Candidate Higgs boson events fromcollisions betweenprotons in theLHC. The top event in theCMS experiment shows a decay into twophotons (dashed yellow lines and green towers). The lower event in theATLAS experiment shows a decay into fourmuons (red tracks).[a]
The Higgs field is ascalar field with two neutral and two electrically charged components that form a complexdoublet of theweak isospin SU(2) symmetry. Its "sombrero potential" leads it to take a nonzero value everywhere (including otherwise empty space), whichbreaks theweak isospin symmetry of theelectroweak interaction and, via theHiggs mechanism, gives a rest mass to all massive elementary particles of the Standard Model, including the Higgs boson itself. 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".[14][15]
Both the field and theboson are named after physicistPeter Higgs, who in 1964,along with five other scientists in three teams, proposed theHiggs mechanism, a way forsome particles to acquire mass. 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. If these ideas were correct, a particle known as a scalar boson (with certain properties) should also exist. This particle was called the Higgs boson and could be used to test whether the Higgs field was the correct explanation.
After a40-year search, a subatomic particle with the expected properties was discovered in 2012 by theATLAS andCMS experiments at theLarge Hadron Collider (LHC) atCERN nearGeneva, Switzerland. The new particle was subsequently confirmed to match the expected properties of a Higgs boson. Physicists from two of the three teams,Peter Higgs andFrançois Englert, were awarded theNobel Prize in Physics in 2013 for their theoretical predictions. 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 the media, the Higgs boson has often been called the "God particle" after the 1993 bookThe God Particle by Nobel LaureateLeon M. Lederman. The name has been criticised by physicists,[16][17] including Peter Higgs.[18]
"It is only slightly overstating the case to say that physics is the study of symmetry" –Philip Anderson, Nobel Prize Physics[21]
Gauge-invariant theories are theories with a useful feature, namely that changes to certain quantities make no difference to experimental outcomes. For example, increasing theelectric potential of anelectromagnet by 100 volts does not itself cause any change to themagnetic field that it produces. Similarly, the measuredspeed of light in vacuum remains unchanged, whatever the location in time and space, and whatever the localgravitational field.
In these theories, the gauge is a quantity that can be changed with no resultant effect. This independence of the results from some changes is called gauge invariance, and these changes reflect symmetries of the underlying physics. These symmetries provide constraints on the fundamental forces and particles of the physical world. Gauge invariance is therefore an important property within particle physics theory. The gauge symmetries are closely connected toconservation laws and are described mathematically usinggroup theory. Quantum field theory and the Standard Model are both gauge-invariant theories – meaning that the gauge symmetries allow theoretical derivation of properties of the universe.
Quantum field theories based on gauge invariance had been used with great success in understanding theelectromagnetic andstrong forces, but by around 1960, all attempts to create agauge invariant theory for theweak force (and its combination with the electromagnetic force, known together as theelectroweak interaction) had consistently failed. As a result of these failures, gauge theories began to fall into disrepute. The problem was thatsymmetry requirements for these two forces incorrectly predicted that the weak force's gauge bosons (W and Z) would have zero mass (in the specialized terminology of particle physics, "mass" refers specifically to a particle'srest mass). But experiments showed the W and Z gauge bosons had non-zero (rest) mass.[22]
Further, many promising solutions seemed to require the existence of extra particles known asGoldstone bosons, but evidence suggested these did not exist. This meant that either gauge invariance was an incorrect approach, or something unknown was giving the weak force's W and Z bosons their mass, and doing it in a way that did not imply the existence of Goldstone bosons. By the late 1950s and early 1960s, physicists were at a loss as to how to resolve these issues, or how to create a comprehensive theory for particle physics.
In the late 1950s,Yoichiro Nambu recognised thatspontaneous symmetry breaking, a process whereby a symmetric system becomes asymmetric, could occur under certain conditions.[d] Symmetry breaking is when some variable takes on a value that does not reflect the symmetries that the underlying laws have, such as when the space of all stable configurations possesses a given symmetry but the stable configurations do not individually possess that symmetry.[e] In 1962, physicistPhilip Anderson, an expert incondensed matter physics, observed that symmetry breaking plays a role insuperconductivity, and suggested that it could also be part of the answer to the problem of gauge invariance in particle physics.
Specifically, Anderson suggested that theGoldstone bosons that would result from symmetry breaking might instead, in some circumstances, be "absorbed"[f] by the masslessW and Z bosons. If so, perhaps the Goldstone bosons would not exist, and the W and Z bosons couldgain mass, solving both problems at once. Similar behaviour was already theorised in superconductivity.[23] In 1964, this was shown to be theoretically possible by physicistsAbraham Klein andBenjamin Lee, at least for some limited (non-relativistic) cases.[24]
Following the 1963[25] and early 1964[24] papers, three groups of researchers independently developed these theories more completely, in what became known as the1964 PRL symmetry breaking papers. All three groups reached similar conclusions and for all cases, not just some limited cases. They showed that the conditions for electroweak symmetry would be "broken" if an unusual type offield existed throughout the universe, and indeed, there would be no Goldstone bosons and some existing bosons wouldacquire mass.
The field required for this to happen (which was purely hypothetical at the time) became known as theHiggs field (afterPeter Higgs, one of the researchers) and the mechanism by which it led to symmetry breaking became known as theHiggs mechanism. A key feature of the necessary field is that the field would haveless energy when it had a non-zero value than when it was zero, unlike every other known field; therefore, the Higgs field has a non-zero value (orvacuum expectation) everywhere. This non-zero value could in theory break electroweak symmetry. It was the first proposal that was able to show, within a gauge invariant theory, how the weak force gauge bosons could have mass despite their governing symmetry.
To allow symmetry breaking, the Standard Model includes afield of the kind needed to "break" electroweak symmetry and give particles their correct mass. This field, which became known as the Higgs field, was hypothesized to exist throughout space, and to break some symmetry laws of theelectroweak interaction, triggering the Higgs mechanism. It would therefore cause the W and Z gauge bosons of the weak force to be massive at all temperatures below an extremely high value.[h] When the weak force bosons acquire mass, this affects the distance they can freely travel, which becomes very small, also matching experimental findings.[i] Furthermore, it was later realised that the same field would also explain, in a different way, why other fundamental constituents of matter (includingelectrons andquarks) have mass.
Prior to the discovery of the Higgs Boson, there was no direct evidence that the Higgs field exists, but even without direct evidence, the accuracy of predictions within the Standard Model led scientists to believe the theory might be correct. By the 1980s, the question of whether the Higgs field exists, and whether the entire Standard Model is correct, had come to be regarded as one of the most importantunanswered questions in particle physics. The existence of the Higgs field became the last unverified part of the Standard Model of particle physics, and for several decades was considered "the central problem in particle physics".[14][15]
For many decades, scientists had no way to determine whether the Higgs field exists because the technology needed for its detection did not exist at that time. If the Higgs field did exist, then it would be unlike any other known fundamental field, but it also was possible that these key ideas, or even the entire Standard Model, were somehow incorrect.[j]
The hypothesised Higgs theory made several key predictions.[g][27]: 22 One crucial prediction was that a matchingparticle, called the Higgs boson, should also exist. Proving the existence of the Higgs boson would prove the existence of the Higgs field, and therefore finally prove the Standard Model. Therefore, there was an extensivesearch for the Higgs boson as a way to prove the Higgs field itself exists.[11][12]
Although the Higgs field would exist and be nonzero everywhere, proving its existence was far from easy. In principle, it can be proved to exist by detecting itsexcitations, which manifest as Higgs particles (Higgs bosons), but these are extremely difficult to produce and detect due to the energy required to produce them and their very rare production even if there is sufficient energy available. It was, therefore, several decades before the first evidence of the Higgs boson would be found.Particle colliders, detectors, and computers capable of looking for Higgs bosons took more than 30 years(c. 1980–2010) to develop. The importance of thisfundamental question led to a40-year search, and the construction of one of the world's mostexpensive and complex experimental facility to date,CERN'sLarge Hadron Collider (LHC),[28] 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 between125 and 127 GeV/c2 was announced; physicists suspected that it was the Higgs boson.[29][k][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, including having evenparity and zerospin,[7][8] two fundamental attributes of a Higgs boson. This also means it is the first elementaryscalar particle discovered in nature.[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.[29][31][7] The presence of the field, now confirmed by experimental investigation, explainswhy some fundamental particles have (a rest) mass, despite thesymmetries controlling their interactions implying that they should be "massless". It also resolves several other long-standing problems, such as the reason for the extremely short distance travelled by theweak force bosons, and therefore the weak force's extremely short range. As of 2018, in-depth research shows the particle continuing to behave in line with predictions for the Standard Model's Higgs boson. More studies are needed to verify with higher precision that the discovered particle has all of the properties predicted or whether, as described by some theories, multiple Higgs bosons exist.[33]
The nature and properties of this field are now being investigated further, using more data collected at the LHC.[34]
Various analogies have been used to describe the Higgs field and boson, including analogies with well-known symmetry-breaking effects such as therainbow andprism,electric fields, and ripples on the surface of water.
Other analogies based on the resistance of macroscopic objects moving through media (such as people moving through crowds, or some objects moving throughsyrup ormolasses) are commonly used but misleading, since the Higgs field does not actually resist particles, and the effect of mass is not caused by resistance.
Thesombrero potential of the Higgs field is responsible for some particles gaining mass.
In the Standard Model, theHiggsboson is a massivescalar boson whose mass must be found experimentally. Its mass has been determined to be125.35±0.15 GeV/c2 by CMS (2022)[35] and125.11±0.11 GeV/c2 by ATLAS (2023). It is the only particle that remains massive even at very high energies. It has zerospin, even (positive)parity, noelectric charge, nocolour charge, and itcouples to (interacts with) mass.[13] It is also very unstable,decaying into other particles almost immediately via several possible pathways.
TheHiggs field is ascalar field, with two neutral and two electrically charged components that form a complexdoublet of theweak isospin SU(2) symmetry. Unlike any other known quantum field, it has asombrero potential. This shape means that below extremely high cross-over temperature of159.5±1.5 GeV/kB[36] such asthose seen during the firstpicosecond (10−12 s) of theBig Bang, the Higgs field in itsground state has less energy when it is nonzero, resulting in a nonzerovacuum expectation value. Therefore, in today's universe the Higgs field has a nonzero value everywhere (including in otherwise empty space). This nonzero value in turn breaks the weak isospin SU(2) symmetry of theelectroweak interaction everywhere. (Technically the non-zero expectation value converts theLagrangian'sYukawa coupling terms into mass terms.) When this happens, three components of the Higgs field are "absorbed" by the SU(2) and U(1)gauge bosons (theHiggs mechanism) to become the longitudinal components of the now-massiveW and Z bosons of theweak force. The remaining electrically neutral component either manifests as a Higgs boson, or may couple separately to other particles known asfermions (via Yukawa couplings), causing these toacquire mass as well.[37]
Even though the knowledge of many of the Higgs boson properties has advanced significantly since its discovery, the Higgs boson's self-coupling remains unmeasured. The shape of the Higgs potential in theStandard Model includes both trilinear and quartic self-couplings, which are key to understanding the complete shape of the potential and the nature of the Higgs field and EWSB.Higgs boson pair production offers a direct experimental probe of the self-coupling λ at the electroweak scale.
Evidence for the Higgs field and its properties has been extremely significant for many reasons. The primary importance of the Higgs boson is that it completes the mechanism by which the heavy electroweak bosons acquire mass, and it is fortunate that the mass is such that it is able to be examined using existing experimental technology, as a way to confirm and study the entire Higgs field theory.[11][12] Conversely, evidence that the Higgs field and boson didnot exist within the expected mass range would have also been significant.
The Higgs boson validates theStandard Model mechanism ofmass generation for the weak bosons, and can provide masses to the fermions. As more precise measurements of its properties are made, more advanced extensions may be suggested or excluded. As experimental means to measure the Higgs field behaviour and interactions are developed, this fundamental field may be better understood. If the Higgs boson had not been discovered, the Standard Model would have needed to be modified or superseded.
Related to this, it is a widely held belief among many physicists that there is likely to be "new"physics beyond the Standard Model, and the Standard Model will at some point be extended or superseded. The discovery of the Higgs boson, as well as the many measured collisions occurring at the LHC, provide physicists with a sensitive tool to search their data for any evidence of the failure of the Standard Model, and might provide considerable evidence to guide researchers into future theoretical developments.
Below an extremely high temperature,electroweak symmetry breaking causes theelectroweak interaction to manifest in part as the short-rangedweak force, which is carried by massivegauge bosons. In thehistory of the universe, electroweak symmetry breaking is believed to have happened at about1picosecond (10−12 s) after theBig Bang, when the universe was at a temperature159.5±1.5 GeV/kB.[38] This symmetry breaking is required foratoms and other structures to form, as well as for nuclear reactions in stars, such as theSun. The Higgs field is responsible for this symmetry breaking.
The Higgs field is pivotal ingenerating the masses ofquarks and chargedleptons (through Yukawa coupling) and theW and Z gauge bosons (through the Higgs mechanism), although it was the generation of mass for the weak bosons which is the most significant factor – providing terms in the Standard Model Lagrangian that allow for the generation of fermion masses, was a useful, but less significant by product. The fermion masses must be entered by hand, essentially determining the relative strength of the coupling of the fermion to the Higgs field.
The Higgs field is the only scalar (spin-0) field to be detected; all the other fundamental fields in the Standard Model are spin- 1 /2fermions or spin-1 bosons.[l]According toRolf-Dieter Heuer, director general of CERN when the Higgs boson was discovered, this existence proof of a scalar field is almost as important as the Higgs's role in determining the mass of other particles. It suggests that other hypothetical scalar fields suggested by other theories, from theinflaton toquintessence, could perhaps exist as well.[41][42]
There has been considerable scientific research on possible links between the Higgs field and theinflaton – a hypothetical field suggested as the explanation for theexpansion of space duringthe first fraction of a second of theuniverse (known as the "inflationary epoch"). Some theories suggest that a fundamental scalar field might be responsible for this phenomenon; the Higgs field is such a field, and its existence has led to papers analysing whether it could also be theinflaton responsible for thisexponential expansion of the universe during theBig Bang. Such theories are highly tentative and face significant problems related tounitarity, but may be viable if combined with additional features such as large non-minimal coupling, aBrans–Dicke scalar, or other "new" physics, and they have received treatments suggesting that Higgs inflation models are still of interest theoretically.
Diagram showing the Higgs boson andtop quark masses, which could indicate whether our universe is stable, or along-lived 'bubble'. As of 2012, the 2σ ellipse based onTevatron and LHC data still allows for both possibilities.[43]
In the Standard Model, there exists the possibility that the underlying state of our universe – known as the "vacuum" – islong-lived, but not completely stable. In this scenario, the universe as we know it could effectively be destroyed by collapsing into amore stable vacuum state.[44][45][46][47][48] This was sometimes misreported as the Higgs boson "ending" the universe.[m] If the masses of the Higgs boson andtop quark are known more precisely, and the Standard Model provides an accurate description of particle physics up to extreme energies of thePlanck scale, then it is possible to calculate whether the vacuum is stable or merely long-lived.[51][52][53] A Higgs mass of125–127 GeV/c2 seems to be extremely close to the boundary for stability, but a definitive answer requires much more precise measurements of thepole mass of the top quark.[43] New physics can change this picture.[54]
If measurements of the Higgs boson suggest that our universe lies within afalse vacuum of this kind, then it would imply – more than likely in many billions of years[55][n] – 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 tonucleate.[55][o] It also suggests that the Higgsself-couplingλ and itsβλ function could be very close to zero at the Planck scale, with "intriguing" implications, including theories of gravity and Higgs-based inflation.[43]: 218 [57][58] A future electron–positron collider would be able to provide the precise measurements of the top quark needed for such calculations.[43]
More speculatively, the Higgs field has also been proposed as theenergy of the vacuum, which at the extreme energies of the first moments of theBig 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 aGrand 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, atphase transitions that the presently known forces and fields of the universe arise.[59]
The relationship (if any) between the Higgs field and the presently observedvacuum 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 densities predicted from the Higgs field, supersymmetry, and other current theories are typically many orders of magnitude larger. It is unclear how these should be reconciled. Thiscosmological constant problem remains a majorunanswered problem in physics.
One known problem was thatgauge invariant approaches, includingnon-abelian models such asYang–Mills theory (1954), which held great promise for unified theories, also seemed to predict known massive particles as massless.[23]Goldstone's theorem, relating tocontinuous symmetries within some theories, also appeared to rule out many obvious solutions,[61] since it appeared to show that zero-mass particles known asGoldstone bosons would also have to exist that simply were "not seen".[62] According toGuralnik, physicists had "no understanding" how these problems could be overcome.[62]
Nobel Prize LaureatePeter Higgs in Stockholm, December 2013
Particle physicist and mathematician Peter Woit summarised the state of research at the time:
Yang and Mills work onnon-abelian gauge theory had one huge problem: inperturbation 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 ofconfinement realized inQCD, 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. WhatPhilip Anderson realized and worked out in the summer of 1962 was that, when you haveboth gauge symmetryand spontaneous symmetry breaking, the massless Nambu–Goldstone mode [which gives rise to Goldstone bosons] can combine with the massless gauge field modes [which give rise to massless gauge bosons] to produce a physical massive vector field [gauge bosons with mass]. This is what happens insuperconductivity, a subject about which Anderson was (and is) one of the leading experts.[23][text condensed]
The Higgs mechanism is a process by whichvector bosons can acquirerest masswithoutexplicitly breaking gauge invariance, as a byproduct ofspontaneous symmetry breaking.[63][64] Initially, the mathematical theory behind spontaneous symmetry breaking was conceived and published within particle physics byYoichiro Nambu in 1960[65] (andsomewhat anticipated byErnst 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.[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][25] and in March 1964,Abraham Klein andBenjamin 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.[24]
These approaches were quickly developed into a fullrelativistic model, independently and almost simultaneously, by three groups of physicists: byFrançois Englert andRobert Brout in August 1964;[69] byPeter Higgs in October 1964;[70] and byGerald Guralnik,Carl Hagen, andTom Kibble (GHK) in November 1964.[71] Higgs also wrote a short, but important,[63] response published in September 1964 to an objection byGilbert,[72] which showed that if calculating within the radiation gauge, Goldstone's theorem and Gilbert's objection would become inapplicable.[p] Higgs later described Gilbert's objection as prompting his own paper.[73] Properties of the model were further considered by Guralnik in 1965,[74] by Higgs in 1966,[75] by Kibble in 1967,[76] and further by GHK in 1967.[77] The original three 1964 papers demonstrated that when agauge theory is combined with an additional charged scalar field that spontaneously breaks the symmetry, the gauge bosons may consistently acquire a finite mass.[63][64][78]In 1967,Steven Weinberg[79]andAbdus Salam[80]independently showed how a Higgs mechanism could be used to break the electroweak symmetry ofSheldon Glashow'sunified model for the weak and electromagnetic interactions,[81](itself an extension of work bySchwinger), forming what became theStandard Model of particle physics. Weinberg was the first to observe that this would also provide mass terms for the fermions.[82][q]
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 berenormalised. In 1971–72,Martinus Veltman andGerard 't Hooft proved renormalisation of Yang–Mills was possible in two papers covering massless, and then massive, fields.[82] Their contribution, and the work of others on therenormalisation group – including "substantial" theoretical work by Russian physicistsLudvig Faddeev,Andrei Slavnov,Efim Fradkin, andIgor Tyutin[83] – was eventually "enormously profound and influential",[84] 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[85] and discussed byDavid Politzer in his 2004 Nobel speech.[84] – now the most cited in particle physics[86] – 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.[84] In practice, Politzer states, almost everyone learned of the theory due to physicistBenjamin Lee, who combined the work of Veltman and 't Hooft with insights by others, and popularised the completed theory.[84] In this way, from 1971, interest and acceptance "exploded"[84] and the ideas were quickly absorbed in the mainstream.[82][84]
The resulting electroweak theory and Standard Model haveaccurately predicted (among other things)weak neutral currents,three bosons, thetop andcharm quarks, and with great precision, the mass and other properties of some of these.[g] Many of those involved eventually won Nobel Prizes or other renowned awards. A 1974 paper and comprehensive review inReviews 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",[87] adding that the theory had so far produced accurate answers that accorded with experiment, but it was unknown whether the theory was fundamentally correct.[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".[14][15]
The three papers written in 1964 were each recognised as milestone papers duringPhysical Review Letters's 50th anniversary celebration.[78] Their six authors were also awarded the 2010J. J. Sakurai Prize for Theoretical Particle Physics for this work.[89] (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.[90]) Two of the three PRL papers (by Higgs and by GHK) contained equations for the hypotheticalfield that eventually would become known as the Higgs field and its hypotheticalquantum, the Higgs boson.[70][71] 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 ofscalar andvector bosons".[70] (Frank Close comments that 1960s gauge theorists were focused on the problem of masslessvector bosons, and the implied existence of a massivescalar boson was not seen as important; only Higgs directly addressed it.[91]: 154, 166, 175 ) In the paper by GHK the boson is massless and decoupled from the massive states.[71] 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 masslessGoldstone bosons in the model and to give a complete analysis of the general Higgs mechanism.[62][92] All three reached similar conclusions, despite their very different approaches: Higgs's 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 was avoided.[63][93] Some versions of the theory predicted more than one kind of Higgs fields and bosons, and alternative"Higgsless" models were considered until the discovery of the Higgs boson.
Toproduce Higgs bosons, two beams of particles are accelerated to very high energies and allowed to collide within aparticle detector. Occasionally, although rarely, a Higgs boson will be created fleetingly as part of the collision byproducts. Because the Higgs bosondecays very quickly, particle detectors cannot detect it directly. Instead the detectors register all the decay products (thedecay signature) and from the data the decay process is reconstructed. If the observed decay products match a possible decay process (known as adecay 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),[r]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 thestatistical analysis of two independent particle detectors each indicate that there is less than a one-in-a-million chance that the observed decay signatures are due to just background random Standard Model events – i.e., that the observed number of events is more than fivestandard 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 powerfulparticle accelerator was needed, because Higgs bosons might not be seen in lower-energy experiments. The collider needed to have a highluminosity 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.[96] For the announcement of 4 July 2012, a new collider known as theLarge Hadron Collider was constructed atCERN 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 theLHC Computing Grid, the world's largestcomputing grid (as of 2012), comprising over 170 computing facilities in aworldwide network across 36 countries.[96][97][98]
The first extensive search for the Higgs boson was conducted at theLarge 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.[s]This implied that if the Higgs boson were to exist it would have to be heavier than114.4 GeV/c2.[99]
The search continued atFermilab in the United States, where theTevatron – the collider that discovered thetop 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 theLarge Hadron Collider (LHC) was still under construction and the plannedSuperconducting 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 between147 GeV/c2 and180 GeV/c2. In addition, there was a small (but not significant) excess of events possibly indicating a Higgs boson with a mass between115 GeV/c2 and140 GeV/c2.[100]
TheLarge Hadron Collider atCERN 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 nearGeneva originally inhabited by LEP, it was designed to collide two beams of protons, initially at energies of3.5 TeV per beam (7 TeV total), or almost 3.6 times that of the Tevatron, and upgradeable to2 × 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 themost complicated scientific instruments ever built, its operational readiness was delayed for 14 months by amagnet 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.[101][102][103]
Data collection at the LHC finally commenced in March 2010.[104] By December 2011 the two main particle detectors at the LHC,ATLAS andCMS, had narrowed down the mass range where the Higgs could exist to around116–130 GeV/c2 (ATLAS) and115–127 GeV/c2 (CMS).[105][106] 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,[107] 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 around125 GeV/c2.[107] By around November 2011, the anomalous data at125 GeV/c2 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.[107] On 28 November 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 at125 GeV/c2, and initial preparations commenced in case of a successful finding.[107] While this information was not known publicly at the time, the narrowing of the possible Higgs range to around115–130 GeV/2 and the repeated observation of small but consistent event excesses across multiple channels at both ATLAS and CMS in the124–126 GeV/c2 region (described as "tantalising hints" of around 2–3 sigma) were public knowledge with "a lot of interest".[108] 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.[108][109]
Feynman diagrams showing the cleanest channels associated with the low-mass (~125 GeV/c2) Higgs boson candidate observed byATLAS andCMS at theLHC. The dominant production mechanism at this mass involves twogluons from each proton fusing to aTop-quark Loop, which couples strongly to the Higgs field to produce a Higgs boson.
Left: Diphoton channel: Boson subsequently decays into two gamma ray photons by virtual interaction with aW boson loop ortop quark loop.
Right: The four-lepton "golden channel": Boson emits twoZ bosons, which each decay into twoleptons (electrons, muons).
Experimental analysis of these channels reached a significance of more than fivestandard deviations (sigma) in both experiments.[110][111][112]
On 22 June 2012CERN announced an upcoming seminar covering tentative findings for 2012,[113][114] and shortly afterwards (from around 1 July 2012 according to an analysis of the spreading rumour in social media[115]) 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.[116][117] Speculation escalated to a "fevered" pitch when reports emerged thatPeter Higgs, who proposed the particle, was to be attending the seminar,[118][119] 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).[120]
On 4 July 2012 both of the CERN experiments announced they had independently made the same discovery:[121] CMS of a previously unknown boson with mass125.3±0.6 GeV/c2[122][123] and ATLAS of a boson with mass126.0±0.6 GeV/c2.[124][125] 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 one in three million. When additional channels were taken into account, the CMS significance was reduced to 4.9 sigma.[123]
The two teams had been working 'blinded' from each other from around late 2011 or early 2012,[107] meaning they did not discuss their results with each other, providing additional certainty that any common finding was genuine validation of a particle.[96] 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 mass126.0 ± 0.4 (stat) ± 0.4 (sys) GeV/c2,[125] and CMS improved the significance to 5-sigma and mass125.3 ± 0.4 (stat) ± 0.5 (sys) GeV/c2.[122]
Following the 2012 discovery, it was still unconfirmed whether the125 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.[126] To allow more opportunity for data collection, the LHC's proposed 2012 shutdown and 2013–14 upgrade were postponed by seven weeks into 2013.[127]
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.[128] PhysicistMatt Strassler highlighted "considerable" evidence that the new particle is not apseudoscalar negativeparity 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 withW and Z bosons, absence of "significant new implications" for or againstsupersymmetry, and in general no significant deviations to date from the results expected of a Standard Model Higgs boson.[t] However some kinds of extensions to the Standard Model would also show very similar results;[130] 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.[128][t]
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,[29][31] and scientists did not yet positively say it was the Higgs boson.[131] Despite this, in late 2012, widespread media reports announced (incorrectly) that a Higgs boson had been confirmed during the year.[137]
In January 2013, CERN director-generalRolf-Dieter Heuer stated that based on data analysis to date, an answer could be possible 'towards' mid-2013,[138] and the deputy chair of physics atBrookhaven National Laboratory stated in February 2013 that a "definitive" answer might require "another few years" after thecollider's 2015 restart.[139] 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.[140]
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.[7]
This also makes the particle the first elementaryscalar particle to be discovered in nature.[32]
The following are examples of tests used to confirm that the discovered particle is the Higgs boson:[t][13]
Examining decay patterns. Spin-1 had been ruled out at the time of initial discovery by the observed decay to twophotons (γ γ), leaving spin-0 and spin-2 as remaining candidates.
Spin-0 confirmed.[8][7][141][142] The spin-2 hypothesis is excluded with a confidence level exceeding 99.9%.[142]
Studying the angles at which decay products fly apart. Negative parity was also disfavoured if spin-0 was confirmed.[143]
Even parity tentatively confirmed.[7][141][142] The spin-0 negative parity hypothesis is excluded with a confidence level exceeding 99.9%.[141][8]
Decay channels (outcomes of particle decaying) are as predicted
The Standard Model predicts the decay patterns of a125 GeV/c2 Higgs boson. Are these all being seen, and at the right rates?
Particularly significant, we should observe decays into pairs ofphotons (γ γ),W and Z bosons (W− W+ and Z Z),bottom quarks (b b), andtau leptons (τ−τ+), among the possible outcomes.
b b, γ γ, τ− τ+, W− W+ and Z Z observed. All observed signal strengths are consistent with the Standard Model prediction.[144][34]
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 whichalso couples to mass (W and Z bosons); proving spin-0 alone is insufficient.[13]
Couplings to mass strongly evidenced ("At 95% confidence levelcV is within 15% of the standard model valuecV = 1").[13]
Higher energy results remain consistent
After theLHC's 2015 restart at the higher energy of 13 TeV, searches for multiple Higgs particles (as predicted in some theories) and tests targeting other versions of particle theory continued. These higher energy results must continue to give results consistent with Higgs theories.
Analysis of collisions up to July 2017 do not show deviations from the Standard Model, with experimental precisions better than results at lower energies.[34]
Coupling strength to Higgs boson in (top) and ratio to the standard model prediction (bottom) derived from cross section and branching ratio data. In theκ framework[145] the couplings are and for the vector bosons V (=Z,W) and for the fermions F ( =t, b, τ (μ not confirmed as 2022 but there is evidence)) respectively, where the masses and thevacuum expectation value ( the absolute coupling strength).[146]
In July 2017, CERN confirmed that all measurements still agree with the predictions of the Standard Model, and called the discovered particle simply "the Higgs boson".[34] As of 2019, theLarge Hadron Collider has continued to produce findings that confirm the 2013 understanding of the Higgs field and particle.[147][148]
The LHC's experimental work since restarting in 2015 has included probing the Higgs field and boson to a greater level of detail, and confirming whether less common predictions were correct. In particular, exploration since 2015 has provided strong evidence of the predicted direct decay intofermions such as pairs ofbottom quarks (3.6 σ) – described as an "important milestone" in understanding its short lifetime and other rare decays – and also to confirm decay into pairs oftau leptons (5.9 σ). This was described by CERN as being "of paramount importance to establishing the coupling of the Higgs boson to leptons and represents an important step towards measuring its couplings to third generation fermions, the very heavy copies of the electrons and quarks, whose role in nature is a profound mystery".[34] Published results as of 19 March 2018 at 13 TeV for ATLAS and CMS had their measurements of the Higgs mass at124.98±0.28 GeV/c2 and125.26±0.21 GeV/c2 respectively.
In July 2018, the ATLAS and CMS experiments reported observing the Higgs boson decay into a pair of bottom quarks, which makes up approximately 60% of all of its decays.[149][150][151]
"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 "sombrero 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 theStandard Model, partly due to its success in other areas of fundamental physics such aselectromagnetism and thestrong interaction (quantum chromodynamics). However, beforeSheldon Glashow extended theelectroweak unification models in 1961, there were great difficulties in developing gauge theories for theweak nuclear force or a possible unifiedelectroweak interaction.Fermions with a mass term would violate gauge symmetry and therefore cannot be gauge invariant. (This can be seen by examining theDirac Lagrangian for a fermion in terms of left and right handed components; we find none of the spin-half particles could ever fliphelicity as required for mass, so they must be massless.[u])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 thatnone of the standard model fermionsor bosons could "begin" with mass as an inbuilt property except by abandoning gauge invariance. If gauge invariance were to be retained, then these particles had to be acquiring their mass by some other mechanism or interaction.
Additionally, solutions based on spontaneous symmetry breaking appeared to fail, seemingly an inevitable result ofGoldstone's theorem. Because there is no potential energy cost to moving around the complex plane's "circular valley" responsible for spontaneous symmetry breaking, the resulting quantum excitation is pure kinetic energy, and therefore a massless boson ("Goldstone boson"), which in turn implies a new long range force. But no new long range forces or massless particles were detected either. So whatever was giving these particles their mass had to not "break" gauge invariance as the basis for other parts of the theories where it worked well,and had to not require or predict unexpected massless particles or long-range forces which did not actually seem to exist in nature.
A solution to all of these overlapping problems came from the discovery of a previously unnoticed borderline case hidden in the mathematics of Goldstone's theorem,[p]that under certain conditions itmight theoretically be possible for a symmetry to be brokenwithout disrupting gauge invariance andwithout any new massless particles or forces, and having "sensible" (renormalisable) results mathematically. This became known as theHiggs mechanism.
The Standard Model hypothesises afield which is responsible for this effect, called the Higgs field (symbol:), which has the unusual property of a non-zero amplitude in itsground state; i.e., a non-zerovacuum expectation value. It can have this effect because of its unusual "sombrero" shaped potential whose lowest "point" is not at its "centre". In simple terms, unlike all other known fields, the Higgs field requiresless energy to have a non-zero value than a zero value, so it ends up having a non-zero valueeverywhere. Below a certain extremely high energy level the existence of this non-zero vacuum expectationspontaneously breaks electroweakgauge 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 becausescalar field components of the Higgs field are "absorbed" by the massive bosons asdegrees of freedom, and couple to the fermions viaYukawa coupling, thereby producing the expected mass terms. When symmetry breaks under these conditions, theGoldstone bosons that ariseinteract 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 thegauge bosons while remaining compatible withgauge theories.[152] Itsquantum would be ascalar boson, known as the Higgs boson.[153]
Simple explanation of the theory, from its origins in superconductivity
The proposed Higgs mechanism arose as a result of theories proposed to explain observations insuperconductivity. A superconductor does not allow penetration by external magnetic fields (theMeissner effect). This strange observation implies that somehow, the electromagnetic field becomes short ranged during this phenomenon. Successful theories arose to explain this during the 1950s, first for fermions (Ginzburg–Landau theory, 1950), and then for bosons (BCS theory, 1957).
In these theories, superconductivity is interpreted as arising from acharged condensate field. Initially, the condensate value does not have any preferred direction, implying it is scalar, but itsphase is capable of defining a gauge, in gauge based field theories. To do this, the field must be charged. A charged scalar field must also be complex (or described another way, it contains at least two components, and a symmetry capable of rotating each into the other(s)). In naïve gauge theory, a gauge transformation of a condensate usually rotates the phase. But in these circumstances, it instead fixes a preferred choice of phase. However, it turns out that fixing the choice of gauge so that the condensate has the same phase everywhere also causes the electromagnetic field to gain an extra term. This extra term causes the electromagnetic field to become short range.
Once attention was drawn to this theory within particle physics, the parallels were clear. A change of the usually long range electromagnetic field to become short ranged, within a gauge invariant theory, was exactly the needed effect sought for the weak force bosons (because a long range force has massless gauge bosons, and a short ranged force implies massive gauge bosons, suggesting that a result of this interaction is that the field's gauge bosons acquired mass, or a similar and equivalent effect). The features of a field required to do this were also quite well defined – it would have to be a charged scalar field, with at least two components, and complex in order to support a symmetry able to rotate these into each other.[v]
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 thetwo-Higgs-doublet models (2HDM), which predict the existence of aquintet of scalar particles: twoCP-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 a125 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.[154] The heavily researchedMinimal Supersymmetric Standard Model (MSSM) includes a Type-II 2HDM Higgs sector, so it could be disproven by evidence of a Type-I 2HDM Higgs.[citation needed]
In other models the Higgs scalar is a composite particle. For example, intechnicolour the role of the Higgs field is played by strongly bound pairs of fermions calledtechniquarks. Other models feature pairs oftop quarks (seetop quark condensate). In yet other models, there isno Higgs field at all and the electroweak symmetry is broken using extra dimensions.[155][156]
A one-loopFeynman 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-calledhierarchy problem.
The Standard Model leaves the mass of the Higgs boson as aparameter to be measured, rather than a value to be calculated. This is seen as theoretically unsatisfactory, particularly as quantum corrections (related to interactions withvirtual 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 massof the order of100 to 1000 GeV/c2 to ensureunitarity (in this case, to unitarise longitudinal vector boson scattering).[157] Reconciling these points appears to require explaining why there is an almost-perfect cancellation resulting in the visible mass of ~ 125 GeV/c2, and it is not clear how to do this. Because the weak force is about 1032 times stronger than gravity, and (linked to this) the Higgs boson's mass is so much less than thePlanck mass or thegrand 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 precisefine-tuning of parameters – however at present neither of these explanations is proven. This is known as ahierarchy problem.[158] More broadly, the hierarchy problem amounts to the worry thata 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.[157] Anumber of solutions have been proposed, includingsupersymmetry, conformal solutions and solutions via extra dimensions such asbraneworld models.
There are also issues ofquantum triviality, which suggests that it may not be possible to create a consistent quantum field theory involving elementary scalar particles. This can also lead to a predictable Higgs mass inasymptotic safety scenarios.[159]
In the Standard Model, the Higgs field is a scalartachyonic field – scalar meaning it does not transform underLorentz transformations, andtachyonic meaning the field (butnot the particle) hasimaginary mass, and in certain configurations must undergosymmetry breaking. It consists of four components: Two neutral ones and two charged componentfields. Both of the charged components and one of the neutral fields areGoldstone bosons, which act as the longitudinal third-polarisation components of the massiveW+, W−, and Z bosons. The quantum of the remaining neutral component corresponds to (and is theoretically realised as) the massive Higgs boson.[160] This component can interact withfermions viaYukawa coupling to give them mass as well.
Mathematically, the Higgs field has imaginary mass and is therefore atachyonic field.[w] Whiletachyons (particles that movefaster than light) are a purely hypothetical concept,fields with imaginary mass have come to play an important role in modern physics.[162][163] 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 ofcausality).[164] 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 astachyon 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, thefield operators atspacelike separated points stillcommute (or anticommute), and information and particles still do not propagate faster than light.[165] 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.[166]
This section needs to beupdated. The reason given is: With the Higgs boson now empirically confirmed, the paragraphs on the mass should be rephrased to make it clear that they are about what could be predicted before that observation. Please help update this article to reflect recent events or newly available information.(July 2018)
The Standard Model does not predict the mass of the Higgs boson.[168] If that mass is between115 and 180 GeV/c2 (consistent with empirical observations of125 GeV/c2), then the Standard Model can be valid at energy scales all the way up to thePlanck scale (1019 GeV/c2).[169] It should be the only particle in the Standard Model that remains massive even at high energies. Many theorists expect newphysics beyond the Standard Model to emerge at the TeV-scale, based on unsatisfactory properties of the Standard Model.[170]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, becauseunitarity is violated in certain scattering processes.[171]
It is also possible, although experimentally difficult, to estimate the mass of the Higgs boson indirectly: In the Standard Model, the Higgs boson has a number of indirect effects; most notably, Higgs loops result in tiny corrections to masses of the W and Z bosons. Precision measurements of electroweak parameters, such as theFermi constant and masses of the W and Z bosons, can be used to calculate constraints on the mass of the Higgs. As of July 2011, the precision electroweak measurements tell us that the mass of the Higgs boson is likely to be less than about161 GeV/c2 at 95%confidence level.[x] These indirect constraints rely on the assumption that the Standard Model is correct. It may still be possible to discover a Higgs boson above these masses, if it is accompanied by other particles beyond those accommodated by the Standard Model.[173]
The LHC cannot directly measure the Higgs boson's lifetime, due to its extreme brevity. It is predicted as1.56×10−22 s based on the predicteddecay width of4.07×10−3 GeV.[2] However it can be measured indirectly, based upon comparing masses measured from quantum phenomena occurring in theon shell production pathways and in the, much rarer,off shell production pathways, derived from Dalitz decay via a virtual photon(H → γ*γ → ℓℓγ). Using this technique, the lifetime of the Higgs boson was tentatively measured in 2021 as1.2 –4.6×10−22 s, at sigma 3.2 (1 in 1000) significance.[3][4]
If Higgs particle theories are valid, then a Higgs particle can be produced much like other particles that are studied, in aparticle collider. This involves accelerating a large number of particles to extremely high energies and extremely close to thespeed of light, then allowing them to smash together.Protons and leadions (the barenuclei of leadatoms) 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,[94][174][175] although the probability of producing a Higgs boson in any collision is always expected to be very small – for example, only one Higgs boson per 10 billion collisions in the Large Hadron Collider.[r] The most common expected processes for Higgs boson production are:
Gluon fusion
If the collided particles arehadrons such as theproton orantiproton – as is the case in the LHC and Tevatron – then it is most likely that two of thegluons binding the hadron together collide. The easiest way to produce a Higgs particle is if the two gluons combine to form a loop ofvirtual 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 virtualtop andbottom 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.[94][174]
Higgs Strahlung
If an elementaryfermion collides with an anti-fermion – e.g., a quark with an anti-quark or anelectron with apositron – 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 asassociated production.[94][174][175]
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, anup 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.[94][175]
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.[94][174]
The Standard Model prediction for thedecay 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.[176] This is also true for the Higgs boson. The likelihood with which this happens depends on a variety of factors including: the difference in mass, the strength of the interactions, etc. Most of these factors are fixed by the Standard Model (SM), except for the mass of the Higgs boson itself. Given that the Higgs boson has a mass of125 GeV/c2, the SM then predicts a mean life time of about1.6×10−22 s.[b]
The Standard Model prediction for thebranching 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 thebranching 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 (seeplot, right).
Higgs boson decays into (a) heavy vector boson pairs, (b) fermion–antifermion pairs, and (c,d) paired photonsγγ orZγ.[177]
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.[126] By this logic the most common decay should be into atop–antitop quark pair. However, such a decay would only be possible if the Higgs were heavier than ~346 GeV/c2, twice the mass of the top quark. Given a Higgs mass of125 GeV/c2, the SM predicts that the most common decay is into abottom–antibottom quark pair, which happens 57.7% of the time.[2] The second most common fermion decay at that mass is atau–antitau pair, which happens only about 6.3% of the time.[2]
Another possibility is for the Higgs to split into a pair of massive gauge bosons. The most likely possibility is for the Higgs to decay into a pair of W bosons (the light blue line in the plot), which happens about 21.5% of the time for a Higgs boson with a mass of125 GeV/c2.[2] The W bosons can subsequently decay either into a quark and an antiquark or into a charged lepton and a neutrino. The decays of W bosons into quarks are difficult to distinguish from the background, and the decays into leptons cannot be fully reconstructed (because neutrinos are impossible to detect in particle collision experiments). A cleaner signal is given by decay into a pair of Z bosons (which happens about 2.6% of the time for a Higgs with a mass of125 GeV/c2),[2] if each of the bosons subsequently decays into a pair of easy-to-detect charged leptons (electrons ormuons).
Decay into massless gauge bosons (i.e.,gluons orphotons) is also possible, but requires intermediate loop of virtual heavy quarks (top or bottom) or massive gauge bosons.[126] 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 8.6% of the time for a Higgs boson with a mass of125 GeV/c2. 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.[2] 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.[126]
In 2021 the extremely rareDalitz decay was tentatively observed,[citation needed] into twoleptons (electrons or muons) and a photon( ℓℓγ ), viavirtual photon decay. This can happen in three ways:
Higgs to virtual photon to ℓℓγ in which the virtual photon( γ* ) has very small but nonzero mass,
Higgs to Z boson toℓℓγ ,
Higgs to two leptons, one of which emits a final-state photon leading toℓℓγ .
ATLAS searched for evidence of the first of these( H → γ*γ → ℓℓγ ) for low lepton-pair masses( ≤30 GeV/c2 ), where this process should dominate. The observation is atsignificance 3.2 sigma (1 chance in 1000 of being wrong).[3][4] This decay path is important because it facilitates measuring theon- and off-shell mass of the Higgs boson (allowing indirect measurement of decay time), and the decay into two charged particles allows exploration ofcharge conjugation andcharge parity (CP) violation.[4]
At the Large Hadron Collider (LHC),Higgs boson pair production occurs through several distinct mechanisms, similarly as single Higgs production:[178][179]
Gluon–gluon fusion (ggF) is the dominant production mode. It proceeds via loop diagrams involving heavy quarks, primarily the top quark, and includes bothbox andtriangle topologies. The triangle diagram explicitly depends on the Higgs trilinear self-coupling, and its interference with the box diagram significantly affects the total cross section.
Vector boson fusion (VBF) involves the radiation of Higgs bosons from virtual W or Z bosons exchanged between incoming quarks. Although subdominant in rate, VBF offers distinctive event topologies and complementary sensitivity to new physics.
Associated production channels, such asttHH (with top quark pairs) andVHH (with vector bosons), become increasingly important at higher center-of-mass energies and provide unique sensitivity to the Higgs-top and Higgs-gauge boson interactions.
Each of these production mechanisms offers different levels of sensitivity to the Higgs self-coupling λ, making them essential components in a comprehensive search for deviations from the Standard Model prediction.
Higgs boson pairs can decay through various channels. The most studied final states include:
HH → bb̄bb̄: Has the highest branching fraction (~34%) but suffers from large QCD background.
HH → bb̄γγ: Low branching fraction (~0.3%) but excellent mass resolution due to clean photon identification.
HH → bb̄τ⁺τ⁻: Offers a good compromise between signal rate and background contamination (~7.3% branching ratio).
The choice of decay mode affects the sensitivity of LHC experiments to the HH signal.
The name most strongly associated with the particle and field is the Higgs boson[91]: 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,[y] and these are still used at times.[63][181] Fuelled in part by the issue of recognition and a potential shared Nobel Prize,[181][182]the most appropriate name was still occasionally a topic of debate until 2013.[181]Higgs himself preferred to call the particle either by an acronym of all those involved, or "the scalar boson", or "the so-called Higgs particle".[182]
A considerable amount has been written on how Higgs's name came to be exclusively used. Two main explanations are offered. The first is that Higgs undertook a step which was either unique, clearer or more explicit in his paper in formally predicting and examining the particle. Of the PRL papers' authors, only the paper by Higgsexplicitly offered as a prediction that a massive particle would exist and calculated some of its properties;[183][91]: 167 he was therefore "the first to postulate the existence of a massive particle" according toNature.[181]Physicist and authorFrank Close and physicist-bloggerPeter Woit both comment that the paper by GHK was also completed after Higgs and Brout–Englert were submitted toPhysical Review Letters,[184][91]: 167 and that Higgs alone had drawn attention to a predicted massivescalar boson, while all others had focused on the massivevector bosons.[184][91]: 154,166,175 In this way, Higgs's contribution also provided experimentalists with a crucial "concrete target" needed to test the theory.[185]
However, in Higgs's view, Brout and Englert did not explicitly mention the boson since its existence is plainly obvious in their work,[68]: 6 while according to Guralnik the GHK paper was a complete analysis of the entire symmetry breaking mechanism whosemathematical rigour is absent from the other two papers, and a massive particle may exist in some solutions.[92]: 9 Higgs's paper also provided an "especially sharp" statement of the challenge and its solution according toscience historian David Kaiser.[182]
The alternative explanation is that 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's own[68]: 7 ) credit the "Higgs" name to physicistBenjamin Lee.[z]Lee was a significant populariser of the theory in its early days, and habitually attached the name "Higgs" as a "convenient shorthand" for its components from 1972,[16][181][186][187][188]and in at least one instance from as early as 1966.[189] Although Lee clarified in his footnotes that "'Higgs' is an abbreviation for Higgs, Kibble, Guralnik, Hagen, Brout, Englert",[186]his use of the term (and perhaps also Steven Weinberg's mistaken cite of Higgs's paper as the first in his seminal 1967 paper[91][190][189]) meant that by around 1975–1976 others had also begun to use the name "Higgs" exclusively as a shorthand.[aa]In 2012, physicistFrank Wilczek, who was credited for naming the elementary particle, theaxion (over an alternative proposal "Higglet", by Weinberg), endorsed the "Higgs boson" name, stating "History is complicated, and wherever you draw the line, there will be somebody just below it."[182]
The Higgs boson is often referred to as the "God particle" in popular media outside the scientific community.[191][192][193][194][195] 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? byPhysics Nobel Prize winner andFermilab directorLeon M. Lederman.[27] Lederman wrote it in the context of failing US government support for theSuperconducting Super Collider,[196] a partially constructed titanic[197][198] competitor to theLarge Hadron Collider with planned collision energies of2 × 20 TeV that was championed by Lederman since its 1983 inception[196][ab][199][200] 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.[201] Lederman, a leading researcher in the field, writes that he wanted to title his bookThe Goddamn Particle: If the Universe is the Answer, What is the Question? Lederman's editor decided that the title was too controversial and convinced him to change the title toThe God Particle: If the Universe is the Answer, What is the Question?[202]
While media use of this term may have contributed to wider awareness and interest,[203] many scientists feel the name is inappropriate[16][17][204] since it is sensationalhyperbole and misleads readers;[205] the particle also has nothing to do with any God, leaves open numerousquestions in fundamental physics, and does not explain the ultimateorigin of the universe.Higgs, anatheist, 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".[205][206][207] The nickname has been satirised in mainstream media as well.[208] 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 thehistory of physics, but that (according to Lederman) the publisher rejected all titles mentioning "Higgs" as unimaginative and too unknown.[209]
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 theBig Bang, and the apparent chaos of structures, particles, forces and interactions that resulted and shaped our present universe, with the biblical story ofBabel in which the primordial single language of earlyGenesis wasfragmented into many disparate languages and cultures.[210]
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, toanother book, amuch older one ...
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".[211]
A renaming competition by British newspaperThe Guardian in 2009 resulted in their science correspondent choosing the name "thechampagne bottle boson" as the best submission: "The bottom of a champagne bottle is in the shape of theHiggs 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."[212]The nameHiggson was suggested as well, in an opinion piece in theInstitute of Physics' online publicationphysicsworld.com.[213]
Photograph of light passing through adispersive prism: the rainbow effect arises becausephotons are not all affected to the same degree by the dispersive material of the prism.
There has been considerable public discussion of analogies and explanations for the Higgs particle and how the field creates mass,[214][215]including coverage of explanatory attempts in their own right and a competition in 1993 for the best popular explanation by then-UK Minister for ScienceSir William Waldegrave[216]and articles in newspapers worldwide.
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:[218]
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 anelectric 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.
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 thesmoking 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.[ac]He also drew attention to well-known effects insolid state physics where an electron's effective mass can be much greater than usual in the presence of a crystal lattice.[220]
Analogies based ondrag 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 withNewton's third law.[222]
The Higgs boson is commonly misunderstood as responsible for mass, rather than the Higgs field, and as relating to most mass in the universe.[223][224][225] About 91% of the proton mass is due to the quark and gluon fields and the QCDconformal anomaly rather than the Higgs interaction.[226]
There was considerable discussion prior to late 2013 of how to allocate the credit if the Higgs boson is proven, made more pointed as aNobel Prize had been expected, and the very wide basis of people entitled to consideration. These include a range of theoreticians who made the Higgs mechanism theory possible, the theoreticians of the 1964 PRL papers (including Higgs himself), the theoreticians who derived from these a working electroweak theory and the Standard Model itself, and also the experimentalists at CERN and other institutions who made possible the proof of the Higgs field and boson in reality. The Nobel Prize has a limit of three persons to share an award, and some possible winners are already prize holders for other work, or are deceased (the prize is only awarded to persons in their lifetime). Existing prizes for works relating to the Higgs field, boson, or mechanism include:
Nobel Prize in Physics (1979) –Glashow,Salam, andWeinberg,for contributions to the theory of the unified weak and electromagnetic interaction between elementary particles[227]
Nobel Prize in Physics (1999) –'t Hooft andVeltman,for elucidating the quantum structure of electroweak interactions in physics[228]
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[89] (for the 1964 papers describedabove)
Special Breakthrough Prize in Fundamental Physics (2013) – Fabiola Gianotti andPeter Jenni, spokespersons of the ATLAS Collaboration and Michel Della Negra, Tejinder Singh Virdee, Guido Tonelli, and Joseph Incandela spokespersons, past and present, of the CMS collaboration, "For [their] leadership role in the scientific endeavour that led to the discovery of the new Higgs-like particle by the ATLAS and CMS collaborations at CERN's Large Hadron Collider".[229]
Nobel Prize in Physics (2013) –Peter Higgs andFrançois 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[230]
Following reported observation of the Higgs-like particle in July 2012, severalIndian media outlets reported on the supposed neglect of credit to Indian physicistSatyendra Nath Bose after whose work in the 1920s the class of particles "bosons" is named[232][233](although physicists have described Bose's connection to the discovery as tenuous).[234]
where and are thegauge bosons of the SU(2) and U(1) symmetries, and their respectivecoupling constants, are thePauli matrices (a complete set of generators of the SU(2) symmetry), and and, so that theground 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 topick a gauge such that in the ground state. The expectation value of in the ground state (thevacuum expectation value or VEV) is then, where. The measured value of this parameter is ~246 GeV/c2.[126] 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:[235]
with their ratio determining theWeinberg angle,, and leave a massless U(1)photon,. The mass of the Higgs boson itself is given by
The quarks and the leptons interact with the Higgs field throughYukawa interaction terms:
where are left-handed and right-handed quarks and leptons of theithgeneration, are matrices of Yukawa couplings whereh.c. denotes the hermitian conjugate of all the preceding 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.[235]
Quantum gauge theory – Physical theory with fields invariant under the action of local "gauge" Lie groupsPages displaying short descriptions of redirect targets
W and Z bosons – Bosons that mediate the weak interaction
^Note that such events also occur due to other processes. Detection involves astatistically significant excess of such events at specific energies.
^ab In theStandard Model, the totaldecay width of a Higgs boson with a mass of125 GeV/c2 is predicted to be4.07×10−3 GeV.[2] The mean lifetime is given by.
^In Higgs-based theories, the Higgs boson itself should be an exception, being massive even at high energies.
^In physics, it is possible for alaw 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 whererelativistic 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.
^An example to illustrate this is where a pencil is balancing on its tip, any disturbance will lead it to fall over in some direction. The underlying system is symmetric with respect to direction, but the pencil will fall in some direction, leading to a broken directional symmetry.
^In theoretical particle physics, one says that particleA "absorbs" particleB 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 andB, 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 theoreticalW3 andB0electroweak bosons is called theZ boson).
^abcThe success of the Higgs-based electroweak theory and Standard Model is illustrated by theirpredictions of the mass of two particles that were 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 theweak neutral current, thegluon, and thetop andcharm quarks, all later proven to exist.
^Electroweak symmetry is broken by the Higgs field in its lowest energy state, called itsground 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.
^The range of a force is inversely proportional to the mass of the particles transmitting it.[26]
In the Standard Model, forces are carried byvirtual particles. The movement and interactions of these particles with each other are limited by the energy–timeuncertainty 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.
^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.
'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]
^The statement excludes spin-0mesons, such as thepion, since they are known to be composites of pairs of spin- 1 /2 fermions.
^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 eventhe nearest galaxy being over 2 millionlight 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]
^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 sufficientlyperturbed). 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, fromsubatomic particles togalaxies, and allfundamental 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.
^abGoldstone's theorem only applies to gauges havingmanifest Lorentz covariance, a condition that took time to become questioned. But the process ofquantisation requires agauge 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 toBernstein (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 allLorentz frames, thephoton field Aμ(x) cannot transform like afour-vector. This is no catastrophe, since the photonfield is not anobservable, and one can readily show that the S-matrix elements, whichare 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 Goldstoneet al. proof breaks down, the zero mass Goldstone mesons need not appear. [emphasis in original]
^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 bothg and are constants, this looks exactly like the mass term for a fermion of mass. The field is then theHiggs field.
^abThe 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,[94] while the total cross-section for a proton–proton collision is 110 millibarn.[95]
^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.
^abcATLAS 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)[129]
^In the Standard Model, the mass term arising from the Dirac Lagrangian for any fermion is. This isnot 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 particlechirality. Since the spin-half particles have no right/left helicity pair with the sameSU(2) andSU(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.
^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 asGoldstone bosons. Because zero mass gauge bosons always mediate long range interactions, a new long range force should exist as well.
^People initially thought of tachyons as particles travelling faster than the speed of light ... But we now know that atachyon indicates an instability in a theory that contains it. Regrettably for science fiction fans, tachyons are not real physical particles that appear in nature.[161]
^ This upper limit would increase to185 GeV/c2 if the lower bound of114.4 GeV/c2 from the LEP-2 direct search is allowed for.[172]
^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".
^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.[196]
^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.[220][221]
^abcdStrassler, M. (12 October 2012)."The Higgs FAQ 2.0".ProfMattStrassler.com.Archived from the original on 12 October 2013. Retrieved8 January 2013.[Q] Why do particle physicists care so much about the Higgs particle?[A] Well, actually, they don't. What they really care about is the Higgsfield, because it isso important. [emphasis in original]
^abcdeFalkowski, Adam (writing as 'Jester') (27 February 2013)."When shall we call it Higgs?" (blog). Résonaances particle physics.Archived from the original on 29 June 2017. Retrieved7 March 2013.
^abcGunion; Dawson; Kane; Haber (1990).The Higgs Hunter's Guide (1st ed.). Basic Books. p. 11.ISBN978-0-2015-0935-9.Archived from the original on 25 January 2022. Retrieved5 September 2020. Cited by Peter Higgs in his talk "My Life as a Boson", 2001, ref#25.
^Strassler, M. (8 October 2011)."The known particles – if the Higgs field were zero".ProfMattStrassler.com.Archived from the original on 17 March 2021. Retrieved13 November 2012.The Higgs field: So important it merited an entire experimental facility, the Large Hadron Collider, dedicated to understanding it.
^Siegfried, T. (20 July 2012)."Higgs hysteria".Science News.Archived from the original on 31 October 2012. Retrieved9 December 2012.In terms usually reserved for athletic achievements, news reports described the finding as a monumental milestone in the history of science.
^abcDel Rosso, A. (19 November 2012)."Higgs: The beginning of the exploration" (Press release).CERN.Archived from the original on 19 April 2019. Retrieved9 January 2013.Even in the most specialized circles, the new particle discovered in July is not yet being called the "Higgs boson". Physicists still hesitate to call it that before they have determined that its properties fit with those the Higgs theory predicts the Higgs boson has.
^abNaik, G. (14 March 2013)."New data boosts case for Higgs boson find".The Wall Street Journal.Archived from the original on 4 January 2018. Retrieved15 March 2013.'We've never seen an elementary particle with spin zero', said Tony Weidberg, a particle physicist at the University of Oxford who is also involved in the CERN experiments.
^Klotz, Irene (18 February 2013). Adams, David; Eastham, Todd (eds.)."Universe has finite lifespan, Higgs boson calculations suggest".Huffington Post. Reuters.Archived from the original on 20 February 2013. Retrieved21 February 2013.Earth will likely be long gone before any Higgs boson particles set off an apocalyptic assault on the universe
^abcBoyle, Alan (19 February 2013)."Will our universe end in a 'big slurp'? Higgs-like particle suggests it might".NBC News' Cosmic blog.Archived from the original on 21 February 2013. Retrieved21 February 2013.[T]he bad news is that its mass suggests the universe will end in a fast-spreading bubble of doom. The good news? It'll probably be tens of billions of years. The article quotesFermilab's Joseph Lykken: "[T]he parameters for our universe, including the Higgs [and top quark's masses] suggest that we're just at the edge of stability, in a "metastable" state. Physicists have been contemplating such a possibility for more than 30 years. Back in 1982, physicists Michael Turner and Frank Wilczek wrote inNature that "without warning, a bubble of true vacuum could nucleate somewhere in the universe and move outwards ..."
^Peralta, Eyder (19 February 2013)."If Higgs boson calculations are right, a catastrophic 'bubble' could end universe".The Two-Way. NPR News.Archived from the original on 21 February 2013. Retrieved21 February 2013. Article citesFermilab's Joseph Lykken: "The bubble forms through an unlikely quantum fluctuation, at a random time and place," Lykken tells us. "So in principle it could happen tomorrow, but then most likely in a very distant galaxy, so we are still safe for billions of years before it gets to us."
^Cole, K. C. (14 December 2000)."One Thing Is Perfectly Clear: Nothingness Is Perfect".Los Angeles Times.Archived from the original on 25 January 2022. Retrieved17 January 2013.[T]he Higgs' influence (or the influence of something like it) could reach much further. For example, something like the Higgs—if not exactly the Higgs itself—may 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 began to separate from their primordial sameness—taking on the distinct characters they have today—they released energy in the same way as water releases energy when it turns to ice. Except in this case, the freezing packed enough energy to blow up the universe. ... However it happened, the moral is clear: Only when the perfection shatters can everything else be born.
^Higgs, Peter (24 November 2010).My Life as a Boson(PDF) (Report). Talk given by Peter Higgs at King's College, London, 24 November 2010.King's College, London. Archived fromthe original(PDF) on 4 November 2013. Retrieved17 January 2013.Gilbert ... wrote a response to [Klein and Lee's paper] saying 'No, you cannot do that in a relativistic theory. You cannot have a preferred unit time-like vector like that.' This is where I came in, because the next month was when I responded to Gilbert's paper by saying 'Yes, you can have such a thing' but only in a gauge theory with a gauge field coupled to the current.
^Salam, A. (1968). Svartholm, N. (ed.).Elementary Particle Physics: Relativistic Groups and Analyticity. Eighth Nobel Symposium. Stockholm, SV: Almquvist and Wiksell. p. 367.
^abcdefPolitzer, David (8 December 2004)."The Dilemma of Attribution".The Nobel Prize.Archived from the original on 21 March 2013. Retrieved22 January 2013.Sidney Coleman published in Science magazine in 1979 a citation search he did documenting that essentially no one paid any attention 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 contributions.
^"Welcome to the Worldwide LHC Computing Grid".WLCG – Worldwide LHC Computing Grid. CERN.Archived from the original on 25 July 2018. Retrieved14 November 2012.[A] global collaboration of more than 170 computing centres in 36 countries ... to store, distribute and analyse the ~25 Petabytes (25 million Gigabytes) of data annually generated by the Large Hadron Collider
^"The Worldwide LHC Computing Grid".The Worldwide LHC Computing Grid. CERN. November 2017.Archived from the original on 7 November 2017. Retrieved5 November 2017.It now links thousands of computers and storage systems in over 170 centres across 41 countries. ... The WLCG is the world's largest computing grid
^The CDF Collaboration; The D0 Collaboration; The Tevatron New Physics, Higgs Working Group (2012). "Updated combination of CDF and D0 searches for Standard Model Higgs boson production with up to10.0 fb−1 of data".arXiv:1207.0449 [hep-ex].
^"LHC to restart in 2009".Media and Press relations (Press release). CERN. 5 December 2008.Archived from the original on 12 November 2016. Retrieved12 November 2016.
^"LHC progress report".CERN Bulletin (18). 3 May 2010.Archived from the original on 26 May 2018. Retrieved7 December 2011.
^ab"ATLAS and CMS experiments present Higgs search status" (Press release). CERN Press Office. 13 December 2011.Archived from the original on 13 December 2012. Retrieved14 September 2012.the statistical significance is not large enough to say anything conclusive. As of today what we see is consistent either with a background fluctuation or with the presence of the boson. Refined analyses and additional data delivered in 2012 by this magnificent machine will definitely give an answer
^"Welcome".WLCG – Worldwide LHC Computing Grid. CERN. Archived fromthe original on 10 November 2012. Retrieved29 October 2012.
^Strassler, Matt (14 November 2012)."Higgs Results at Kyoto".Of Particular Significance: Conversations about science with theoretical physicist Matt Strassler (personal website).Archived from the original on 8 March 2021. Retrieved10 January 2013.
^Heilprin, John (27 January 2013)."CERN chief: Higgs boson quest could wrap up by midyear".NBCNews.com. AP.Archived from the original on 21 February 2013. Retrieved20 February 2013.Rolf Heuer, director of [CERN], said he is confident that "towards the middle of the year, we will be there." – Interview by AP, at the World Economic Forum, 26 January 2013.
^Aad, G.; et al. (ATLAS & CMS Collaborations) (2016). "Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at√s = 7 and 8 TeV".Journal of High Energy Physics.2016 (8): 45.arXiv:1606.02266.Bibcode:2016JHEP...08..045A.doi:10.1007/JHEP08(2016)045.S2CID118523967.
^Lykken, Joseph D. (27 June 2009). "Beyond the Standard Model".Proceedings of the 2009 European School of High-Energy Physics. Bautzen, Germany.arXiv:1005.1676.Bibcode:2010arXiv1005.1676L.
^abPeskin, M. (July 2012)."40 years of the Higgs boson"(PDF). 2012SLAC Summer Institute Conferences.Presentation at SSI 2012.Stanford University. pp. 3–5.Archived(PDF) from the original on 1 May 2014. Retrieved21 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.
^abCho, A. (14 September 2012)."Why the 'Higgs'?"(PDF). Particle physics.Science.337 (6100): 1287.doi:10.1126/science.337.6100.1287.PMID22984044. Archived fromthe original(PDF) on 4 July 2013. Retrieved12 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 theNew York Review of Books in May 2012.(See also original article in
^"A supercompetition for Illinois".Chicago Tribune. 31 October 1986.Archived from the original on 15 May 2013. Retrieved16 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
^Abbott, Charles (June 1987)."Super competition for superconducting super collider".Illinois Issues Journal. p. 18.Archived from the original on 1 November 2013. Retrieved16 January 2013.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.
^Kevles, Dan (Winter 1995)."Good-bye to the SSC: On the life and death of the superconducting super collider"(PDF).Engineering & Science.58 (2).California Institute of Technology:16–25.Archived(PDF) from the original on 11 May 2013. Retrieved16 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.
^Calder, Nigel (2005).Magic Universe: A grand tour of modern science. OUP Oxford. pp. 369–370.ISBN978-0-19-162235-9.Archived from the original on 25 January 2022. Retrieved5 September 2020.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
^Cole, K. (14 December 2000)."One thing is perfectly clear: Nothingness is perfect". Science File.Los Angeles Times.Archived from the original on 5 October 2015. Retrieved17 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'
^Lederman, p. 22et 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."
Carroll, Sean (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.ISBN978-0-14-218030-3.
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 King's College, London, 24 November 2010. Archived fromthe original(PDF) on 4 November 2013. Retrieved17 January 2013. (also:Higgs, Peter (24 November 2010). "My Life As a Boson: The Story of "the Higgs"".International Journal of Modern Physics A.17 (supp01):86–88.Bibcode:2002IJMPA..17S..86H.doi:10.1142/S0217751X02013046.)
Electroweak Symmetry Breaking – A pedagogic introduction to electroweak symmetry breaking with step by step derivations of many key relations, by Robert D. Klauber, 15 January 2018 (archived at Wayback Machine)
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