Higgs boson
One possible signature of a Higgs boson from a simulated collision between two protons. It decays almost immediately into two jets of hadrons and two electrons, visible as lines.[Note 1]
Composition | Elementary particle
Statistics | Bosonic
Status | Tentatively observed;? a boson "consistent with" the Higgs boson was observed in July 2012,[1] and its behaviour (up to November 2012) remains consistent with a Standard Model Higgs boson, but it may take considerable time to prove conclusively whether or not this particle is in fact a Higgs boson.[2][3]
Symbol | H0
Theorised | R. Brout, F. Englert, P. Higgs, G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble (1964)
Discovered | Tentatively announced 4 July 2012 (see above), by the ATLAS and CMS teams at the Large Hadron Collider
Mass | 125.3 ? 0.4 (stat) ? 0.5 (sys) GeV/c2,[4] 126.0 ? 0.4 (stat) ? 0.4 (sys) GeV/c2[5]
Mean lifetime | 1.56×10−22 s[Note 2] (predicted in the Standard Model)
Electric charge | 0
Color charge | 0
Spin | 0

The Higgs boson or Higgs particle is an elementary particle in the Standard Model of particle physics. It is the last unobserved particle of that model and has been predicted to exist since the 1960s. It may have been detected at the Large Hadron Collider in 2012. Proving its existence would settle questions about the existence of the extremely significant[6] Higgs field?the simplest[7] of several proposed causes for electroweak symmetry breaking and the means by which elementary particles acquire mass.[Note 3]

According to the current leading theory, particles acquire mass by interacting with the Higgs field which exists and has non-zero strength everywhere?even in otherwise empty space. If this is true, a matching particle known as a Higgs boson?the smallest possible excitation of the Higgs field?should also exist and would prove the theory essentially correct. Consequently the Higgs boson has been the target of a long search in particle physics, and its importance is such that the answer eventually required the construction of one of the most expensive and complex experimental facilities to date, the Large Hadron Collider.[6]

The Higgs boson is named after Peter Higgs, who?along with R. Brout and F. Englert, and with G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble?proposed the mechanism that suggested such a particle in 1964?[9][10][11] and was the only one who emphasised the existence of the particle and calculated some of its properties.[12] In mainstream media it is often referred to as the "God particle", after the title of Leon Lederman's book on the topic (1993). However, the epithet is strongly disliked by many physicists, who regard it as inappropriate sensationalism.[13][14]

In the Standard Model, the Higgs particle is a boson, a type of particle that allows multiple identical particles to exist in the same place in the same quantum state. It has no spin, electric charge, or colour charge. It is also very unstable, decaying into other particles almost immediately. Some extensions of the Standard Model predict the existence of more than one kind of Higgs boson.

On 4 July 2012, the CMS and the ATLAS experimental teams at the Large Hadron Collider independently announced that they each confirmed the formal discovery of a previously unknown boson of mass between 125 and 127 GeV/c2, whose behaviour so far has been consistent with a Standard Model Higgs boson. If confirmed, proof of the Higgs field and evidence of its properties is likely to greatly affect human understanding of the universe, validate the final unconfirmed part of the Standard Model as essentially correct, indicate which of several current particle physics theories are more likely correct, and open up "new" physics beyond current theories.[15] If the Higgs boson were shown not to exist, other alternative sources for the Higgs mechanism would need to be considered.

## Useful background and terminology[edit]

See also: Introduction to the Higgs field

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Standard model of particle physics
Large Hadron Collider tunnel at CERN
Background Particle physics Standard Model Quantum field theory Gauge theory Spontaneous symmetry breaking Higgs mechanism
Constituents Electroweak interaction Quantum chromodynamics CKM matrix
Limitations Strong CP problem Hierarchy problem Neutrino oscillations See also: Physics beyond the Standard Model
Scientists Rutherford · Thomson · Chadwick · Bose · Sudarshan · Koshiba · Davis, Jr. · Anderson · Fermi · Dirac · Feynman · Rubbia · Gell-Mann · Kendall · Taylor · Friedman · Powell · P. W. Anderson · Glashow · Meer · Cowan · Nambu · Chamberlain · Cabibbo · Schwartz · Perl · Majorana · Weinberg · Lee · Ward · Salam · Kobayashi · Maskawa · Yang · Yukawa · 't Hooft · Veltman · Gross · Politzer · Wilczek · Cronin · Fitch · Vleck · Higgs · Englert · Brout · Hagen · Guralnik · Kibble · Ting · Richter

In particle physics, elementary particles and forces give rise to the world around us. Physicists explain the behaviour of these particles and how they interact using the Standard Model?a widely accepted and "remarkably" accurate[16]:22 framework based on quantum fields and symmetries believed to explain most of the world we see around us.[17] Initially, when this model was being developed, it seemed that the mathematics behind the model, which was satisfactory in areas already tested, would forbid elementary particles from having any mass, which showed clearly that these initial models were incomplete. In 1964 three groups of physicists almost simultaneously released papers describing how masses could be given to these particles, using an approach known as spontaneous symmetry breaking. Symmetry breaking allows the necessary particles to acquire a mass, without explicitly breaking the symmetries that prevent the theory from going haywire. This idea became known as the Higgs mechanism, and later experiments confirmed that such a mechanism does exist?but they could not show exactly how it happens.

While there are several symmetries in nature that are spontaneously broken through a form of the Higgs mechanism, in the context of the Standard Model the term "Higgs mechanism" almost always signifies the mechanism responsible for symmetry breaking of the electroweak field. Electroweak symmetry breaking (EWSB) itself is considered proven, and believed responsible for the mass of fundamental particles and also the differences between the electromagnetic and weak nuclear interactions which cease to be unified below a very high temperature of about 1015?K. But the exact cause has been exceedingly difficult to prove; the lack of adequate data in this area has also limited the development and testing of more advanced ideas.

The leading and simplest theory is that a particular kind of "field" (known as the Higgs field) exists, which in contrast to the more familiar gravitational field and electromagnetic field has constant strength everywhere. This kind of field was shown in the 1960s to be theoretically capable of producing a Higgs mechanism in nature, and particles interacting with this field would acquire mass. During the 1960s and 1970s the Standard Model of physics was developed on this basis, and it included a prediction and requirement that for these things to be true, there had to be an undiscovered fundamental particle as the counterpart of this field. This particle would be the Higgs boson (or "Higgs particle"), the last unobserved particle of the Standard Model. The Higgs boson's existence would confirm this part of the Standard Model and allow further development, while its non-existence would confirm that other theories are needed instead.

Useful terminology

- A Higgs mechanism in particle physics is a term that describes some kinds of local symmetry breaking mechanisms.[18] A Higgs mechanism of some kind is believed responsible for elementary particles being able to gain mass without affecting parts of current physics theory believed approximately correct. (More exactly, it shows how gauge-dependent expressions for some particles' mass can arise even in a gauge-invariant theory). In the Standard Model the term almost always refers to electroweak symmetry breaking (EWSB) which is responsible for the mass of some gauge bosons (a kind of elementary particle). The existence of some kind of Higgs mechanism is believed proven, although there are a number of ways it could happen and physicists have not yet determined which of these takes place in nature.

- The Higgs field is the current preferred theory of how the Higgs mechanism and symmetry breaking are believed to happen for the electroweak field. If correct, then a field exists throughout space that is responsible for the Higgs mechanism and the resultant electroweak symmetry breaking. The field ? if it exists ? would have a related particle, which would be a previously unknown type of boson. That field can be proven to exist and its properties studied, by finding and examining the boson and studying its properties. The Standard Model allows for extensions where the details of the Higgs field and number of related Higgs bosons can differ. If the Higgs field does not exist then other approaches (known as "Higgsless" models) could explain how the Higgs mechanism arises, and these would be examined instead.

- The Higgs boson is the massive and fleetingly short-lived boson associated with a Higgs field, and also the Higgs field's smallest possible excitation, or quantum. If the preferred theory is correct, then this massive boson will exist, and can be detected in experiments and tested to confirm whether it is actually a Higgs boson. If the Higgs boson is shown to exist, this would prove the Higgs field exists, which in turn will confirm how the Higgs mechanism takes place. Further studies would still be needed to test which model among the Standard Model and its extensions best describes the experimental findings. At present as of 2012, a particle has been detected but not yet tested fully to show if it is a Higgs boson.

## History[edit]

See also: 1964 PRL symmetry breaking papers and Higgs mechanism

?? 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.

Particle physicists study matter made from fundamental particles whose interactions are mediated by exchange particles known 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.[citation needed] 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.[19] Goldstone's theorem, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions,[20] since it appeared to show that zero-mass particles would have to also exist that were "simply not seen".[21] According to Guralnik, physicists had "no understanding" how these problems could be overcome.[21]

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] [19]

The Higgs mechanism is a process by which vector bosons can get rest mass without explicitly breaking gauge invariance.[22][23] The proposal for such a spontaneous symmetry breaking mechanism originally[citation needed] was suggested in 1962 by Philip Warren Anderson[24] and developed into a full relativistic model, independently and almost simultaneously, by three groups of physicists: by Fran?ois Englert and Robert Brout in August 1964;[9] by Peter Higgs in October 1964;[10] and by Gerald Guralnik, C. R. Hagen, and Tom Kibble (GHK) in November 1964.[11] Properties of the model were further considered by Guralnik in 1965,[25] by Higgs in 1966 [26], by Kibble in 1967 [27], and further by GHK in 1967.[28] The original 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.[29] [22][23] In 1967, Steven Weinberg[30] and Abdus Salam[31] 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[32], 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.[33]

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 fundamentally flawed, because they were not renormalizable. This rapidly changed when Gerard 't Hooft and Tini Veltman explicitly demonstrated the renormalizability of spontaneously broken gauge theories, after which the ideas were quickly absorbed in the mainstream.[33]

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2010 Sakurai Prize awarded for 1964 Higgs Boson theory work Prospective Nobel Prize for Higgs boson work disputed (2010)

The three papers written in 1964 were each recognised as milestone papers during Physical Review Letters's 50th anniversary celebration.[29] Their six authors were also awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work.[34] (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.[35] ) 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.[10] [11] Higgs's subsequent 1966 paper showed the decay mechanism of the boson; only a massive boson can decay and the decays can prove the mechanism.[citation needed]

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".[10] In the paper by GHK the boson is massless and decoupled from the massive states.[11] 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.[36][37]

In addition to explaining how mass is acquired by vector bosons, the Higgs mechanism also predicts the ratio between the W boson and Z boson masses as well as their couplings with each other and with the Standard Model quarks and leptons.[citation needed] Subsequently, many of these predictions have been verified by precise measurements performed at the LEP and the SLC colliders, thus overwhelmingly confirming that some kind of Higgs mechanism does take place in nature,[38] but the exact manner by which it happens has not yet been discovered.[citation needed] The results of searching for the Higgs boson are expected to provide evidence about how this is realized in nature.[citation needed]

## Theoretical properties[edit]

Main article: Higgs mechanism
Summary of interactions between particles described by the Standard Model.
A one-loop Feynman diagram of the first-order correction to the Higgs mass. The Higgs boson couples strongly to the top quark so it may, if heavy enough, decay into top?anti-top quark pairs.

### Theoretical need for the Higgs[edit]

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 4]) 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 un-noticed borderline case hidden in the mathematics of Goldstone's theorem, that under certain conditions it might theoretically be possible for a symmetry to be broken without disrupting gauge invariance and without any new massless particles or forces, and having "sensible" (renormalisable) results mathematically: this became known as the Higgs mechanism.

The Standard Model hypothesizes a field which is responsible for this effect, called the Higgs field (symbol: ), 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.[39] Its quantum would be a scalar boson, known as the Higgs boson.[40]

In layman?s terms 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.[41][42] 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 him/her, paralleling the interaction for particles that do interact with the field and by doing so, acquire a finite mass.

### Properties of the Standard Model Higgs[edit]

In the Standard Model, the Higgs field 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-polarization 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.[43] Since the Higgs field is a scalar field (meaning it does not transform under Lorentz transformations), 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.[44]

The Minimal Standard Model does not predict the mass of the Higgs boson.[45] 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).[46] Many theorists expect new physics beyond the Standard Model to emerge at the TeV-scale, based on unsatisfactory properties of the Standard Model.[47] 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.[48]

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[38]). 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.[49]

### Production[edit]

Feynman diagrams for Higgs production
Gluon fusion | Higgs Strahlung
Vector boson fusion | Top fusion

If Higgs particle theories are correct, 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,[50][51][52] 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 5] 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.[50][51]
- 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.[50][51][52]
- 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.[50][52]
- 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 anti-quark from each pair can then combine to form a Higgs particle.[50][51]

### Decay[edit]

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.[54] 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 Seconds.[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.[56] 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.[55] The second most common fermion decay at that mass is a tau?antitau pair, which happens only about 6% of the time.[55]

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.[55] 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),[55] 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.[56] 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.[55] 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.[55] 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.[56]

### Alternative models[edit]

Main article: Alternatives to the Standard Model Higgs

The Minimal Standard Model as described above contains the simplest possible model for the Higgs mechanism with just one Higgs field. However, it also is possible to have an extended Higgs sector with additional doublets or triplets. 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?. The key method to distinguish different variations of the 2HDM models and the minimal SM involves their coupling and the branching ratios of the Higgs decays. The Type-I model has one Higgs doublet coupling 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 doesn't couple to either fermions (fermiophobic) or gauge bosons (gauge-phobic). In the 2HDM of Type-II, one Higgs doublet only couples to up-type quarks, while the other only couples to down-type quarks.[57]

Many extensions to the Standard Model, including supersymmetry (SUSY), often contain an extended Higgs sector. Supersymmetric models predict relations between the Higgs-boson masses and the masses of the gauge bosons, and can accommodate a neutral Higgs boson with a mass around 125 GeV/c2. The heavily researched Minimal Supersymmetric Standard Model (MSSM) belongs to the class of models with a Type-II two-Higgs-doublet sector and could be ruled out by the observation of a Higgs belonging to a Type-I 2HDM.[citation needed]

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[disambiguation needed].[58][59]

## Experimental search[edit]

Main article: Search for the Higgs boson

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 5] 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 at 2012) produced by the collisions.[60] 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.[60][61][62]

### Search prior to 4 July 2012[edit]

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 6] This implied that if the Higgs boson were to exist it would have to be heavier than 114.4 GeV/c2.[63]

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. 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?140 GeV/c2.[64]

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 27km 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 x 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.[65][66][67]

Data collection at the LHC finally commenced in March 2010.[68] 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 115?130 GeV. In addition, both experiments were starting to see hints of a new particle that could be the Higgs with a mass around 125 GeV.[69][70] It was therefore widely expected around the end of 2011, that the LHC would provide sufficient data to either exclude or confirm the finding of the Standard Model Higgs boson by the end of 2012, when their 2012 collision data (with slightly higher 8?TeV collision energy) had been examined.[71][72]

### Discovery of new boson[edit]

??
Feynman diagrams showing the cleanest channels associated with the Low-Mass, ~125GeV, Higgs Candidate observed by the 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 5-sigma.[73][74] The analysis of additional vector boson fusion channels brought the CMS significance to 4.9-sigma.[73][74]

On 22 June 2012 CERN announced an upcoming seminar covering tentative findings for 2012,[75][76] and shortly afterwards 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.[77][78] Speculation escalated to a "fevered" pitch when reports emerged that Peter Higgs, who proposed the particle, was to be attending the seminar.[79][80] On 4 July 2012 both of the CERN experiments announced they had independently made the same discovery:[81] CMS of a previously unknown boson with mass 125.3 ? 0.6 GeV/c2[73][74] and ATLAS of a boson with mass 126.5 GeV/c2.[82][83] Using the combined analysis of two interaction types (known as 'channels'), both experiments reached a local significance of 5-sigma?or less than a 1 in one million chance of error. When additional channels were taken into account, the CMS significance was reduced to 4.9-sigma.[73]

The two teams had been working 'blinded' from each other for some time[when?], meaning they did not discuss their results with each other, providing additional certainty that any common finding was genuine validation of a particle.[60] This level of evidence, confirmed independently by two separate teams and experiments, meets the formal level of proof required to announce a confirmed discovery. CERN have been cautious, and stated only that the new particle is "consistent with" the Higgs boson, but scientists have not yet positively identified it as being the Higgs boson, pending further data collection and analysis.[1]

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 being due to random background effects) and mass 126.0 ? 0.4 (stat) ? 0.4 (sys) GeV/c2,[5] and CMS improved the significance to 5-sigma and mass 125.3 ? 0.4 (stat) ? 0.5 (sys) GeV/c2.[4]

### Subsequent developments[edit]

As of 2012, observations are consistent with the observed particle being the Standard Model Higgs boson. The particle decays into at least some of the predicted channels. Moreover, the production rates and branching ratios for the observed channels match the predictions by the Standard Model within the experimental uncertainties. However, the experimental uncertainties currently still leave room for alternative explanations. It is therefore too early to conclude that the found particle is indeed the Standard Model Higgs.[56] To allow more opportunity for data collection, the LHC's proposed 2013?14 upgrade was postponed by 7 weeks in 2012.[84]

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.[85] Physicist Matt Strassler highlights "considerable" evidence that the new particle is not a pseudoscalar negative parity particle (a 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.[2] However some kinds of extensions to the Standard Model would also show very similar results;[3] based on other particles that are still being understood long after their discovery, it could take many years to know for sure, and decades to understand the particle that has been found.[2][85]

## In mainstream media[edit]

The Higgs boson is often referred to as the "God particle" by individuals outside the scientific community, after the title of Nobel Physics prizewinner Leon Lederman's popular science book on particle physics, The God Particle: If the Universe Is the Answer, What Is the Question? (1993)[16] While use of this term may have contributed to increased media interest,[86] many scientists dislike it,[13][14][87] since it is sensational and overstates the particle's importance. Its discovery would still leave unanswered questions about the unification of quantum chromodynamics, the electroweak interaction, and gravity, as well as the ultimate origin of the universe. Higgs, an atheist himself, is displeased that the Higgs particle is nicknamed the "God particle",[88] because the term "might offend people who are religious".[89]

In explaining his choice of nickname for the particle, Lederman begins by recounting the long human search for knowledge, commenting:

  "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..." [16]:22

Lederman whimsically asks whether the Higgs boson was added just to make matters more difficult for those seeking knowledge of the universe and whether physicists will be confounded by it as in the biblical story of Babel, or ultimately surmount the challenge and understand "how beautiful is the universe [God has] made".[90]

A renaming competition conducted by the science correspondent for the British Guardian newspaper chose the name "the champagne bottle boson" as the best from among their submissions: "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."[91] The alternative name of higgson was suggested in an opinion piece in "physicsworld.com", an online publication of the IOP.[92]

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,[93][94] although physicists have described Bose's connection to the discovery as tenuous.[95]

## Technical aspects and discussion[edit]

See also: Standard Model (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:

while the field has charge 1/2 under the weak hypercharge U(1) symmetry.[96]

The potential for the Higgs field, plotted as function of and . It has a Mexican-hat or champagne-bottle profile at the ground.

The Higgs part of the Lagrangian is[96]

where and are the gauge bosons of the SU(2) and U(1) symmetries, and their respective coupling constants, (where are the Pauli matrices) a complete set generators of the SU(2) symmetry, and and , 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 . The expectation value of in the ground state (the vacuum expectation value or vev) is then , where . The measured value of this parameter is ~246 GeV/c2.[56] It has units of mass, and is the only free parameter of the Standard Model that is not a dimensionless number. Quadratic terms in and arise, which give masses to the W and Z bosons:[96]

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

where are left-handed and right-handed quarks and leptons of the ith generation, are matrices of Yukawa couplings where h.c. denotes the hermitian conjugate terms. In the symmetry breaking ground state, only the terms containing 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

where the masses of the fermions are , and denote the eigenvalues of the Yukawa matrices.[96]

## See also[edit]

Standard Model

| Book: Particles of the Standard Model

- Symmetry (physics)
- Quantum field
- Introduction to gauge theory and Quantum gauge theory
- Yang-Mills theory?precursor to the Standard Model in which the 'mass problem' was noticed

  - Also related: Yang-Mills existence and mass gap, Yang-Mills-Higgs equations

- Hierarchy problem (and especially the section on the Higgs Mass)
- Standard Model (mathematical formulation) (and especially Standard Model fields overview and mass terms and the Higgs mechanism)
- Noncommutative standard model and noncommutative geometry generally
- Physics beyond the Standard Model

Other

- Dalitz plot
- Higgs boson in fiction
- Quantum triviality
- ZZ diboson
- Bose?Einstein statistics

## Notes[edit]

1. ^ Note that such events also occur due to other processes. Detection involves a statistically significant excess of such events at specific energies.
2. ^ a b 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.[55] The mean lifetime is given by .
3. ^ The Higgs field?if it exists?is not responsible for all mass, but only for the masses of elementary particles. For example, only about 1% of the mass of baryons (composite particles such as the proton and neutron) is due to the Higgs mechanism acting to produce the mass of quarks. The rest is due to the mass added by the kinetic energies of quarks and the energies of (massless) gluons of the strong interaction inside the baryons.[8]
4. ^ The Standard Model draws heavily upon gauge-invariant mathematics. 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.
5. ^ 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,[50] while the total cross-section for a proton?proton collision is 110 millibarn.[53]
6. ^ 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.

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## Further reading[edit]

- G.S. Guralnik, C.R. Hagen and T.W.B. Kibble (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 978-0470170571.
- P. Higgs (1964). "Broken Symmetries, Massless Particles and Gauge Fields". Physics Letters 12 (2): 132. Bibcode:1964PhL....12..132H. doi:10.1016/0031-9163(64)91136-9.
- Y. Nambu and G. Jona-Lasinio (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.
- P.W. Anderson (1963). "Plasmons, Gauge Invariance, and Mass". Physical Review 130: 439. Bibcode:1963PhRv..130..439A. doi:10.1103/PhysRev.130.439.
- A. Klein and B.W. Lee (1964). "Does Spontaneous Breakdown of Symmetry Imply Zero-Mass Particles?". Physical Review Letters 12 (10): 266. Bibcode:1964PhRvL..12..266K. doi:10.1103/PhysRevLett.12.266.
- W. Gilbert (1964). "Broken Symmetries and Massless Particles". Physical Review Letters 12 (25): 713. Bibcode:1964PhRvL..12..713G. doi:10.1103/PhysRevLett.12.713.

## External links[edit]

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- Video (04:38)?? CERN Announcement of Higgs Boson Discovery (4 July 2012).
- Video1 (07:44) Video2 (07:44)?? Higgs Boson Explained by CERN Physicist, Dr. Daniel Whiteson (16 June 2011).
- Hunting the Higgs boson at C.M.S. Experiment, at CERN
- The Higgs boson" by the CERN exploratorium.
- Particle Data Group: Review of searches for Higgs bosons.
- The Atom Smashers, a documentary film about the search for the Higgs boson at Fermilab.
- 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.
- Collected Articles at the Guardian
- 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

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