Higgs boson

Higgs boson

Candidate Higgs boson events from collisions between protons in the LHC. The top event in the CMS experiment shows a decay into two photons (dashed yellow lines and green towers). The lower event in the ATLAS experiment shows a decay into 4 muons (red tracks).[Note 1]
Composition	Elementary particle
Statistics	Bosonic
Status	A Higgs boson of mass ≈125 GeV was tentatively confirmed by CERN on 14 March 2013,[1][2][3] although it is unclear as yet which model the particle best supports or whether multiple Higgs bosons exist.[2] (See: Current status)
Symbol	H0
Theorised	R. Brout, F. Englert, P. Higgs, G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble (1964)
Discovered	Large Hadron Collider (2011–2013)
Mass	125.09±0.21 (stat.)±0.11 (syst.) GeV/c^2 (CMS+ATLAS)[4]
Mean lifetime	1.56×10^−22 s [Note 2] (predicted)
Decays into	bottom-antibottom pair (predicted) two W bosons (observed) two gluons (predicted) tau-antitau pair (observed) two Z bosons (observed) two photons (observed) various other decays (predicted)
Electric charge	0 e
Colour charge	0
Spin	0 (tentatively confirmed)[1]
Weak isospin	-1/2
Weak hypercharge	+1
Parity	+1 (tentatively confirmed)[1]

The Higgs boson is an elementary particle in the Standard Model of particle physics. It is the quantum excitation of the Higgs field,^[6][7] a fundamental field of crucial importance to particle physics theory^[7] first suspected to exist in the 1960s. Unlike other known fields such as the electromagnetic field, it has a non-zero constant value in vacuum. The question of the Higgs field's existence has been the last unverified part of the Standard Model of particle physics and, according to some, "the central problem in particle physics".^[8][9]

The presence of this field, now believed to be confirmed, explains why some fundamental particles have mass when, based on the symmetries controlling their interactions, they should be massless. The existence of the Higgs field would also resolve several other long-standing puzzles, such as the reason for the weak force's extremely short range.

Although it is hypothesised that the Higgs field permeates the entire Universe, evidence for its existence has been very difficult to obtain. In principle, the Higgs field can be detected through its excitations, manifested as Higgs particles, but these are extremely difficult to produce and detect. 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 facilities to date, CERN's Large Hadron Collider,^[10] 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.^[11][12][13] Since then, the particle has been shown to behave, interact, and decay in many of the ways predicted by the Standard Model. It was also tentatively confirmed to have even parity and zero spin,^[1] two fundamental attributes of a Higgs boson. This appears to be the first elementary scalar particle discovered in nature.^[14] More studies are needed to verify that the discovered particle has properties matching those predicted for the Higgs boson by the Standard Model, or whether, as predicted by some theories, multiple Higgs bosons exist.^[3]

The Higgs boson is named after Peter Higgs, one of six physicists who, in 1964, proposed the mechanism that suggested the existence of such a particle. On December 10, 2013, two of them, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their work and prediction (Englert's co-researcher Robert Brout had died in 2011 and the Nobel Prize is not ordinarily given posthumously).^[15] Although Higgs's name has come to be associated with this theory, several researchers between about 1960 and 1972 independently developed different parts of it. In mainstream media the Higgs boson has often been called the "God particle", from a 1993 book on the topic;^[16] the nickname is strongly disliked by many physicists, including Higgs, who regard it as sensationalistic.^[17][18][19]

In the Standard Model, the Higgs particle is a boson with no spin, electric charge, or colour charge. It is also very unstable, decaying into other particles almost immediately. It is a quantum excitation of one of the four components of the Higgs field. The latter constitutes a scalar field, with two neutral and two electrically charged components that form a complex doublet of the weak isospin SU(2) symmetry. The Higgs field is tachyonic -- does not refer to faster-than-light speeds, but means that symmetry-breaking through condensation of a particle must occur under certain conditions. The Higgs field has a "Mexican hat" shaped potential with nonzero strength everywhere (including otherwise empty space), which in its vacuum state breaks the weak isospin symmetry of the electroweak interaction. 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 separately couples to other particles known as fermions (via Yukawa couplings), causing these to acquire mass as well. Some versions of the theory predict more than one kind of Higgs fields and bosons. Alternative "Higgsless" models may have been considered if the Higgs boson had not been discovered.

A non-technical summary

"Higgs" terminology

A simple explanation – what are the Higgs mechanism, field and boson?
Gauge symmetries	In the Standard Model of particle physics, the fundamental forces of nature arise from laws of nature called gauge symmetries, and these forces are transmitted by particles known as gauge bosons. According to the gauge theory, the weak force's gauge symmetry should cause its gauge bosons to have zero mass, but experiments show that the weak force's gauge bosons, the W and Z, have mass.[20]^:372–373 But it has proved difficult to find any way to explain their unexpected mass.
Higgs mechanism	By the early 1960s, physicists had realised that a given symmetry law might not always be followed (or 'obeyed') under certain conditions.[Note 3] The Higgs mechanism is a mathematical model devised by three groups of researchers in 1964 that explains why and how gauge bosons could still be massive despite their governing symmetry. It showed that the conditions for the symmetry would be 'broken' if an unusual type of field existed throughout the Universe, and then why some fundamental particles would be able to have mass.
Higgs field	According to the Standard Model, a field of the necessary kind (the "Higgs field") exists throughout space, and breaks certain symmetry laws of the electroweak interaction.[Note 4] The existence of this field triggers the Higgs mechanism, causing the gauge bosons responsible for the weak force to be massive, and explaining their very short range.[Note 5] Some years after the original theory was articulated scientists realised that the same field would also explain, in a different way, why other fundamental constituents of matter (including electrons and quarks) have mass. For many years scientists had no way to tell whether or not the Higgs field existed. If it did, then it would be unlike other fundamental fields. But it was also possible that these key ideas, or even the entire Standard Model itself, were somehow incorrect.[Note 6] Only discovering what was breaking this symmetry would solve the problem.
Higgs boson	The existence of the Higgs field could be supported by searching for a matching particle associated with it — the "Higgs boson".[6][7] Detecting Higgs bosons would prove that the Higgs field exists, and further support the validity of the Standard Model. But for decades scientists had no way to discover whether Higgs bosons actually existed in nature either, because they would be very difficult to produce, and would break apart in about a ten-sextillionth (10^−22) of a second. Although the theory gave "remarkably" [22]^:22[Note 7] accurate predictions, particle colliders, detectors, and computers capable of looking for Higgs bosons took over 30 years (c. 1980–2010) to develop. As of March 2016, scientists are confident that they have discovered the existence of the Higgs boson, and therefore the concept of some type of Higgs field throughout space is highly supported. Further testing over the coming years should eventually tell us more about these, and is likely to have significant impact in the future (see below).[11][13]

Overview

Physicists explain the properties and forces between elementary particles in terms of the Standard Model—a widely accepted and "remarkably" accurate^[22] framework based on gauge invariance and symmetries, believed to explain almost everything in the known universe, other than gravity.^[23] But by around 1960 all attempts to create a gauge invariant theory for two of the four fundamental forces had consistently failed at one crucial point: although gauge invariance seemed extremely important, it seemed to make any theory of electromagnetism and the weak force go haywire, by demanding that either many particles with mass were massless or that non-existent forces and massless particles had to exist. Scientists had no idea how to get past this point.

In 1962 physicist Philip Anderson wrote a paper that built upon work by Yoichiro Nambu concerning "broken symmetries" in superconductivity and particle physics. He suggested that "broken symmetries" might also be the missing piece needed to solve the problems of gauge invariance. In 1964 a theory was created almost simultaneously by 3 different groups of researchers, that showed Anderson's suggestion was possible – the gauge theory and "mass problems" could indeed be resolved if an unusual kind of field, now generally called the "Higgs field", existed throughout the universe; if the Higgs field did exist, it would apparently cause existing particles to acquire mass instead of new massless particles being formed. Although these ideas did not gain much initial support or attention, by 1972 they had been developed into a comprehensive theory and proved capable of giving "sensible" results that accurately described particles known at the time, and which accurately predicted several other particles discovered during the following years.^{[Note 7]} During the 1970s these theories rapidly became the "standard model". There was not yet any direct evidence that the Higgs field actually existed, but even without proof of the field, the accuracy of its predictions led scientists to believe the theory might be true. By the 1980s the question whether or not the Higgs field existed had come to be regarded as one of the most important unanswered questions in particle physics.

If the Higgs field could be shown to exist, it would be a monumental discovery for science and human knowledge, and would open doorways to new knowledge in many disciplines. If not, then other more complicated theories would need to be considered. The simplest means to test the existence of the Higgs field would be a search for a new elementary particle that the field would have to give off, a particle known as the "Higgs boson" or the "Higgs particle". This particle would be extremely difficult to find. After significant technological advancements, by the 1990s two large experimental installations were being designed and constructed that allowed a search for the Higgs boson.

While several symmetries in nature are spontaneously broken through a form of the Higgs mechanism, in the context of the Standard Model the term "Higgs mechanism" almost always means symmetry breaking of the electroweak field. It is considered confirmed, but revealing the exact cause has been difficult. Various analogies have also been invented to describe the Higgs field and boson, including analogies with well-known symmetry breaking effects such as the rainbow and prism, electric fields, ripples, and resistance of macro objects moving through media, like people moving through crowds or some objects moving through syrup or molasses. However, analogies based on simple resistance to motion are inaccurate as the Higgs field does not work by resisting motion.

Significance

Scientific impact

Evidence of the Higgs field and its properties has been extremely significant scientifically, for many reasons. The Higgs boson's importance is largely that it is able to be examined using existing knowledge and experimental technology, as a way to confirm and study the entire Higgs field theory.^[6][7] Conversely, proof that the Higgs field and boson do not exist would also have been significant. In discussion form, the relevance includes:

Validating the Standard Model, or choosing between extensions and alternatives	Does the Higgs field exist, which fundamentally validates the Standard Model through the mechanism of Mass generation? If it does, then which more advanced extensions are suggested or excluded based upon measurements of its properties? What else can we learn about this fundamental field, now that we have the experimental means to study its behaviour and interactions? Alternatively, if the Higgs field doesn't exist, which alternatives and modifications to the Standard Model are likely to be preferred? Will the data suggest an extension, or a completely different approach (such as supersymmetry or string theory)? Related to this, a belief generally exists among physicists that there is likely to be "new" physics beyond the Standard Model—the Standard Model will at some point be extended or superseded. The Higgs field and related issues present a promising "doorway" to understand better the places where the Standard Model might become inadequate or fail, and could provide considerable evidence guiding researchers into future enhancements or successors.
Finding how symmetry breaking happens within the electroweak interaction	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. Without this, the universe we see around us could not exist, because atoms and other structures could not form, and reactions in stars such as our Sun would not occur. But it is not clear how this actually happens in nature. Is the Standard Model correct in its approach, and can it be made more exact with actual experimental measurements? If not the Higgs field, then what is breaking symmetry in its place?
Finding how certain particles acquire mass	Electroweak symmetry breaking (due to a Higgs field or otherwise) is believed proven responsible for the masses of fundamental particles such as elementary fermions (including electrons and quarks) and the massive W and Z gauge bosons. Finding how this happens is pivotal to particle physics. It is worth noting that the Higgs field does not "create" mass out of nothing (which would violate the law of conservation of energy), nor is the Higgs field responsible for the mass of all particles. For example, about 99% of the mass of baryons (composite particles such as the proton and neutron) is due instead to quantum chromodynamics 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.[24] In Higgs-based theories, the property of "mass" is a manifestation of potential energy transferred to particles when they interact ("couple") with the Higgs field, which had contained that mass in the form of energy.[25]
Evidence whether or not scalar fields exist in nature, and "new" physics	The significance of proof of a scalar field such as the Higgs field would be hard to overestimate: "[The] verification of real scalar fields would be nearly as important as its role in generating mass".[12] Rolf-Dieter Heuer, director general of CERN, stated in a 2011 talk on the Higgs field:[26] All the matter particles are spin-1/2 fermions. All the force carriers are spin-1 bosons. Higgs particles are spin-0 bosons (scalars). The Higgs is neither matter nor force. The Higgs is just different. This would be the first fundamental scalar ever discovered. The Higgs field is thought to fill the entire universe. Could it give some handle of dark energy (scalar field)? Many modern theories predict other scalar particles like the Higgs. Why, after all, should the Higgs be the only one of its kind? [The] LHC can search for and study new scalars with precision.
Insight into cosmic inflation	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 therefore 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 have received treatments suggesting that Higgs inflation models are still of interest theoretically.
Insight into the nature of the universe, and its possible fates	Diagram showing the Higgs boson and top quark masses, which could indicate whether our universe is stable, or a long-lived 'bubble'. As of 2012, the 2σ ellipse based on Tevatron and LHC data still allows for both possibilities.[27] For decades, scientific models of our universe have included the possibility that it exists as a long-lived, but not completely stable, sector of space, which could potentially at some time be destroyed upon 'toppling' into a more stable vacuum state.[28][29][30][31][32] If the masses of the Higgs boson and top quark are known more exactly, 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 universe's present vacuum state is stable or merely long-lived.[33][34][35] (This was sometimes misreported as the Higgs boson "ending" the universe[Note 8]). A 125 – 127 GeV Higgs mass seems to be extremely close to the boundary for stability (estimated in 2012 as 123.8 – 135.0 GeV[27]) but a definitive answer requires much more precise measurements of the top quark's pole mass.[27] New physics can change this picture.[39] 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[40][Note 9] – 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.[40][Note 10] 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.[27]^:218[42][43] A future electron–positron collider would be able to provide the precise measurements of the top quark needed for such calculations.[27]
Insight into the 'energy of the vacuum'	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 present universe's known forces and fields arise.[44]
Link to the 'cosmological constant' problem	The relationship (if any) between the Higgs field and the presently observed vacuum energy density of the universe has also come under scientific study. As observed, the present vacuum energy density is extremely close to zero, but the energy density expected from the Higgs field, supersymmetry, and other current theories are typically many orders of magnitude larger. It is unclear how these should be reconciled. This cosmological constant problem remains a further major unanswered problem in physics.

Practical and technological impact of discovery

As yet, there are no known immediate technological benefits of finding the Higgs particle. However, a common pattern for fundamental discoveries is for practical applications to follow later, once the discovery has been explored further, at which point they become the basis for new technologies of importance to society.^[45][46][47]

The challenges in particle physics have furthered major technological progress of widespread importance. For example, the World Wide Web began as a project to improve CERN's communication system. CERN's requirement to process massive amounts of data produced by the Large Hadron Collider also led to contributions to the fields of distributed and cloud computing.

History

The six authors of the 1964 PRL papers, who received the 2010 J. J. Sakurai Prize for their work. From left to right: Kibble, Guralnik, Hagen, Englert, Brout. Right: Higgs.

Nobel Prize Laureate Peter Higgs in Stockholm, December 2013

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.^[48]:150 However, attempts to unify known fundamental forces such as the electromagnetic force and the weak nuclear force were known to be incomplete. One known omission 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.^[49] Goldstone's theorem, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions,^[50] since it appeared to show that zero-mass particles would have to also exist that were "simply not seen".^[51] According to Guralnik, physicists had "no understanding" how these problems could be overcome.^[51]

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 Nambu–Goldstone massless mode can combine with the massless gauge field modes to produce a physical massive vector field. This is what happens in superconductivity, a subject about which Anderson was (and is) one of the leading experts. [text condensed] ^[49]

The Higgs mechanism is a process by which vector bosons can get rest mass without explicitly breaking gauge invariance, as a byproduct of spontaneous symmetry breaking.^[52][53] The mathematical theory behind spontaneous symmetry breaking was initially conceived and published within particle physics by Yoichiro Nambu in 1960,^[54] 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^[55] and concluded in his 1963 paper on 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"),^{[56]:4–5[57]} and Abraham Klein and Benjamin Lee showed in March 1964 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.^[58]

These approaches were quickly developed into a full relativistic model, independently and almost simultaneously, by three groups of physicists: by François Englert and Robert Brout in August 1964;^[59] by Peter Higgs in October 1964;^[60] and by Gerald Guralnik, Carl Hagen, and Tom Kibble (GHK) in November 1964.^[61] Higgs also wrote a short but important^[52] response published in September 1964 to an objection by Gilbert,^[62] which showed that if calculating within the radiation gauge, Goldstone's theorem and Gilbert's objection would become inapplicable.^{[Note 11]} (Higgs later described Gilbert's objection as prompting his own paper.^[63]) Properties of the model were further considered by Guralnik in 1965,^[64] by Higgs in 1966,^[65] by Kibble in 1967,^[66] and further by GHK in 1967.^[67] The original three 1964 papers showed that when a gauge theory is combined with an additional field that spontaneously breaks the symmetry, the gauge bosons can consistently acquire a finite mass.^[52][53][68] In 1967, Steven Weinberg^[69] and Abdus Salam^[70] independently showed how a Higgs mechanism could be used to break the electroweak symmetry of Sheldon Glashow's unified model for the weak and electromagnetic interactions^[71] (itself an extension of work by Schwinger), forming what became the Standard Model of particle physics. Weinberg was the first to observe that this would also provide mass terms for the fermions.^{[72] [Note 12]}

However, the seminal papers on spontaneous breaking of gauge symmetries were at first largely ignored, because it was widely believed that the (non-Abelian gauge) theories in question were a dead-end, and in particular that they could not be renormalised. In 1971–72, Martinus Veltman and Gerard 't Hooft proved renormalisation of Yang–Mills was possible in two papers covering massless, and then massive, fields.^[72] Their contribution, and others' work on the renormalisation group – including "substantial" theoretical work by Russian physicists Ludvig Faddeev, Andrei Slavnov, Efim Fradkin and Igor Tyutin^[73] – was eventually "enormously profound and influential",^[74] but even with all key elements of the eventual theory published there was still almost no wider interest. For example, Coleman found in a study that "essentially no-one paid any attention" to Weinberg's paper prior to 1971^[75] and discussed by David Politzer in his 2004 Nobel speech.^[74] – now the most cited in particle physics^[76] – and even in 1970 according to Politzer, Glashow's teaching of the weak interaction contained no mention of Weinberg's, Salam's, or Glashow's own work.^[74] In practice, Politzer states, almost everyone learned of the theory due to physicist Benjamin Lee, who combined the work of Veltman and 't Hooft with insights by others, and popularised the completed theory.^[74] In this way, from 1971, interest and acceptance "exploded" ^[74] and the ideas were quickly absorbed in the mainstream.^[72][74]

The resulting electroweak theory and Standard Model have accurately predicted (among other things) weak neutral currents, three bosons, the top and charm quarks, and with great precision, the mass and other properties of some of these.^{[Note 7]} Many of those involved eventually won Nobel Prizes or other renowned awards. A 1974 paper and comprehensive review in Reviews of Modern Physics commented that "while no one doubted the [mathematical] correctness of these arguments, no one quite believed that nature was diabolically clever enough to take advantage of them",^[77]:9 adding that the theory had so far produced accurate answers that accorded with experiment, but it was unknown whether the theory was fundamentally correct.^{[77]:9,36(footnote),43–44,47} By 1986 and again in the 1990s it became possible to write that understanding and proving the Higgs sector of the Standard Model was "the central problem today in particle physics".^[8][9]

Summary and impact of the PRL papers

The three papers written in 1964 were each recognised as milestone papers during Physical Review Letters's 50th anniversary celebration.^[68] Their six authors were also awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work.^[78] (A controversy also arose the same year, because in the event of a Nobel Prize only up to three scientists could be recognised, with six being credited for the papers.^[79] ) Two of the three PRL papers (by Higgs and by GHK) contained equations for the hypothetical field that eventually would become known as the Higgs field and its hypothetical quantum, the Higgs boson.^[60][61] Higgs' subsequent 1966 paper showed the decay mechanism of the boson; only a massive boson can decay and the decays can prove the mechanism.

In the paper by Higgs the boson is massive, and in a closing sentence Higgs writes that "an essential feature" of the theory "is the prediction of incomplete multiplets of scalar and vector bosons".^[60] (Frank Close comments that 1960s gauge theorists were focused on the problem of massless vector bosons, and the implied existence of a massive scalar boson was not seen as important; only Higgs directly addressed it.^{[80]:154, 166, 175}) In the paper by GHK the boson is massless and decoupled from the massive states.^[61] In reviews dated 2009 and 2011, Guralnik states that in the GHK model the boson is massless only in a lowest-order approximation, but it is not subject to any constraint and acquires mass at higher orders, and adds that the GHK paper was the only one to show that there are no massless Goldstone bosons in the model and to give a complete analysis of the general Higgs mechanism.^[51][81] All three reached similar conclusions, despite their very different approaches: Higgs' paper essentially used classical techniques, Englert and Brout's involved calculating vacuum polarisation in perturbation theory around an assumed symmetry-breaking vacuum state, and GHK used operator formalism and conservation laws to explore in depth the ways in which Goldstone's theorem may be worked around.^[52]

Theoretical properties

Theoretical need for the Higgs

"Symmetry breaking illustrated": – At high energy levels (left) the ball settles in the centre, and the result is symmetrical. At lower energy levels (right), the overall "rules" remain symmetrical, but the "Mexican hat" potential comes into effect: "local" symmetry inevitably becomes broken since eventually the ball must at random roll one way or another.

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, 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.^{[Note 13]}) 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, 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 and long-range forces (seemingly an inevitable consequence of Goldstone's theorem) 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,^{[Note 11]} 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.

The Standard Model hypothesises a field which is responsible for this effect, called the Higgs field (symbol: $\phi$), which has the unusual property of a non-zero amplitude in its ground state; i.e., a non-zero vacuum expectation value. It can have this effect because of its unusual "Mexican hat" shaped potential whose lowest "point" is not at its "centre". Below a certain extremely high energy level the existence of this non-zero vacuum expectation spontaneously breaks electroweak gauge symmetry which in turn gives rise to the Higgs mechanism and triggers the acquisition of mass by those particles interacting with the field. This effect occurs because scalar field components of the Higgs field are "absorbed" by the massive bosons as degrees of freedom, and couple to the fermions via Yukawa coupling, thereby producing the expected mass terms. In effect when symmetry breaks under these conditions, the Goldstone bosons that arise interact with the Higgs field (and with other particles capable of interacting with the Higgs field) instead of becoming new massless particles, the intractable problems of both underlying theories "neutralise" each other, and the residual outcome is that elementary particles acquire a consistent mass based on how strongly they interact with the Higgs field. It is the simplest known process capable of giving mass to the gauge bosons while remaining compatible with gauge theories.^[82] Its quantum would be a scalar boson, known as the Higgs boson.^[83]

Summary of interactions between certain particles described by the Standard Model.

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,^[84] 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.^[85] 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.^[86][87] 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).^[88] 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.^[89] 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.^[90]

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 and is CP-even, and has zero electric and colour charge.^[91]

The Minimal Standard Model does not predict the mass of the Higgs boson.^[92] If that mass is between 115 and 180 GeV/c², then the Standard Model can be valid at energy scales all the way up to the Planck scale (10¹⁹ GeV).^[93] Many theorists expect new physics beyond the Standard Model to emerge at the TeV-scale, based on unsatisfactory properties of the Standard Model.^[94] 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.^[95]

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 W and Z bosons. Precision measurements of electroweak parameters, such as the Fermi constant and masses of W/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 (this upper limit would increase to 185 GeV/c² if the lower bound of 114.4 GeV/c² from the LEP-2 direct search is allowed for^[96]). 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 predicted by the Standard Model.^[97]

Production

Feynman diagrams for Higgs production

Gluon fusion	Higgs Strahlung
Vector boson fusion	Top fusion

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,^{[98][99][100]} although the probability of producing a Higgs boson in any collision is always expected to be very small—for example, only 1 Higgs boson per 10 billion collisions in the Large Hadron Collider.^{[Note 14]} 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. 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.^[98][99]
• 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.^{[98][99][100]}
• Weak boson fusion. Another possibility when two (anti-)fermions collide is that the two exchange a virtual W or Z boson, which emits a Higgs boson. The colliding fermions do not need to be the same type. So, for example, an up quark may exchange a Z boson with an anti-down quark. This process is the second most important for the production of Higgs particle at the LHC and LEP.^[98][100]
• Top fusion. The final process that is commonly considered is by far the least likely (by two orders of magnitude). This process involves two colliding gluons, which each decay into a heavy quark–antiquark pair. A quark and antiquark from each pair can then combine to form a Higgs particle.^[98][99]

Decay

The Standard Model prediction for the decay width of the Higgs particle depends on the value of its mass.

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.^[101] 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, except for the mass of the Higgs boson itself. For a Higgs boson with a mass of 126 GeV/c² the SM predicts a mean life time of about 1.6×10⁻²² s.^{[Note 2]}

The Standard Model prediction for the branching ratios of the different decay modes of the Higgs particle depends on the value of its mass.

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).

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.^[102] By this logic the most common decay should be into a top–antitop quark pair. However, such a decay is only possible if the Higgs is heavier than ~346 GeV/c², twice the mass of the top quark. For a Higgs mass of 126 GeV/c² the SM predicts that the most common decay is into a bottom–antibottom quark pair, which happens 56.1% of the time.^[5] The second most common fermion decay at that mass is a tau–antitau pair, which happens only about 6% of the time.^[5]

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 23.1% of the time for a Higgs boson with a mass of 126 GeV/c².^[5] The W bosons can subsequently decay either into a quark and an antiquark or into a charged lepton and a neutrino. However, 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 2.9% of the time for a Higgs with a mass of 126 GeV/c²),^[5] if each of the bosons subsequently decays into a pair of easy-to-detect charged leptons (electrons or muons).

Decay into massless gauge bosons (i.e., gluons or photons) is also possible, but requires intermediate loop of virtual heavy quarks (top or bottom) or massive gauge bosons.^[102] The most common such process is the decay into a pair of gluons through a loop of virtual heavy quarks. This process, which is the reverse of the gluon fusion process mentioned above, happens approximately 8.5% of the time for a Higgs boson with a mass of 126 GeV/c².^[5] Much rarer is the decay into a pair of photons mediated by a loop of W bosons or heavy quarks, which happens only twice for every thousand decays.^[5] However, this process is very relevant for experimental searches for the Higgs boson, because the energy and momentum of the photons can be measured very precisely, giving an accurate reconstruction of the mass of the decaying particle.^[102]

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.^[103] 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 technicolor 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.^[104][105]

A one-loop Feynman diagram of the first-order correction to the Higgs mass. In the Standard Model the effects of these corrections are potentially enormous, giving rise to the so-called hierarchy problem.

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 to ensure unitarity (in this case, to unitarise longitudinal vector boson scattering).^[106] Reconciling these points appears to require explaining why there is an almost-perfect cancellation resulting in the visible mass of ~ 125 GeV, 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.^[107] 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.^[106] 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.

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),^{[Note 14]} 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 lesser 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 5 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.^[109] 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.^{[109][110][111]}

Search before 4 July 2012

The first extensive search for the Higgs boson was conducted at the Large Electron–Positron Collider (LEP) at CERN in the 1990s. At the end of its service in 2000, LEP had found no conclusive evidence for the Higgs.^{[Note 15]} This implied that if the Higgs boson were to exist it would have to be heavier than 114.4 GeV/c².^[112]

The search continued at Fermilab in the United States, where the Tevatron—the collider that discovered the top quark in 1995—had been upgraded for this purpose. There was no guarantee that the Tevatron would be able to find the Higgs, but it was the only supercollider that was operational since the Large Hadron Collider (LHC) was still under construction and the planned Superconducting Super Collider had been cancelled in 1993 and never completed. The Tevatron was only able to exclude further ranges for the Higgs mass, and was shut down on 30 September 2011 because it no longer could keep up with the LHC. The final analysis of the data excluded the possibility of a Higgs boson with a mass between 147 GeV/c² and 180 GeV/c². In addition, there was a small (but not significant) excess of events possibly indicating a Higgs boson with a mass between 115 GeV/c² and 140 GeV/c².^[113]

The Large Hadron Collider at CERN in Switzerland, was designed specifically to be able to either confirm or exclude the existence of the Higgs boson. Built in a 27 km tunnel under the ground near Geneva originally inhabited by LEP, it was designed to collide two beams of protons, initially at energies of 3.5 TeV per beam (7 TeV total), or almost 3.6 times that of the Tevatron, and upgradeable to 2 × 7 TeV (14 TeV total) in future. Theory suggested if the Higgs boson existed, collisions at these energy levels should be able to reveal it. As one of the most complicated scientific instruments ever built, its operational readiness was delayed for 14 months by a magnet quench event nine days after its inaugural tests, caused by a faulty electrical connection that damaged over 50 superconducting magnets and contaminated the vacuum system.^{[114][115][116]}

Data collection at the LHC finally commenced in March 2010.^[117] By December 2011 the two main particle detectors at the LHC, ATLAS and CMS, had narrowed down the mass range where the Higgs could exist to around 116-130 GeV (ATLAS) and 115-127 GeV (CMS).^[118][119] There had also already been a number of promising event excesses that had "evaporated" and proven to be nothing but random fluctuations. However, from around May 2011,^[120] both experiments had seen among their results, the slow emergence of a small yet consistent excess of gamma and 4-lepton decay signatures and several other particle decays, all hinting at a new particle at a mass around 125 GeV.^[120] By around November 2011, the anomalous data at 125 GeV was becoming "too large to ignore" (although still far from conclusive), and the team leaders at both ATLAS and CMS each privately suspected they might have found the Higgs.^[120] On November 28, 2011, at an internal meeting of the two team leaders and the director general of CERN, the latest analyses were discussed outside their teams for the first time, suggesting both ATLAS and CMS might be converging on a possible shared result at 125 GeV, and initial preparations commenced in case of a successful finding.^[120] While this information was not known publicly at the time, the narrowing of the possible Higgs range to around 115–130 GeV and the repeated observation of small but consistent event excesses across multiple channels at both ATLAS and CMS in the 124-126 GeV region (described as "tantalising hints" of around 2-3 sigma) were public knowledge with "a lot of interest".^[121] It was therefore widely anticipated around the end of 2011, that the LHC would provide sufficient data to either exclude or confirm the finding of a Higgs boson by the end of 2012, when their 2012 collision data (with slightly higher 8 TeV collision energy) had been examined.^[121][122]

Discovery of candidate boson at CERN

Feynman diagrams showing the cleanest channels associated with the low-mass (~125 GeV) Higgs boson candidate observed by ATLAS and CMS at the LHC. The dominant production mechanism at this mass involves two gluons from each proton fusing to a Top-quark Loop, which couples strongly to the Higgs field to produce a Higgs boson. Left: Diphoton channel: Boson subsequently decays into 2 gamma ray photons by virtual interaction with a W boson loop or top quark loop. Right: 4-Lepton "golden channel": Boson emits 2 Z bosons, which each decay into 2 leptons (electrons, muons). Experimental analysis of these channels reached a significance of more than 5 sigma in both experiments.[123][124][125]

On 22 June 2012 CERN announced an upcoming seminar covering tentative findings for 2012,^[126][127] and shortly afterwards (from around 1 July 2012 according to an analysis of the spreading rumour in social media^[128]) rumours began to spread in the media that this would include a major announcement, but it was unclear whether this would be a stronger signal or a formal discovery.^[129][130] Speculation escalated to a "fevered" pitch when reports emerged that Peter Higgs, who proposed the particle, was to be attending the seminar,^[131][132] and that "five leading physicists" had been invited – generally believed to signify the five living 1964 authors – with Higgs, Englert, Guralnik, Hagen attending and Kibble confirming his invitation (Brout having died in 2011).^[133][134]

On 4 July 2012 both of the CERN experiments announced they had independently made the same discovery:^[135] CMS of a previously unknown boson with mass 125.3 ± 0.6 GeV/c^2[136][137] and ATLAS of a boson with mass 126.0 ± 0.6 GeV/c².^[138][139] Using the combined analysis of two interaction types (known as 'channels'), both experiments independently reached a local significance of 5 sigma — implying that the probability of getting at least as strong a result by chance alone is less than 1 in 3 million. When additional channels were taken into account, the CMS significance was reduced to 4.9 sigma.^[137]

The two teams had been working 'blinded' from each other from around late 2011 or early 2012,^[120] meaning they did not discuss their results with each other, providing additional certainty that any common finding was genuine validation of a particle.^[109] This level of evidence, confirmed independently by two separate teams and experiments, meets the formal level of proof required to announce a confirmed discovery.

On 31 July 2012, the ATLAS collaboration presented additional data analysis on the "observation of a new particle", including data from a third channel, which improved the significance to 5.9 sigma (1 in 588 million chance of obtaining at least as strong evidence by random background effects alone) and mass 126.0 ± 0.4 (stat) ± 0.4 (sys) GeV/c², ^[139] and CMS improved the significance to 5-sigma and mass 125.3 ± 0.4 (stat) ± 0.5 (sys) GeV/c².^[136]

The new particle tested as a possible Higgs boson

Following the 2012 discovery, it was still unconfirmed whether or not the 125 GeV/c² particle was a Higgs boson. On one hand, observations remained consistent with the observed particle being the Standard Model Higgs boson, and the particle decayed into at least some of the predicted channels. Moreover, the production rates and branching ratios for the observed channels broadly matched the predictions by the Standard Model within the experimental uncertainties. However, the experimental uncertainties currently still left room for alternative explanations, meaning an announcement of the discovery of a Higgs boson would have been premature.^[102] To allow more opportunity for data collection, the LHC's proposed 2012 shutdown and 2013–14 upgrade were postponed by 7 weeks into 2013.^[140]

In November 2012, in a conference in Kyoto researchers said evidence gathered since July was falling into line with the basic Standard Model more than its alternatives, with a range of results for several interactions matching that theory's predictions.^[141] Physicist Matt Strassler highlighted "considerable" evidence that the new particle is not a pseudoscalar negative parity particle (consistent with this required finding for a Higgs boson), "evaporation" or lack of increased significance for previous hints of non-Standard Model findings, expected Standard Model interactions with W and Z bosons, absence of "significant new implications" for or against supersymmetry, and in general no significant deviations to date from the results expected of a Standard Model Higgs boson.^[142] However some kinds of extensions to the Standard Model would also show very similar results;^[143] so commentators noted that based on other particles that are still being understood long after their discovery, it may take years to be sure, and decades to fully understand the particle that has been found.^[141][142]

These findings meant that as of January 2013, scientists were very sure they had found an unknown particle of mass ~ 125 GeV/c², and had not been misled by experimental error or a chance result. They were also sure, from initial observations, that the new particle was some kind of boson. The behaviours and properties of the particle, so far as examined since July 2012, also seemed quite close to the behaviours expected of a Higgs boson. Even so, it could still have been a Higgs boson or some other unknown boson, since future tests could show behaviours that do not match a Higgs boson, so as of December 2012 CERN still only stated that the new particle was "consistent with" the Higgs boson,^[11][13] and scientists did not yet positively say it was the Higgs boson.^[144] Despite this, in late 2012, widespread media reports announced (incorrectly) that a Higgs boson had been confirmed during the year.^{[Note 16]}

In January 2013, CERN director-general Rolf-Dieter Heuer stated that based on data analysis to date, an answer could be possible 'towards' mid-2013,^[150] and the deputy chair of physics at Brookhaven National Laboratory stated in February 2013 that a "definitive" answer might require "another few years" after the collider's 2015 restart.^[151] In early March 2013, CERN Research Director Sergio Bertolucci stated that confirming spin-0 was the major remaining requirement to determine whether the particle is at least some kind of Higgs boson.^[152]

Preliminary confirmation of existence and current status

On 14 March 2013 CERN confirmed that:

"CMS and ATLAS have compared a number of options for the spin-parity of this particle, and these all prefer no spin and even parity [two fundamental criteria of a Higgs boson consistent with the Standard Model]. This, coupled with the measured interactions of the new particle with other particles, strongly indicates that it is a Higgs boson." ^[1]

This also makes the particle the first elementary scalar particle to be discovered in nature.^[14]

Examples of tests used to validate whether the 125 GeV particle is a Higgs boson:^[142][153]

Requirement	How tested / explanation	Current status (August 2016)
Zero spin	Examining decay patterns. Spin-1 had been ruled out at the time of initial discovery by the observed decay to two photons (γ γ), leaving spin-0 and spin-2 as remaining candidates.	Spin-0 tentatively confirmed.[1][154][155] The spin-2 hypothesis is excluded with a confidence level exceeding 99.9%.[155]
Even (Positive) parity	Studying the angles at which decay products fly apart. Negative parity was also disfavoured if spin-0 was confirmed.[156]	Even parity tentatively confirmed.[1][154][155] The spin-0 negative parity hypothesis is excluded with a confidence level exceeding 99.9%.[154]
Decay channels (outcomes of particle decaying) are as predicted	The Standard Model predicts the decay patterns of a 125–126 GeV Higgs boson. Are these all being seen, and at the right rates? Particularly significant, we should observe decays into pairs of photons (γ γ), W and Z bosons (WW and ZZ), bottom quarks (bb), and tau leptons (τ τ), among the possible outcomes.	γ γ, τ τ, WW and ZZ observed; bb not yet confirmed. All observed signal strengths are consistent with the Standard Model prediction.[157]
Couples to mass (i.e., strength of interaction with Standard Model particles proportional to their mass)	Particle physicist Adam Falkowski states that the essential qualities of a Higgs boson are that it is a spin-0 (scalar) particle which also couples to mass (W and Z bosons); proving spin-0 alone is insufficient.[153]	Couplings to mass strongly evidenced ("At 95% confidence level cV is within 15% of the standard model value cV=1").[153]
Higher energy results remain consistent	After the LHC's 2015 restart at the LHC's full planned energies of 13–14 TeV, searches for multiple Higgs particles (as predicted in some theories) and tests targeting other versions of particle theory will take place. These higher energy results must continue to give results consistent with Higgs theories	Analysis of collisions up to July do not show deviations from the Standard Model, with experimental precisions approaching the earlier measurements at lower collision energy.[158][159][160]

Public discussion

Naming

Names used by physicists

The name most strongly associated with the particle and field is the Higgs boson^[80]:168 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,^{[Note 17]} and these are still used at times.^[52][162] Fuelled in part by the issue of recognition and a potential shared Nobel Prize,^[162][163] the most appropriate name is still occasionally a topic of debate as of 2012.^[162] (Higgs himself prefers to call the particle either by an acronym of all those involved, or "the scalar boson", or "the so-called Higgs particle".^[163])

A considerable amount has been written on how Higgs' name came to be exclusively used. Two main explanations are offered.

Reason	Basis of explanation
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;[80]^:167[164] he was therefore "the first to postulate the existence of a massive particle" according to Nature.[162] 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.[80]^:167[165] and that Higgs alone had drawn attention to a predicted massive scalar boson, while all others had focused on the massive vector bosons;[80]^:154, 166, 175[165] In this way, Higgs' contribution also provided experimentalists with a crucial "concrete target" needed to test the theory.[166] However, in Higgs' view, Brout and Englert did not explicitly mention the boson since its existence is plainly obvious in their work,[56]^:6 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.[81]^:9 Higgs' paper also provided an "especially sharp" statement of the challenge and its solution according to science historian David Kaiser.[163]
The name was popularised in the 1970s due to its use as a convenient shorthand or because of a mistake in citing.	Many accounts (including Higgs' own[56]^:7) credit the "Higgs" name to physicist Benjamin Lee (in Korean: Lee Whi-soh). Lee was a significant populist for the theory in its early stages, and habitually attached the name "Higgs" as a "convenient shorthand" for its components from 1972[17][162][167][168][169] and in at least one instance from as early as 1966.[170] Although Lee clarified in his footnotes that "'Higgs' is an abbreviation for Higgs, Kibble, Guralnik, Hagen, Brout, Englert",[167] his use of the term (and perhaps also Steven Weinberg's mistaken cite of Higgs' paper as the first in his seminal 1967 paper[80][171][170]) meant that by around 1975–76 others had also begun to use the name 'Higgs' exclusively as a shorthand.[172]

Nickname

The Higgs boson is often referred to as the "God particle" in popular media outside the scientific community.^{[173][174][175][176][177]} The nickname comes from the title of the 1993 book on the Higgs boson and particle physics, The God Particle: If the Universe Is the Answer, What Is the Question? by Nobel Physics prizewinner and Fermilab director Leon Lederman.^[22] Lederman wrote it in the context of failing US government support for the Superconducting Super Collider,^[178] a part-constructed titanic^[179][180] competitor to the Large Hadron Collider with planned collision energies of 2 × 20 TeV that was championed by Lederman since its 1983 inception^{[178][181][182]} and shut down in 1993. The book sought in part to promote awareness of the significance and need for such a project in the face of its possible loss of funding.^[183] Lederman, a leading researcher in the field, wanted to title his book The Goddamn Particle: If the Universe is the Answer, What is the Question? But his editor decided that the title was too controversial and convinced Lederman to change the title to The God Particle: If the Universe is the Answer, What is the Question?^[184]

While media use of this term may have contributed to wider awareness and interest,^[185] many scientists feel the name is inappropriate^{[17][18][186]} since it is sensational hyperbole and misleads readers;^[187] the particle also has nothing to do with God, leaves open numerous questions in fundamental physics, and does not explain the ultimate origin of the universe. Higgs, an atheist, was reported to be displeased and stated in a 2008 interview that he found it "embarrassing" because it was "the kind of misuse... which I think might offend some people".^{[187][188][189]} Science writer Ian Sample stated in his 2010 book on the search that the nickname is "universally hate[d]" by physicists and perhaps the "worst derided" in the history of physics, but that (according to Lederman) the publisher rejected all titles mentioning "Higgs" as unimaginative and too unknown.^[190]

Lederman begins with a review of the long human search for knowledge, and explains that his tongue-in-cheek title draws an analogy between the impact of the Higgs field on the fundamental symmetries at the Big Bang, and the apparent chaos of structures, particles, forces and interactions that resulted and shaped our present universe, with the biblical story of Babel in which the primordial single language of early Genesis was fragmented into many disparate languages and cultures.^[191]

Today ... we have the standard model, which reduces all of reality to a dozen or so particles and four forces. ... It's a hard-won simplicity [...and...] remarkably accurate. But it is also incomplete and, in fact, internally inconsistent... This boson is so central to the state of physics today, so crucial to our final understanding of the structure of matter, yet so elusive, that I have given it a nickname: the God Particle. Why God Particle? Two reasons. One, the publisher wouldn't let us call it the Goddamn Particle, though that might be a more appropriate title, given its villainous nature and the expense it is causing. And two, there is a connection, of sorts, to another book, a much older one...

— Leon M. Lederman and Dick Teresi, The God Particle: If the Universe is the Answer, What is the Question^[22] p. 22

Lederman asks whether the Higgs boson was added just to perplex and confound those seeking knowledge of the universe, and whether physicists will be confounded by it as recounted in that story, or ultimately surmount the challenge and understand "how beautiful is the universe [God has] made".^[192]

Other proposals

A renaming competition by British newspaper The Guardian in 2009 resulted in their science correspondent choosing the name "the champagne bottle boson" as the best submission: "The bottom of a champagne bottle is in the shape of the Higgs potential and is often used as an illustration in physics lectures. So it's not an embarrassingly grandiose name, it is memorable, and [it] has some physics connection too."^[193] The name Higgson was suggested as well, in an opinion piece in the Institute of Physics' online publication physicsworld.com.^[194]

Media explanations and analogies

There has been considerable public discussion of analogies and explanations for the Higgs particle and how the field creates mass,^[195][196] 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^[197] and articles in newspapers worldwide.

Photograph of light passing through a dispersive prism: the rainbow effect arises because photons are not all affected to the same degree by the dispersive material of the prism.

An educational collaboration involving an LHC physicist and a High School Teachers at CERN educator suggests that dispersion of light – responsible for the rainbow and dispersive prism – is a useful analogy for the Higgs field's symmetry breaking and mass-causing effect.^[198]

Symmetry breaking in optics	In a vacuum, light of all colours (or photons of all wavelengths) travels at the same velocity, a symmetrical situation. In some substances such as glass, water or air, this symmetry is broken (See: Photons in matter). The result is that light of different wavelengths appears to have different velocities (as seen from outside).
Symmetry breaking in particle physics	In 'naive' gauge theories, gauge bosons and other fundamental particles are all massless – also a symmetrical situation. In the presence of the Higgs field this symmetry is broken. The result is that particles of different types will have different masses.

Matt Strassler uses electric fields as an analogy:^[199]

Some particles interact with the Higgs field while others don’t. Those particles that feel the Higgs field act as if they have mass. Something similar happens in an electric field – charged objects are pulled around and neutral objects can sail through unaffected. So you can think of the Higgs search as an attempt to make waves in the Higgs field [create Higgs bosons] to prove it’s really there.

A similar explanation was offered by The Guardian:^[200]

The Higgs boson is essentially a ripple in a field said to have emerged at the birth of the universe and to span the cosmos to this day ... The particle is crucial however: it is the smoking gun, the evidence required to show the theory is right.

The Higgs field's effect on particles was famously described by physicist David Miller as akin to a room full of political party workers spread evenly throughout a room: the crowd gravitates to and slows down famous people but does not slow down others.^{[Note 18]} He also drew attention to well-known effects in solid state physics where an electron's effective mass can be much greater than usual in the presence of a crystal lattice.^[201]

Analogies based on drag effects, including analogies of "syrup" or "molasses" are also well known, but can be somewhat misleading since they may be understood (incorrectly) as saying that the Higgs field simply resists some particles' motion but not others' – a simple resistive effect could also conflict with Newton's third law.^[203]

Recognition and awards

There has been considerable discussion 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 3 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 ^[204]
• Nobel Prize in Physics (1999) – 't Hooft and Veltman, for elucidating the quantum structure of electroweak interactions in physics ^[205]
• Nobel Prize in Physics (2008) – Nambu (shared), for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics ^[54]
• 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 ^[78] (for the 1964 papers described above)
• Wolf Prize (2004) – Englert, Brout, and Higgs
• 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 ^[206]

Additionally Physical Review Letters' 50-year review (2008) recognised the 1964 PRL symmetry breaking papers and Weinberg's 1967 paper A model of Leptons (the most cited paper in particle physics, as of 2012) "milestone Letters".^[76]

Following reported observation of the Higgs-like particle in July 2012, several Indian media outlets reported on the supposed neglect of credit to Indian physicist Satyendra Nath Bose after whose work in the 1920s the class of particles "bosons" is named^[207][208] (although physicists have described Bose's connection to the discovery as tenuous).^[209]

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:

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

(1)

while the field has charge +1/2 under the weak hypercharge U(1) symmetry (in the convention where the electric charge, Q, the weak isospin, I₃, and the weak hypercharge, Y, are related by Q = I₃ + Y).^[210]

The potential for the Higgs field, plotted as function of $\phi ^{0}$ and $\phi ^{3}$. It has a Mexican-hat or champagne-bottle profile at the ground.

The Higgs part of the Lagrangian is^[210]

${\mathcal {L}}_{H}=\left|\left(\partial _{\mu }-igW_{\mu }^{a}\tau ^{a}-i{\frac {g'}{2}}B_{\mu }\right)\phi \right|^{2}+\mu ^{2}\phi ^{\dagger }\phi -\lambda (\phi ^{\dagger }\phi )^{2},$

(2)

where $W_{\mu }^{a}$ and $B_{\mu }$ are the gauge bosons of the SU(2) and U(1) symmetries, $g$ and $g'$ their respective coupling constants, $\tau ^{a}=\sigma ^{a}/2$ (where $\sigma ^{a}$ are the Pauli matrices) a complete set generators of the SU(2) symmetry, and $\lambda >0$ and $\mu ^{2}>0$, so that the ground state breaks the SU(2) symmetry (see figure). The ground state of the Higgs field (the bottom of the potential) is degenerate with different ground states related to each other by a SU(2) gauge transformation. It is always possible to pick a gauge such that in the ground state $\phi ^{1}=\phi ^{2}=\phi ^{3}=0$. The expectation value of $\phi ^{0}$ in the ground state (the vacuum expectation value or vev) is then ${\displaystyle \langle \phi ^{0}\rangle ={\tfrac {v}{\sqrt {2}}}}$, where $v={\tfrac {|\mu |}{\sqrt {\lambda }}}$. The measured value of this parameter is ~246 GeV/c².^[102] It has units of mass, and is the only free parameter of the Standard Model that is not a dimensionless number. Quadratic terms in $W_{\mu }$ and $B_{\mu }$ arise, which give masses to the W and Z bosons:^[210]

$M_{W}={\frac {v|g|}{2}},$

(3)

$M_{Z}={\frac {v{\sqrt {g^{2}+{g'}^{2}}}}{2}},$

(4)

with their ratio determining the Weinberg angle, $\cos \theta _{W}={\frac {M_{W}}{M_{Z}}}={\frac {|g|}{\sqrt {g^{2}+{g'}^{2}}}}$, and leave a massless U(1) photon, $\gamma$.

The quarks and the leptons interact with the Higgs field through Yukawa interaction terms:

${\begin{aligned}{\mathcal {L}}_{Y}=&-\lambda _{u}^{ij}{\frac {\phi ^{0}-i\phi ^{3}}{\sqrt {2}}}{\overline {u}}_{L}^{i}u_{R}^{j}+\lambda _{u}^{ij}{\frac {\phi ^{1}-i\phi ^{2}}{\sqrt {2}}}{\overline {d}}_{L}^{i}u_{R}^{j}\\&-\lambda _{d}^{ij}{\frac {\phi ^{0}+i\phi ^{3}}{\sqrt {2}}}{\overline {d}}_{L}^{i}d_{R}^{j}-\lambda _{d}^{ij}{\frac {\phi ^{1}+i\phi ^{2}}{\sqrt {2}}}{\overline {u}}_{L}^{i}d_{R}^{j}\\&-\lambda _{e}^{ij}{\frac {\phi ^{0}+i\phi ^{3}}{\sqrt {2}}}{\overline {e}}_{L}^{i}e_{R}^{j}-\lambda _{e}^{ij}{\frac {\phi ^{1}+i\phi ^{2}}{\sqrt {2}}}{\overline {\nu }}_{L}^{i}e_{R}^{j}+{\textrm {h.c.}},\end{aligned}}$

(5)

where $(d,u,e,\nu )_{L,R}^{i}$ are left-handed and right-handed quarks and leptons of the ith generation, $\lambda _{u,d,e}^{ij}$are matrices of Yukawa couplings where h.c. denotes the hermitian conjugate terms. In the symmetry breaking ground state, only the terms containing $\phi ^{0}$ remain, giving rise to mass terms for the fermions. Rotating the quark and lepton fields to the basis where the matrices of Yukawa couplings are diagonal, one gets

${\mathcal {L}}_{m}=-m_{u}^{i}{\overline {u}}_{L}^{i}u_{R}^{i}-m_{d}^{i}{\overline {d}}_{L}^{i}d_{R}^{i}-m_{e}^{i}{\overline {e}}_{L}^{i}e_{R}^{i}+{\textrm {h.c.}},$

(6)

where the masses of the fermions are $m_{u,d,e}^{i}=\lambda _{u,d,e}^{i}v/{\sqrt {2}}$, and $\lambda _{u,d,e}^{i}$ denote the eigenvalues of the Yukawa matrices.^[210]

See also

Standard Model

• Quantum gauge theory
• History of quantum field theory
• Introduction to quantum mechanics
• Noncommutative standard model and noncommutative geometry generally
• Standard Model (mathematical formulation) (and especially Standard Model fields overview and mass terms and the Higgs mechanism)
• W and Z bosons

Other

• Bose–Einstein statistics
• Dalitz plot
• Higgs boson in fiction
• Quantum triviality
• ZZ diboson
• Scalar boson
• Stueckelberg action
• Tachyonic field

Notes

1. Note that such events also occur due to other processes. Detection involves a statistically significant excess of such events at specific energies.
2. In the Standard Model, the total decay width of a Higgs boson with a mass of 126 GeV/c² is predicted to be 4.21×10⁻³ GeV.^[5] The mean lifetime is given by $\tau =\hbar /\Gamma$.
3. It is quite common for a law of physics to hold true only if certain assumptions held true or only under certain conditions. For example, Newton's laws of motion apply only at speeds where relativistic effects are negligible; and laws related to conductivity, gases, and classical physics (as opposed to quantum mechanics) may apply only within certain ranges of size, temperature, pressure, or other conditions.
4. Electroweak symmetry is broken by the Higgs field in its lowest energy state, called its "ground state". At high energy levels this does not happen, and the gauge bosons of the weak force would therefore be expected to be massless.
5. The range of a force is inversely proportional to the mass of the particles transmitting it.^[21] In the Standard Model, forces are carried by virtual particles. These particles' movement and interactions with each other are limited by the energy–time uncertainty principle. As a result, the more massive a single virtual particle is, the greater its energy, and therefore the shorter the distance it can travel. A particle's mass therefore determines the maximum distance at which it can interact with other particles and on any force it mediates. By the same token, the reverse is also true: massless and near-massless particles can carry long distance forces. (See also: Compton wavelength and Static forces and virtual-particle exchange) Since experiments have shown that the weak force acts over only a very short range, this implies that there must exist massive gauge bosons. And indeed, their masses have since been confirmed by measurement.
6. By the 1960s, many had already started to see gauge theories as failing to explain particle physics because theorists had been unable to solve the mass problem or even explain how gauge theory could provide a solution. So the idea that the Standard Model – which relied on a Higgs field, not yet proved to exist – could be fundamentally incorrect. Against this, once the model was developed around 1972, no better theory existed, and its predictions and solutions were so accurate, that it became the preferred theory anyway. It then became crucial to science, to know whether it was correct.
7. The success of the Higgs-based electroweak theory and Standard Model is illustrated by their predictions of the mass of two particles later detected: the W boson (predicted mass: 80.390 ± 0.018 GeV, experimental measurement: 80.387 ± 0.019 GeV), and the Z boson (predicted mass: 91.1874 ± 0.0021, experimental measurement: 91.1876 ± 0.0021 GeV). The existence of the Z boson was itself another prediction. Other accurate predictions included the weak neutral current, the gluon, and the top and charm quarks, all later proven to exist as the theory said.
8. For example, Huffington Post/Reuters^[36] and others^[37][38]
9. The bubble's effects would be expected to propagate across the universe at the speed of light from wherever it occurred. However space is vast – with even the nearest galaxy being over 2 million lightyears from us, and others being many billions of lightyears distant, so the effect of such an event would be unlikely to arise here for billions of years after first occurring.^[40][41]
10. If the Standard Model is valid, then the particles and forces we observe in our universe exist as they do, because of underlying quantum fields. Quantum fields can have states of differing stability, including 'stable', 'unstable' and 'metastable' states (the latter remain stable unless sufficiently perturbed). If a more stable vacuum state were able to arise, then existing particles and forces would no longer arise as they presently do. Different particles or forces would arise from (and be shaped by) whatever new quantum states arose. The world we know depends upon these particles and forces, so if this happened, everything around us, from subatomic particles to galaxies, and all fundamental forces, would be reconstituted into new fundamental particles and forces and structures. The universe would potentially lose all of its present structures and become inhabited by new ones (depending upon the exact states involved) based upon the same quantum fields.
11. Goldstone's theorem only applies to gauges having manifest Lorentz covariance, a condition that took time to become questioned. But the process of quantisation requires a gauge to be fixed and at this point it becomes possible to choose a gauge such as the 'radiation' gauge which is not invariant over time, so that these problems can be avoided. According to Bernstein (1974, p.8):

    "the "radiation gauge" condition ∇⋅A(x) = 0 is clearly noncovariant, which means that if we wish to maintain transversality of the photon in all Lorentz frames, the photon field A_μ(x) cannot transform like a four-vector. This is no catastrophe, since the photon field is not an observable, and one can readily show that the S-matrix elements, which are observable have covariant structures .... in gauge theories one might arrange things so that one had a symmetry breakdown because of the noninvariance of the vacuum; but, because the Goldstone et al. proof breaks down, the zero mass Goldstone mesons need not appear." [Emphasis in original]

    Bernstein (1974) contains an accessible and comprehensive background and review of this area, see external links
12. A field with the "Mexican hat" potential $V(\phi )=\mu ^{2}\phi ^{2}+\lambda \phi ^{4}$ and $\mu ^{2}<0$ has a minimum not at zero but at some non-zero value $\phi _{0}$. By expressing the action in terms of the field ${\tilde {\phi }}=\phi -\phi _{0}$ (where $\phi _{0}$ is a constant independent of position), we find the Yukawa term has a component $g\phi _{0}{\bar {\psi }}\psi$. Since both g and $\phi _{0}$ are constants, this looks exactly like the mass term for a fermion of mass $g\phi _{0}$. The field ${\tilde {\phi }}$ is then the Higgs field.
13. In the Standard Model, the mass term arising from the Dirac Lagrangian for any fermion $\psi$ is $-m{\bar {\psi }}\psi$. This is not invariant under the electroweak symmetry, as can be seen by writing $\psi$ in terms of left and right handed components:

    $-m{\bar {\psi }}\psi \;=\;-m({\bar {\psi }}_{L}\psi _{R}+{\bar {\psi }}_{R}\psi _{L})$

    i.e., contributions from ${\bar {\psi }}_{L}\psi _{L}$ and ${\bar {\psi }}_{R}\psi _{R}$ terms do not appear. We see that the mass-generating interaction is achieved by constant flipping of particle chirality. Since the spin-half particles have no right/left helicity pair with the same SU(2) and SU(3) representation and the same weak hypercharge, then assuming these gauge charges are conserved in the vacuum, none of the spin-half particles could ever swap helicity. Therefore, in the absence of some other cause, all fermions must be massless.
14. The example is based on the production rate at the LHC operating at 7 TeV. The total cross-section for producing a Higgs boson at the LHC is about 10 picobarn,^[98] while the total cross-section for a proton–proton collision is 110 millibarn.^[108]
15. Just before LEP's shut down, some events that hinted at a Higgs were observed, but it was not judged significant enough to extend its run and delay construction of the LHC.
16. Announced in articles in Time,^[145] Forbes,^[146] Slate,^[147] NPR,^[148] and others.^[149]
17. Other names have included: the "Anderson–Higgs" mechanism,^[161] "Higgs–Kibble" mechanism (by Abdus Salam)^[80] and "ABEGHHK'tH" mechanism [for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble and 't Hooft] (by Peter Higgs).^[80]
18. In Miller's analogy, the Higgs field is compared to political party workers spread evenly throughout a room. There will be some people (in Miller's example an anonymous person) who pass through the crowd with ease, paralleling the interaction between the field and particles that do not interact with it, such as massless photons. There will be other people (in Miller's example the British prime minister) who would find their progress being continually slowed by the swarm of admirers crowding around, paralleling the interaction for particles that do interact with the field and by doing so, acquire a finite mass.^[201][202]

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167. Peskin, M. (July 2012). "40 Years of the Higgs Boson" (PDF). Presentation at SSI 2012. Standford/SSI 2012. pp. 3–5. Retrieved 21 January 2013. quoting Lee's ICHEP 1972 presentation at Fermilab: "...which is known as the Higgs mechanism..." and "Lee's locution" – his footnoted explanation of this shorthand
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170. Cho, A (2012-09-14). "Particle physics. Why the 'Higgs'?" (PDF). Science. 337 (6100): 1287. doi:10.1126/science.337.6100.1287. PMID 22984044. Retrieved 12 February 2013. Lee ... apparently used the term 'Higgs Boson' as early as 1966... but what may have made the term stick is a seminal paper Steven Weinberg...published in 1967...Weinberg acknowledged the mix-up in an essay in the New York Review of Books in May 2012. (See also original article in New York Review of Books^[171] and Frank Close's 2011 book The Infinity Puzzle^[80]:372 (Book extract) which identified the error)
171. Weinberg, Steven (2012-05-10). "The Crisis of Big Science". The New York Review of Books. footnote 1. Retrieved 12 February 2013.
172. Examples of early papers using the term "Higgs boson" include 'A phenomenological profile of the Higgs boson' (Ellis, Gaillard and Nanopoulos, 1976), 'Weak interaction theory and neutral currents' (Bjorken, 1977), and 'Mass of the Higgs boson' (Wienberg, received 1975)
173. Leon Lederman; Dick Teresi (2006). The God Particle: If the Universe Is the Answer, What Is the Question?. Houghton Mifflin Harcourt. ISBN 0-547-52462-5.
174. Kelly Dickerson (September 8, 2014). "Stephen Hawking Says 'God Particle' Could Wipe Out the Universe". livescience.com.
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178. Aschenbach, Joy (1993-12-05). "No Resurrection in Sight for Moribund Super Collider : Science: Global financial partnerships could be the only way to salvage such a project. Some feel that Congress delivered a fatal blow". Los Angeles Times. Retrieved 16 January 2013. 'We have to keep the momentum and optimism and start thinking about international collaboration,' said Leon M. Lederman, the Nobel Prize-winning physicist who was the architect of the super collider plan
179. "A Supercompetition For Illinois". Chicago Tribune. 1986-10-31. Retrieved 16 January 2013. The SSC, proposed by the U.S. Department of Energy in 1983, is a mind-bending project ... this gigantic laboratory ... this titanic project
180. Diaz, Jesus (2012-12-15). "This Is [The] World's Largest Super Collider That Never Was". Gizmodo. Retrieved 16 January 2013. ...this titanic complex...
181. Abbott, Charles (June 1987). "Illinois Issues journal, June 1987". p. 18. Lederman, who considers himself an unofficial propagandist for the super collider, said the SSC could reverse the physics brain drain in which bright young physicists have left America to work in Europe and elsewhere.
182. Kevles, Dan. "Good-bye to the SSC: On the Life and Death of the Superconducting Super Collider" (PDF). California Institute of Technology: "Engineering & Science". 58 no. 2 (Winter 1995): 16–25. Retrieved 16 January 2013. Lederman, one of the principal spokesmen for the SSC, was an accomplished high-energy experimentalist who had made Nobel Prize-winning contributions to the development of the Standard Model during the 1960s (although the prize itself did not come until 1988). He was a fixture at congressional hearings on the collider, an unbridled advocate of its merits.
183. Calder, Nigel (2005). Magic Universe:A Grand Tour of Modern Science. pp. 369–370. ISBN 978-0-19-162235-9. The possibility that the next big machine would create the Higgs became a carrot to dangle in front of funding agencies and politicians. A prominent American physicist, Leon lederman [sic], advertised the Higgs as The God Particle in the title of a book published in 1993 ...Lederman was involved in a campaign to persuade the US government to continue funding the Superconducting Super Collider... the ink was not dry on Lederman's book before the US Congress decided to write off the billions of dollars already spent
184. Lederman, Leon (1993). The God Particle If the Universe Is the Answer, What Is the Question? (PDF). Dell Publishing. p. Chapter 2, Page 2. ISBN 0-385-31211-3. Retrieved 30 July 2015.
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191. Cole, K. (2000-12-14). "One Thing Is Perfectly Clear: Nothingness Is Perfect". Los Angeles Times. p. 'Science File'. Retrieved 17 January 2013. Consider the early universe–a state of pure, perfect nothingness; a formless fog of undifferentiated stuff ... 'perfect symmetry' ... What shattered this primordial perfection? One likely culprit is the so-called Higgs field ... Physicist Leon Lederman compares the way the Higgs operates to the biblical story of Babel [whose citizens] all spoke the same language ... Like God, says Lederman, the Higgs differentiated the perfect sameness, confusing everyone (physicists included) ... [Nobel Prizewinner Richard] Feynman wondered why the universe we live in was so obviously askew ... Perhaps, he speculated, total perfection would have been unacceptable to God. And so, just as God shattered the perfection of Babel, 'God made the laws only nearly symmetrical'
192. Lederman, p. 22 et seq:

     "Something we cannot yet detect and which, one might say, has been put there to test and confuse us ... The issue is whether physicists will be confounded by this puzzle or whether, in contrast to the unhappy Babylonians, we will continue to build the tower and, as Einstein put it, 'know the mind of God'."

     "And the Lord said, Behold the people are un-confounding my confounding. And the Lord sighed and said, Go to, let us go down, and there give them the God Particle so that they may see how beautiful is the universe I have made".

193. Sample, Ian (12 June 2009). "Higgs competition: Crack open the bubbly, the God particle is dead". The Guardian. London. Retrieved 4 May 2010.
194. Gordon, Fraser (5 July 2012). "Introducing the higgson". physicsworld.com. Retrieved 25 August 2012.
195. Wolchover, Natalie (2012-07-03). "Higgs Boson Explained: How 'God Particle' Gives Things Mass". Huffington Post. Retrieved 21 January 2013.
196. Oliver, Laura (2012-07-04). "Higgs boson: how would you explain it to a seven-year-old?". The Guardian. London. Retrieved 21 January 2013.
197. Zimmer, Ben (2012-07-15). "Higgs boson metaphors as clear as molasses". The Boston Globe. Retrieved 21 January 2013.
198. "The Higgs particle: an analogy for Physics classroom (section)". www.lhc-closer.es (a collaboration website of LHCb physicist Xabier Vidal and High School Teachers at CERN educator Ramon Manzano). Retrieved 2013-01-09.
199. Flam, Faye (2012-07-12). "Finally – A Higgs Boson Story Anyone Can Understand". The Philadelphia Inquirer (philly.com). Retrieved 21 January 2013.
200. Sample, Ian (2011-04-28). "How will we know when the Higgs particle has been detected?". The Guardian. London. Retrieved 21 January 2013.
201. Miller, David. "A quasi-political Explanation of the Higgs Boson; for Mr Waldegrave, UK Science Minister 1993". Retrieved 10 July 2012.
202. Kathryn Grim. "Ten things you may not know about the Higgs boson". Symmetry Magazine. Retrieved 10 July 2012.
203. David Goldberg, Associate Professor of Physics, Drexel University (2010-10-17). "What's the Matter with the Higgs Boson?". io9.com "Ask a physicist". Retrieved 21 January 2013.
204. The Nobel Prize in Physics 1979 – official Nobel Prize website.
205. The Nobel Prize in Physics 1999 – official Nobel Prize website.
206. – official Nobel Prize website.
207. Daigle, Katy (10 July 2012). "India: Enough about Higgs, let's discuss the boson". AP News. Retrieved 10 July 2012.
208. Bal, Hartosh Singh (19 September 2012). "The Bose in the Boson". New York Times. Retrieved 21 September 2012.
209. Alikhan, Anvar (16 July 2012). "The Spark In A Crowded Field". Outlook India. Retrieved 10 July 2012.
210. Peskin & Schroeder 1995, Chapter 20

Further reading

• Nambu, Yoichiro; Jona-Lasinio, Giovanni (1961). "Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity". Physical Review. 122: 345–358. Bibcode:1961PhRv..122..345N. doi:10.1103/PhysRev.122.345.
• Klein, Abraham; Lee, Benjamin W. (1964). "Does Spontaneous Breakdown of Symmetry Imply Zero-Mass Particles?". Physical Review Letters. 12 (10): 266–268. Bibcode:1964PhRvL..12..266K. doi:10.1103/PhysRevLett.12.266.
• Anderson, Philip W. (1963). "Plasmons, Gauge Invariance, and Mass". Physical Review. 130: 439–442. Bibcode:1963PhRv..130..439A. doi:10.1103/PhysRev.130.439.
• Gilbert, Walter (1964). "Broken Symmetries and Massless Particles". Physical Review Letters. 12 (25): 713–714. Bibcode:1964PhRvL..12..713G. doi:10.1103/PhysRevLett.12.713.
• Higgs, Peter (1964). "Broken Symmetries, Massless Particles and Gauge Fields". Physics Letters. 12 (2): 132–133. Bibcode:1964PhL....12..132H. doi:10.1016/0031-9163(64)91136-9.
• Guralnik, Gerald S.; Hagen, C.R.; Kibble, Tom W.B. (1968). "Broken Symmetries and the Goldstone Theorem". In R.L. Cool and R.E. Marshak. Advances in Physics, Vol. 2. Interscience Publishers. pp. 567–708. ISBN 978-0-470-17057-1.

• The Higgs Boson discovery Karl Jakobs, Chris Seez Scholarpedia 10(9):32413. doi:10.4249/scholarpedia.32413
• Sean Carroll (2013). The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World. Dutton. ISBN 978-0-14-218030-3.

External links

Popular science, mass media, and general coverage

• Hunting the Higgs Boson at C.M.S. Experiment, at CERN
• The Higgs Boson by the CERN exploratorium.
• Particle Fever, documentary film about the search for the Higgs Boson.
• The Atom Smashers, documentary film about the search for the Higgs Boson at Fermilab.
• Collected Articles at the Guardian
• Video (04:38) – CERN Announcement on 4 July 2012, of the discovery of a particle which is suspected will be a Higgs Boson.
• Video1 (07:44) + Video2 (07:44) – Higgs Boson Explained by CERN Physicist, Dr. Daniel Whiteson (16 June 2011).
• HowStuffWorks: What exactly is the Higgs Boson?
• Carroll, Sean. "Higgs Boson with Sean Carroll". Sixty Symbols. University of Nottingham.
• Overbye, Dennis (2013-03-05). "Chasing the Higgs Boson: How 2 teams of rivals at CERN searched for physics' most elusive particle". New York Times Science pages. Retrieved 22 July 2013. - New York Times "behind the scenes" style article on the Higgs' search at ATLAS and CMS
• The story of the Higgs theory by the authors of the PRL papers and others closely associated:
  • Higgs, Peter (2010). "My Life as a Boson" (PDF). Talk given at Kings College, London, Nov 24 2010. Retrieved 17 January 2013. (also: )
  • Kibble, Tom (2009). "Englert–Brout–Higgs–Guralnik–Hagen–Kibble mechanism (history)". Scholarpedia. Retrieved 17 January 2013. (also: )
  • Guralnik, Gerald (2009). "The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles". International Journal of Modern Physics A. 24 (14): 2601–2627. arXiv:0907.3466. Bibcode:2009IJMPA..24.2601G. doi:10.1142/S0217751X09045431., Guralnik, Gerald (2011). "The Beginnings of Spontaneous Symmetry Breaking in Particle Physics. Proceedings of the DPF-2011 Conference, Providence, RI, 8–13 August 2011". arXiv:1110.2253v1 [physics.hist-ph]., and Guralnik, Gerald (2013). "Heretical Ideas that Provided the Cornerstone for the Standard Model of Particle Physics". SPG MITTEILUNGEN March 2013, No. 39, (p. 14), and Talk at Brown University about the 1964 PRL papers
  • Philip Anderson (not one of the PRL authors) on symmetry breaking in superconductivity and its migration into particle physics and the PRL papers
• Cartoon about the search
• Cham, Jorge (2014-02-19). "True Tales from the Road: The Higgs Boson Re-Explained". Piled Higher and Deeper. Retrieved 2014-02-25.

Significant papers and other

• Observation of a new particle in the search for the Standard Model Higgs Boson with the ATLAS detector at the LHC
• Observation of a new Boson at a mass of 125 GeV with the CMS experiment at the LHC
• Particle Data Group: Review of searches for Higgs Bosons.
• 2001, a spacetime odyssey: proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics : Michigan, USA, 21–25 May 2001, (p.86 – 88), ed. Michael J. Duff, James T. Liu, ISBN 978-981-238-231-3, containing Higgs' story of the Higgs Boson.
• A.A. Migdal & A.M. Polyakov, Spontaneous Breakdown of Strong Interaction Symmetry and the Absence of Massless Particles, Sov.J.-JETP 24,91 (1966) – example of a 1966 Russian paper on the subject.

Introductions to the field

• Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that (Bernstein, Reviews of Modern Physics Jan 1974) – an introduction of 47 pages covering the development, history and mathematics of Higgs theories from around 1950 to 1974.