• [55][n] 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.

• One known problem was that gauge invariant approaches, including non-abelian models such as Yang–Mills theory (1954), which held great promise for unified theories, also seemed
  to predict known massive particles as massless.

• Some theories suggest that a fundamental scalar field might be responsible for this phenomenon; the Higgs field is such a field, and its existence has led to papers analysing
  whether it could also be the inflaton responsible for this exponential expansion of the universe during the Big Bang.

• History Theorisation[edit] See also: 1964 PRL symmetry breaking papers, Higgs mechanism, and History of quantum field theory Particle physicists study matter made from fundamental
  particles whose interactions are mediated by exchange particles – gauge bosons – acting as force carriers.

• If the Higgs field did exist, then it would be unlike any other known fundamental field, but it also was possible that these key ideas, or even the entire Standard Model,
  were somehow incorrect.

• [29][j] [30][31] Since then, the particle has been shown to behave, interact, and decay in many of the ways predicted for Higgs particles by the Standard Model, as well as
  having even parity and zero spin,[7][8] two fundamental attributes of a Higgs boson.

• [63][64] Initially, the mathematical theory behind spontaneous symmetry breaking was conceived and published within particle physics by Yoichiro Nambu in 1960[65] (and somewhat
  anticipated by Ernst Stueckelberg in 1938[66]), and the concept that such a mechanism could offer a possible solution for the “mass problem” was originally suggested in 1962 by Philip Anderson, who had previously written papers on broken symmetry
  and its outcomes in superconductivity.

• [21] Goldstone’s theorem, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions,[61] since it appeared to show that zero-mass
  particles known as Goldstone bosons would also have to exist that simply were “not seen”.

• [l] If the masses of the Higgs boson and top quark are known more precisely, and the Standard Model provides an accurate description of particle physics up to extreme energies
  of the Planck scale, then it is possible to calculate whether the vacuum is stable or merely long-lived.

• [39] In Higgs-based theories, the property of “mass” is a manifestation of potential energy transferred to fundamental particles when they interact (“couple”) with the Higgs
  field, which had contained that mass in the form of energy.

• 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, with exceptional accuracy, predicted several other particles discovered during the following years.

• More studies are needed to verify with higher precision that the discovered particle has all of the properties predicted or whether, as described by some theories, multiple
  Higgs bosons exist.

• The problem of gauge boson mass[edit] Quantum field theories based on gauge invariance had been used with great success in understanding the electromagnetic and strong forces,
  but by around 1960, all attempts to create a gauge invariant theory for the weak force (and its combination with the electromagnetic force, known together as the electroweak interaction) had consistently failed.

• They showed that the conditions for electroweak symmetry would be “broken” if an unusual type of field existed throughout the universe, and indeed, there would be no Goldstone
  bosons and some existing bosons would acquire mass.

• [88] 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”.

• [i] The existence of the Higgs field became the last unverified part of the Standard Model of particle physics, and for several decades was considered “the central problem
  in particle physics”.

• [h] Furthermore, it was later realised that the same field would also explain, in a different way, why other fundamental constituents of matter (including electrons and quarks)
  have mass.

• The field required for this to happen (which was purely hypothetical at the time) became known as the Higgs field (after Peter Higgs, one of the researchers) and the mechanism
  by which it led to symmetry breaking, known as the Higgs mechanism.

• [82][84] 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.

• [15][16] Composition: Elementary particle; Statistics: Bosonic; 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: 125.11 ± 0.11 GeV/c2[1]; Decays into: Bottom–antibottom pair (observed)[5][6], Two W bosons (observed), Two gluons (predicted), Tau–antitau pair (observed), Two Z bosons (observed), Two photons (observed),
  Two leptons and a photon (Dalitz decay via virtual photon) (tentatively observed at sigma 3.2 (1 in 1000) significance) [4], Muon–antimuon pair (predicted), Various other decays (predicted); Electric charge: 0 e; Colour charge: 0; Spin: 0[7][8];
  Weak isospin: −1/2; Weak hypercharge: +1; Parity: +1[7][8] Introduction The Standard Model[edit] Physicists explain the fundamental particles and forces of our universe in terms of the Standard Model – a widely accepted framework based on
  quantum field theory that predicts almost all known particles and forces aside from gravity with great accuracy.

• By the 1980s, the question of whether the Higgs field existed, and therefore whether the entire Standard Model was correct, had come to be regarded as one of the most important
  unanswered questions in particle physics.

• The importance of the Higgs boson largely is 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.

• The Higgs discovery, as well as the many measured collisions occurring at the LHC, provide physicists a sensitive tool to search their data for any evidence that the Standard
  Model seems to fail, and could provide considerable evidence guiding researchers into future theoretical developments.

• [77] The original three 1964 papers demonstrated that when a gauge theory is combined with an additional charged scalar field that spontaneously breaks the symmetry, the gauge
  bosons may consistently acquire a finite mass.

• Such theories are highly tentative and face significant problems related to unitarity, but may be viable if combined with additional features such as large non-minimal coupling,
  a Brans–Dicke scalar, or other “new” physics, and they have received treatments suggesting that Higgs inflation models are still of interest theoretically.

• [67] Anderson concluded in his 1963 paper on the Yang–Mills theory, that “considering the superconducting analog… [t]hese two types of bosons seem capable of canceling each
  other out… leaving finite mass bosons”),[68][23] and in March 1964, Abraham Klein and Benjamin Lee showed that Goldstone’s theorem could be avoided this way in at least some non-relativistic cases, and speculated it might be possible in
  truly relativistic cases.

• In this kind of speculation, the single unified field of a Grand Unified Theory is identified as (or modelled upon) the Higgs field, and it is through successive symmetry
  breakings of the Higgs field, or some similar field, at phase transitions that the presently known forces and fields of the universe arise.

• The “central problem”[edit] There was not yet any direct evidence that the Higgs field existed, but even without direct proof, the accuracy of its predictions led scientists
  to believe the theory might be true.

• [11][12] Conversely, proof that the Higgs field and boson did not exist would have also been significant.

• 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.

• (All fundamental particles known at the time[c] should be massless at very high energies, but fully explaining how some particles gain mass at lower energies had been extremely
  difficult.)

• [54] 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[55][m]
  – 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.

• [32] By March 2013, the existence of the Higgs boson was confirmed, and therefore, the concept of some type of Higgs field throughout space is strongly supported.

• The 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,[28] in an attempt to create Higgs bosons and other particles for observation and study.

• Higgs field[edit] To allow symmetry breaking, the Standard Model includes a field of the kind needed to “break” electroweak symmetry and give particles their correct mass.

• Similarly, measuring the speed of light in a vacuum seems to give the identical result, whatever the location in time and space, and whatever the local gravitational field.

• [59] The relationship (if any) between the Higgs field and the presently observed vacuum energy density of the universe has also come under scientific study.

• For many decades, scientists had no way to determine whether the Higgs field existed because the technology needed for its detection did not exist at that time.

• As observed, the present vacuum energy density is extremely close to zero, but the energy densities predicted from the Higgs field, supersymmetry, and other current theories
  are typically many orders of magnitude larger.

• In 1962 physicist Philip Anderson, an expert in condensed matter physics, observed that symmetry breaking played a role in superconductivity, and suggested it could also be
  part of the answer to the problem of gauge invariance in particle physics.

• Its “Mexican hat-shaped” potential leads it to take a nonzero value everywhere (including otherwise empty space), which breaks the weak isospin symmetry of the electroweak
  interaction and, via the Higgs mechanism, gives mass to many particles.

• [22] Higgs mechanism[edit] Main articles: Higgs mechanism and Standard Model Following the 1963[23] and early 1964[22] papers, three groups of researchers independently developed
  these theories more completely, in what became known as the 1964 PRL symmetry breaking papers.

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

• [41][42] Cosmology[edit] Inflaton[edit] 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”).

• A key feature of the necessary field is that it would take less energy for the field to have a non-zero value than a zero value, unlike all other known fields, therefore,
  the Higgs field has a non-zero value (or vacuum expectation) everywhere.

• As experimental means to measure the field’s behaviours and interactions are developed, this fundamental field may be better understood.

• [f][27]: 22  One crucial prediction was that a matching particle, called the “Higgs boson”, should also exist.

• [29][31][7] The presence of the field, now confirmed by experimental investigation, explains why some fundamental particles have mass, despite the symmetries controlling their
  interactions, implying that they should be massless.

• It was the first proposal capable of showing how the weak force gauge bosons could have mass despite their governing symmetry, within a gauge invariant theory.

• [82][p] At first, these seminal papers on spontaneous breaking of gauge symmetries were 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.

• [g] When the weak force bosons acquire mass, this affects the distance they can freely travel, which becomes very small, also matching experimental findings.

• 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.

• [20] Further, many promising solutions seemed to require the existence of extra particles known as Goldstone bosons.

• This field, which became known as the “Higgs Field”, was hypothesized to exist throughout space, and to break some symmetry laws of the electroweak interaction, triggering
  the Higgs mechanism.

• [60]: 150  However, attempts to produce quantum field models for two of the four known fundamental forces – the electromagnetic force and the weak nuclear force – and then
  to unify these interactions, were still unsuccessful.

• [17][18] Gauge invariant theories and symmetries[edit] “It is only slightly overstating the case to say that physics is the study of symmetry” – Philip Anderson, Nobel Prize
  Physics[19] Gauge invariant theories are theories which have a useful feature; some kinds of changes to the value of certain items do not make any difference to the outcomes or the measurements we make.

• It was, therefore, several decades before the first evidence of the Higgs boson could be found.

• [43] Vacuum energy and the cosmological constant[edit] Further information: Zero-point energy and Vacuum state 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.

• It suggests that other hypothetical scalar fields suggested by other theories, from the inflaton to quintessence, could perhaps exist as well.

• This also means it is the first elementary scalar particle discovered in nature.

• 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.

• If these ideas were correct, a particle known as a scalar boson should also exist (with certain properties).

• [51][52][53] A Higgs mass of seems to be extremely close to the boundary for stability, but a definitive answer requires much more precise measurements of the pole mass of
  the top quark.

• This meant either gauge invariance was an incorrect approach, or something unknown was giving the weak force’s W and Z bosons their mass, and doing it in a way that did not
  create Goldstone bosons.

• Nature of the universe, and its possible fates[edit] Diagram showing the Higgs boson and top quark masses, which could indicate whether our universe is stable, or a long-lived
  ‘bubble’.

• As of 2018, in-depth research shows the particle continuing to behave in line with predictions for the Standard Model Higgs boson.

• Proving the existence of the Higgs boson would prove whether the Higgs field existed, and therefore finally prove whether the Standard Model’s explanation was correct.

• This shape means that below extremely high energies of about 159.5±1.5 GeV[36] such as those seen during the first picosecond of the Big Bang, the Higgs field in its ground
  state takes less energy to have a nonzero vacuum expectation (value) than a zero value.

• The problem was symmetry requirements for these two forces incorrectly predicted the weak force’s gauge bosons (W and Z) would have zero mass.

 

Works Cited

[‘1. Note that such events also occur due to other processes. Detection involves a statistically significant excess of such events at specific energies.
2. ^ Jump up to:a b In the Standard Model, the total decay width of a Higgs boson with a mass
of 125 GeV/c2 is predicted to be 4.07×10−3 GeV.[2] The mean lifetime is given by .
3. ^ In Higgs-based theories, the Higgs boson itself should be an exception, being massive even at high energies.
4. ^ In physics, it is possible for a law to hold
true only if certain assumptions hold true, or when certain conditions are met. For example, Newton’s laws of motion only apply 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.
5. ^ In theoretical particle physics, one says that particle A “absorbs” particle B when they always act simultaneously, and
their combined effect cannot be separated using observables: Although the mathematical description of the process may have two parts, A and B, the observed preconditions and their outcomes are indistinguishable from the interaction of what appears
to effectively be a single particle (which usually is given another, slightly different name; for example one of the combinations of the theoretical W3 and B0 electroweak bosons is called the Z boson).
6. ^ Jump up to:a b c 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/c2, experimental measurement: 80.387±0.019 GeV/c2), and the Z boson (predicted mass:
91.1874±0.0021 GeV/c2, experimental measurement: 91.1876±0.0021 GeV/c2). 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.
7. ^ 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 be expected to become massless above those energy levels.
8. ^ The range of
a force is inversely proportional to the mass of the particles transmitting it.[24]
In the Standard Model, forces are carried by virtual particles. The movement and interactions of these particles 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.
Since experiments have shown that the weak force acts over only a very short range, this implies
that massive gauge bosons must exist, and indeed, their masses have since been confirmed by measurement.
(See also: Compton wavelength and static forces and virtual-particle exchange)
9. ^ 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, was not unreasonable.
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.
10. ^ Discovery press conference, July 2012:
‘As a layman, I would say, I think we have it’, said Rolf-Dieter Heuer, director general of CERN at Wednesday’s seminar announcing the results of
the search for the Higgs boson. But when pressed by journalists afterwards on what exactly ‘it’ was, things got more complicated.
‘We have discovered a boson; now we have to find out what boson it is’
[Q]: ‘If we don’t know the new particle
is a Higgs, what do we know about it?’
[A]: We know it is some kind of boson, says Vivek Sharma of CMS […]
[Q]: ‘are the CERN scientists just being too cautious? What would be enough evidence to call it a Higgs boson?’
[A]: As there could
be many different kinds of Higgs bosons, there’s no straight answer.[29]
[emphasis in original]
11. ^ The statement excludes spin 0 mesons, such as the pion, since they are known to be composites of pairs of spin  1 /2 fermions.
12. ^
For example: The Huffington Post / Reuters,[49] and others.[50]
13. ^ 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 light years from us, and others being many billions of light years distant, so the effect of such an event would be unlikely to arise here for billions of years after first occurring.[55][56]
14. ^ 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.
15. ^ Jump up to:a b 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 not covariant, which means that if we wish to maintain transversality of the photon
in all Lorentz frames, the photon field Aμ(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.
16. ^ A field with the “Mexican hat” potential and has a minimum not at zero but at some non-zero value By expressing the action in terms of
the field (where is a constant independent of position), we find the Yukawa term has a component Since both g and are constants, this looks exactly like the mass term for a fermion of mass . The field is then the Higgs field.
17. ^ Jump up to:a
b 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,[93] while the total cross-section for a proton–proton collision is 110 millibarn.[94]
18. ^
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.
19. ^ Jump up to:a b c ATLAS and CMS only just co-discovered this particle
in July… We will not know after today whether it is a Higgs at all, whether it is a Standard Model Higgs or not, or whether any particular speculative idea… is now excluded… Knowledge about nature does not come easy. We discovered the top quark
in 1995, and we are still learning about its properties today… we will still be learning important things about the Higgs during the coming few decades. We’ve no choice but to be patient. — M. Strassler (2012)[128]
20. ^ In the Standard Model,
the mass term arising from the Dirac Lagrangian for any fermion is . This is not invariant under the electroweak symmetry, as can be seen by writing in terms of left and right handed components:

i.e., contributions from and 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.
21. ^ Goldstone’s theorem also plays a role in such theories.
The connection is technically, when a condensate breaks a symmetry, then the state reached by acting with a symmetry generator on the condensate has the same energy as before. This means that some kinds of oscillation will not involve change of energy.
Oscillations with unchanged energy imply that excitations (particles) associated with the oscillation are massless. Therefore the outcome is that new massless particles should exist, known as Goldstone bosons. Because zero mass gauge bosons always
mediate long range interactions, a new long range force should exist as well.
22. ^ People initially thought of tachyons as particles travelling faster than the speed of light … But we now know that a tachyon indicates an instability in a theory
that contains it. Regrettably for science fiction fans, tachyons are not real physical particles that appear in nature.[160]
23. ^ 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.[171]
24. ^ Other names have included:
 The “Anderson–Higgs” mechanism,[177]
 “Higgs–Kibble” mechanism (by Abdus Salam)[91] and
 “A-B-E-G-H-H-K-‘tH” mechanism [for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble
and ‘t Hooft] (by Peter Higgs).[91]
25. ^ Benjamin W. Lee also uses the Korean language name Lee Whi-soh.
26. ^ Examples of early papers using the term “Higgs boson” include
 Ellis, Gaillard, & Nanopoulos (1976) “A phenomenological profile
of the Higgs boson”.
 Bjorken (1977) “Weak interaction theory and neutral currents”.
 Wienberg (received, 1975) “Mass of the Higgs boson”.
27. ^ Global financial partnerships could be the only way to salvage such a project. Some
feel that Congress delivered a fatal blow.
‘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.[193]
28. ^
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.[217][218]
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(Report). CERN Report 2 (Tables A.1–A.20). Vol. 1201. p. 3084. arXiv:1201.3084. Bibcode:2012arXiv1201.3084L. doi:10.5170/CERN-2012-002. S2CID 119287417.
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from the original on 2 December 2021. Retrieved 21 January 2021.
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be behind many other unexplained “broken symmetries” in the universe as well … In fact, something very much like the Higgs may have been behind the collapse of the symmetry that led to the Big Bang, which created the universe. When the forces first
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to Weinberg’s Nobel Prize winning paper until the work of ‘t Hooft (as explicated by Ben Lee). In 1971 interest in Weinberg’s paper exploded. I had a parallel personal experience: I took a one-year course on weak interactions from Shelly Glashow
in 1970, and he never even mentioned the Weinberg–Salam model or his own contribution Photo credit: https://www.flickr.com/photos/tabor-roeder/14414100710/’]