕ

1

+

i

ϕ

2

ϕ

0

+

i

ϕ

3

)

{\displaystyle \phi ={\frac {1}{\sqrt {2}}}\left({\begin{array}{c}\phi ^{1}+i\phi ^{2}\\\phi ^{0}+i\phi ^{3}\end{array}}\right)\,}

while the field has charge +⁠1/2⁠ under the weak hypercharge U(1) symmetry.

Note: This article uses the scaling convention where the electric charge, Q, the weak isospin, T3, and the weak hypercharge, YW, are related by Q = T3 + YW. A different convention used in most other Wikipedia articles is Q = T3 + ⁠1/2⁠YW.

The Higgs part of the Lagrangian is

L

H