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Quotation of the Day: Higgs boson – “God particle” Cornerston of the Simple Theory of Everything

September 16, 2014



“I wasn’t sure it would be important.”

PETER HIGGS, on his 1964 prediction about the existence of a subatomic particle – now known as the Higgs boson, or the “God particle” – that won him the 2013 Nobel Prize in Physics.


Higgs boson

From Wikipedia, the free encyclopedia
Higgs boson
Candidate Higgs Events in ATLAS and CMS.png

Candidate Higgs boson events from collisions betweenprotons in the LHC. The top event in the CMSexperiment shows a decay into two photons (dashed yellow lines and green towers). The lower event in theATLAS experiment shows a decay into 4 muons (red tracks).[Note 1]
Composition Elementary particle
Statistics Bosonic
Status A Higgs boson of mass ≈125 GeV has been tentatively confirmed by CERN on 14 March 2013,[1][2][3] although unclear as yet which model the particle best supports or whether multiple Higgs bosons exist.[2]
(See: Current status)
Symbol H0
Theorised R. Brout, F. Englert, P. Higgs, G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble (1964)
Discovered Large Hadron Collider (2011-2013)
Mass 125.03+0.26
−0.27 (stat) +0.13
−0.15  (sys) GeV/c2
(CMS) ,[4]125.36 ± 0.37 (stat) ± 0.18 (sys) GeV/c2(ATLAS) [5]
Mean lifetime 1.56×10−22 s[Note 2] (predicted)
Decays into bottom-antibottom pair (predicted)
two W bosons (observed)
two gluons (predicted)
tau-antitau pair (observed)
two Z-bosons (observed)
two photons (observed)various other decays (predicted)
Electric charge 0
Color charge 0
Spin 0 (tentatively confirmed at 125 GeV)[1]
Parity +1 (tentatively confirmed at 125 GeV)[1]

The Higgs boson or Higgs particle is an elementary particle in the Standard Model of Particle physics. Its main relevance is that it is the smallest possible excitation of the Higgs field[6][7] – a field that unlike the more familiar electromagnetic field cannot be “turned off”, but instead takes a constant value almost everywhere. The presence of this field explains why some fundamental particles have mass while thesymmetries controlling their interactions should require them to be massless, and why the weak force has a much shorter range than the electromagnetic force.

Despite being present everywhere, the existence of the Higgs field has been very hard to confirm, because it is extremely hard to create excitations (i.e. Higgs particles). The search for this elusive particle has taken more than 40 years and led to the construction of one of the world’s most expensive and complex experimental facilities to date, the Large Hadron Collider,[8] able to create Higgs bosons and other particles for observation and study. On 4 July 2012, the discovery of a new particle with a mass between 125 and127 GeV/c2 was announced; physicists suspected that it was the Higgs boson.[9][10][11] By March 2013, the particle had been proven to behave, interact and decay in many of the ways predicted by the Standard Model, and was also tentatively confirmed to have positive parity and zero spin,[1] two fundamental attributes of a Higgs boson. This appears to be the first elementary scalar particle discovered in nature.[12]More data is needed to know if the discovered particle exactly matches the predictions of the Standard Model, or whether, as predicted by some theories, multiple Higgs bosons exist.[3]

The Higgs boson is named after Peter Higgs, one of six physicists who, in 1964, proposed the mechanismthat suggested the existence of such a particle. Although Higgs’s name has come to be associated with this theory, several researchers between about 1960 and 1972 each independently developed different parts of it. In mainstream media the Higgs boson has often been called the “God particle”, from a 1993 book on the topic; the nickname is strongly disliked by many physicists, including Higgs, who regard it as inappropriatesensationalism.[13][14] On December 10, 2013 two of the original researchers, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their work and prediction.[15] Englert’s co-researcherRobert Brout had died in 2011 and the Nobel Prize is not given posthumously except in unusual circumstances.

In the Standard Model, the Higgs particle is a boson with no spin, electric charge, or color charge. It is also very unstable, decaying into other particles almost immediately. It is a quantum excitation of one of the four components of the Higgs field. The latter constitutes a scalar field, with two neutral and two electrically charged components, and forms a complex doublet of the weak isospin SU(2) symmetry. The field has a “Mexican hat” shaped potential with nonzero strength everywhere (including otherwise empty space), which in its vacuum state breaks the weak isospin symmetry of the electroweak interaction. When this happens, three components of the Higgs field are “absorbed” by the SU(2) and U(1) gauge bosons (the “Higgs mechanism“) to become the longitudinal components of the now-massive W and Z bosons of the weak force. The remaining electrically neutral component separately couples to other particles known asfermions (via Yukawa couplings), causing these to acquire mass as well. Some versions of the theory predict more than one kind of Higgs fields and bosons. Alternative “Higgsless” models would have been considered if the Higgs boson was not discovered.

A non-technical summary[edit]

“Higgs” terminology[edit]

[hide]A simple explanation – what are the Higgs mechanism, field and boson?
Symmetriesand forces In the Standard Model of particle physics, the fundamental forces of nature known to science arise from laws of nature called symmetries, and are transmitted by particles known as gauge bosons. The weak force‘s symmetry should cause its gauge bosons to have zero mass, but experiments show that the weak force’s gauge bosons are actually very massive and short-ranging (now calledW and Z bosons).[Note 3] Their very short range – a result of their mass – makes structures likeatoms and stars possible,[citation needed] but it proved exceedingly difficult to find any way to explain their unexpected mass.
Higgs mechanism By the early 1960s, physicists had realized that a given symmetry law might not always be followed (or ‘obeyed’) under certain conditions.[Note 4] The Higgs mechanism is a mathematicalmodel devised by three groups of researchers in 1964 that explains why and how gauge bosons could still be massive despite their governing symmetry. It showed that the conditions for the symmetry would be ‘broken’ if an unusual type of field happened to exist throughout space, and then the particles would be able to have mass.
Higgs field According to the Standard Model, a field of the necessary kind (the “Higgs field”) exists throughout space, and breaks certain symmetry laws of the electroweak interaction.[Note 5] The existence of this field triggers the Higgs mechanism, causing the gauge bosons responsible for the weak force to be massive, and explaining their very short range.[Note 3]Some years after the original theory was articulated scientists realised that the same field would also explain, in a different way, why other fundamental constituents of matter (including electronsand quarks) have mass.For many years scientists had no way to tell whether or not a field of this kind actually existed in reality. If it existed, it would be unlike any other fundamental field known in science. But it was also possible that these key ideas, or even the entire Standard Model itself, were somehow incorrect.[Note 6] Only discovering what was breaking this symmetry would solve the problem.
Higgs boson The existence of the Higgs field – the crucial question[6][7] – could be proven by searching for a matching particle associated with it, which would also have to exist—the “Higgs boson”. Detecting Higgs bosons would automatically prove that the Higgs field exists, which would show that the Standard Model is essentially correct. But for decades scientists had no way to discover whether Higgs bosons actually existed in nature either, because they would be very difficult to produce, and would break apart in about a ten-sextillionth (10−22) of a second. Although the theory gave “remarkably” [17]:22[Note 7] correct answers, particle colliders, detectors, and computers capable of looking for Higgs bosons took over 30 years (c. 1980 – 2010) to develop.As of 2013, scientists are virtually certain that they have proved the Higgs boson exists, and therefore that the concept of some type of Higgs field throughout space is proven. Further testing over the coming years should eventually tell us more about these, and is likely to have significant impact in the future (see below).[9][11]


In particle physics, elementary particles and forces give rise to the world around us. Nowadays, physicists explain the behaviour of these particles and how they interact using the Standard Model—a widely accepted and “remarkably” accurate[17] framework based on gauge invariance and symmetries, believed to explain almost everything in the world we see, other than gravity.[18]

But by around 1960 all attempts to create a gauge invariant theory for two of the four fundamental forces had consistently failed at one crucial point: although gauge invariance seemed extremely important, it seemed to make any theory of electromagnetism and the weak force go haywire, by demanding that either many particles with mass were massless or that non-existent forces and massless particles had to exist. Scientists had no idea how to get past this point.

Work done on superconductivity and “broken” symmetries around 1960 led physicist Philip Anderson to suggest in 1962 a new kind of solution that might hold the key. In 1964 a theory was created by 3 different groups of researchers, that showed the problems could be resolved if an unusual kind of field existed throughout the universe. It would cause existing particles to acquire mass instead of new massless particles being formed. By 1972 it had been developed into a comprehensive theory and proved capable of giving “sensible” results. Although there was not yet any proof of such a field, calculations consistently gave answers and predictions that were confirmed by experiments, including very accurate predictions of several other particles,[Note 7] so scientists began to believe this might be true and to search for proof whether or not a Higgs field exists in nature.

If this field did exist, this would be a monumental discovery for science and human knowledge, and is expected to open doorways to new knowledge in many fields. If not, then other more complicated theories would need to be explored. The easiest proof whether or not the field existed was by searching for a new kind of particle it would have to give off, known as “Higgs bosons” or the “Higgs particle”. These would be extremely difficult to find, so it was only many years later that experimental technology became sophisticated enough to answer the question.

While several symmetries in nature are spontaneously broken through a form of the Higgs mechanism, in the context of the Standard Model the term “Higgs mechanism” almost always means symmetry breaking of the electroweak field. It is considered proven, but the exact cause has been exceedingly difficult to prove. After 50 years, the Higgs boson’s existence – apparently proven in 2013 – would finally confirm that the Standard Model is essentially correct and allow further development, while its non-existence would mean that other theories are needed instead.

Various analogies have also been invented to describe the Higgs field and boson, including analogies with well-known symmetry breaking effects such as therainbow and prism, electric fields, ripples, and resistance of macro objects moving through media, like people moving through crowds or some objects moving through syrup or molasses. However, analogies based on simple resistance to motion are inaccurate as the Higgs field does not work by resisting motion. The Higgs field works by resisting acceleration.


Scientific impact[edit]

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

Validating theStandard Model, or choosing between extensions and alternatives Does the Higgs field exist, which fundamentally validates the Standard Model? If it does, then which more advanced extensions are suggested or excluded based upon measurements of its properties? What else can we learn about this fundamental field, now that we have the experimental means to study its behavior and interactions? Alternatively, if the Higgs field doesn’t exist, which alternatives and modifications to the Standard Model are likely to be preferred? Will the data suggest an extension, or a completely different approach (such as supersymmetry or string theory)?Related to this, a belief generally exists among physicists that there is likely to be “new” physics beyond the Standard Model—the Standard Model will at some point be extended or superseded. The Higgs field and related issues present a promising “doorway” to understand better the places where the Standard Model might become inadequate or fail, and could provide considerable evidence guiding researchers into future enhancements or successors.
Finding howsymmetry breakinghappens within theelectroweak interaction Below an extremely high temperature, electroweak symmetry breaking causes the electroweak interaction to manifest in part as the short-ranged weak force, which is carried by massive gauge bosons. Without this, the universe we see around us could not exist, because atoms and other structures could not form, and reactions in stars such as our Sun would not occur. But it is not clear how this actually happens in nature. Is the Standard Model correct in its approach, and can it be made more exact with actual experimental measurements? If not the Higgs field, then what is breaking symmetry in its place?
Finding how certain particlesacquire mass Electroweak symmetry breaking (due to a Higgs field or otherwise) is believed proven responsible for the masses of fundamental particles such as elementaryfermions (including electrons and quarks) and the massive W and Z gauge bosons. Finding how this happens is pivotal to particle physics.It is worth noting that the Higgs field does not ‘create’ mass out of nothing (which would violate the law of conservation of energy). Nor is the Higgs field responsible for the mass of all particles. For example, about 99% of the mass of baryons (composite particles such as the proton and neutron) is due instead to the kinetic energy of quarks and to the energies of (massless) gluons of the strong interaction inside the baryons.[19] In Higgs-based theories, the property of ‘mass’ is a manifestation of potential energy transferred to particles when they interact (“couple”) with the Higgs field, which had contained that mass in the form of energy.[20]
Evidence whether or not scalar fields exist in nature, and“new” physics Proof of a scalar field such as the Higgs field would be hard to overestimate: “[The] verification of real scalar fields would be nearly as important as its role in generating mass”. [10] Rolf-Dieter Heuer, director general of CERN, stated in a 2011 talk on the Higgs field:[21]

“All the matter particles are spin-1/2 fermions. All the force carriers are spin-1 bosons. Higgs particles are spin-0 bosons (scalars). The Higgs is neither matter nor force. The Higgs is just different. This would be the first fundamental scalar ever discovered. The Higgs field is thought to fill the entire universe. Could it give some handle of dark energy (scalar field)? Many modern theories predict other scalar particles like the Higgs. Why, after all, should the Higgs be the only one of its kind? [The] LHC can search for and study new scalars with precision.”
Insight intocosmic inflation There has been considerable scientific research on possible links between the Higgs field and the inflaton – a hypothetical field suggested as the explanation for the expansion of space during the first fraction of a second of the universe (known as the “inflationary epoch“). Some theories suggest that a fundamental scalar field might be responsible for this phenomenon; the Higgs field is such a field and therefore has led to papers analysing whether it could also be the inflatonresponsible for this exponential expansion of the universe during the Big 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, a Brans–Dicke scalar, or other “new” physics, and have received treatments suggesting that Higgs inflation models are still of interest theoretically.
Insight into the nature of the universe, and itspossible fates
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 on Tevatron and LHC data still allows for both possibilities.[22]

For decades, scientific models of our universe have included the possibility that it exists as a long-lived, but not completely stable, sector of space, which could potentially at some time be destroyed upon ‘toppling‘ into a more stable vacuum state.[23][24][25][26][27] If the masses of the Higgs boson and top quark are known more exactly, and the Standard Model provides a correct description of particle physics up to extreme energies of the Planck scale, then it is possible to calculate whether the universe’s present vacuum state is stable or merely long-lived.[28][29][30](This was sometimes misreported as the Higgs boson “ending” the universe[34]). A125 – 127 GeV Higgs mass seems to be extremely close to the boundary for stability (estimated in 2012 as 123.8 – 135.0 GeV[22]) but a definitive answer requires much more precise measurements of the top quark’s pole mass.[22]

If measurements of the Higgs boson suggest that our universe lies within a false vacuum of this kind, then it would imply – more than likely in many billions of years[35][Note 8] – that the universe’s forces, particles, and structures could cease to exist as we know them (and be replaced by different ones), if a true vacuum happened to nucleate.[35][Note 9] It also suggests that the Higgs self-coupling λ and its βλ function could be very close to zero at the Planck scale, with “intriguing” implications, including theories of gravity and Higgs-based inflation.[22]:218[37][38] A future electron–positron collider would be able to provide the precise measurements of the top quark needed for such calculations.[22]

Insight into the ‘energy of the vacuum’ More speculatively, the Higgs field has also been proposed as the energy of the vacuum, which at the extreme energies of the first moments of the Big Bangcaused the universe to be a kind of featureless symmetry of undifferentiated extremely high energy. In this kind of speculation, the single unified field of a Grand Unified Theory is identified as (or modeled upon) the Higgs field, and it is through successive symmetry breakings of the Higgs field or some similar field atphase transitions that the present universe’s known forces and fields arise.[39]
Link to the‘cosmological constant’ problem The relationship (if any) between the Higgs field and the presently observed vacuum energy density of the universe has also come under scientific study. As observed, the present vacuum energy density is extremely close to zero, but the energy density expected from the Higgs field, supersymmetry, and other current theories are typically many orders of magnitude larger. It is unclear how these should be reconciled. This cosmological constant problem remains a further majorunanswered problem in physics.

Further information: Zero-point energy and Vacuum state

“Real world” impact[edit]

As yet, there are no known immediate technological benefits of finding the Higgs particle. However, observers in both media and science point out that when fundamental discoveries are made about our world, their practical uses can take decades to emerge, but are often world-changing when they do.[40][41][42] A common pattern for fundamental discoveries is for practical applications to follow later, once the discovery has been explored further, at which point they become the basis for social change and new technologies.

For example, in the first half of the 20th century it was not expected that quantum mechanics would make possible transistors and microchips, mobile phones andcomputers, lasers and M.R.I. scanners.[43] Radio waves were described by their co-discoverer in 1888 as “an interesting laboratory experiment” with “no useful purpose” whatsoever,[44] and are now used in innumerable ways (radar, weather prediction, medicine, television, wireless computing and emergency response),positrons are used in hospital tomography scans, and special and general relativity, which explain black holes also enable satellite-based GPS and satellite navigation (“satnav”).[43] Electric power generation and transmission, motors, and lighting all stemmed from previous theoretical work on electricity andmagnetism; air conditioning and refrigeration resulted from thermodynamics. It is impossible to predict how seemingly esoteric knowledge may affect society in the future.[40][42]

Other observers highlight technological spin-offs from this and related particle physics activities, which have already brought major developments to society. For example, the World Wide Web as used today was created by physicists working in global collaborations on particle experiments at CERN to share their results, and the results of massive amounts of data produced by the Large Hadron Collider have already led to significant advances in distributed and cloud computing, now well established within mainstream services.[41]

Stephen Hawking in the preface of his book Starmus wrote, “The Higgs potential has the worrisome feature that it might become metastable at energies above 100bn gigaelectronvolts. This could mean that the universe could undergo catastrophic vacuum decay, with a bubble of the true vacuum expanding at the speed of light. This could happen at any time and we wouldn’t see it coming.” Hawking however clarified that the only way to accelerate particles above 100bn gigaelectronvolts was with a particle accelerator larger than the Earth.[45][46]


AIP-Sakurai-best.JPG  Higgs, Peter (1929) cropped.jpg
The six authors of the 1964 PRL papers, who received the 2010 J. J. Sakurai Prize for their work. From left to right: Kibble, Guralnik,Hagen, Englert, Brout. Right: Higgs.


Nobel Prize Laureate Peter Higgs in Stockholm, December 2013

Particle physicists study matter made from fundamental particles whose interactions are mediated by exchange particles – gauge bosons – acting as force carriers. At the beginning of the 1960s a number of these particles had been discovered or proposed, along with theories suggesting how they relate to each other, some of which had already been reformulated as field theories in which the objects of study are not particles and forces, but quantum fields and their symmetries.[47]:150 However,attempts to unify known fundamental forces such as the electromagnetic force and the weak nuclear force were known to be incomplete. One known omission was that gauge invariant approaches, including non-abelian models such as Yang–Mills theory (1954), which held great promise for unified theories, also seemed to predict known massive particles as massless.[48] Goldstone’s theorem, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions,[49] since it appeared to show that zero-mass particles would have to also exist that were “simply not seen”.[50] According to Guralnik, physicists had “no understanding” how these problems could be overcome.[50]

Particle physicist and mathematician Peter Woit summarised the state of research at the time:

“Yang and Mills work on non-abelian gauge theory had one huge problem: in perturbation theory it has massless particles which don’t correspond to anything we see. One way of getting rid of this problem is now fairly well-understood, the phenomenon of confinement realized in QCD, where the strong interactions get rid of the massless “gluon” states at long distances. By the very early sixties, people had begun to understand another source of massless particles: spontaneous symmetry breaking of a continuous symmetry. What Philip Anderson realized and worked out in the summer of 1962 was that, when you have both gauge symmetry and spontaneous symmetry breaking, the Nambu–Goldstone massless mode can combine with the massless gauge field modes to produce a physical massive vector field. This is what happens in superconductivity, a subject about which Anderson was (and is) one of the leading experts.” [text condensed] [48]

The Higgs mechanism is a process by which vector bosons can get rest mass without explicitly breaking gauge invariance, as a byproduct of spontaneous symmetry breaking.[51][52] The mathematical theory behind spontaneous symmetry breaking was initially conceived and published within particle physics by Yoichiro Nambu in 1960,[53] 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[54] and concluded in his 1963 paper on Yang-Mills theory that “considering the superconducting analog… [t]hese two types of bosons seem capable of canceling each other out… leaving finite mass bosons”),[55]:4–5[56] and Abraham Klein and Benjamin Lee showed in March 1964 that Goldstone’s theorem could be avoided this way in at least some non-relativistic cases and speculated it might be possible in truly relativistic cases.[57]

These approaches were quickly developed into a full relativistic model, independently and almost simultaneously, by three groups of physicists: by François Englert and Robert Brout in August 1964;[58] by Peter Higgs in October 1964;[59] and by Gerald Guralnik, Carl Hagen, and Tom Kibble (GHK) in November 1964.[60] Higgs also wrote a short but important[51] response published in September 1964 to an objection by Gilbert,[61] which showed that if calculating within the radiation gauge, Goldstone’s theorem and Gilbert’s objection would become inapplicable.[Note 10] (Higgs later described Gilbert’s objection as prompting his own paper.[62]) Properties of the model were further considered by Guralnik in 1965,[63] by Higgs in 1966,[64] by Kibble in 1967,[65] and further by GHK in 1967.[66] The original three 1964 papers showed that when a gauge theory is combined with an additional field that spontaneously breaks the symmetry, the gauge bosons can consistently acquire a finite mass.[51][52][67] In 1967, Steven Weinberg[68] and Abdus Salam[69] independently showed how a Higgs mechanism could be used to break the electroweak symmetry of Sheldon Glashow‘s unified model for the weak and electromagnetic interactions[70] (itself an extension of work by Schwinger), forming what became the Standard Model of particle physics. Weinberg was the first to observe that this would also provide mass terms for the fermions.[71] [Note 11]

However, the seminal papers on spontaneous breaking of gauge symmetries were at first largely ignored, because it was widely believed that the (non-Abelian gauge) theories in question were a dead-end, and in particular that they could not be renormalised. In 1971–72, Martinus Veltman and Gerard ‘t Hooft proved renormalisation of Yang–Mills was possible in two papers covering massless, and then massive, fields.[71] Their contribution, and others’ work on therenormalization group – including “substantial” theoretical work by Russian physicists[72] – was eventually “enormously profound and influential”,[73] 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[74] – now the most cited in particle physics[75] – 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.[73] In practice, Politzer states, almost everyone learned of the theory due to physicist Benjamin Lee, who combined the work of Veltman and ‘t Hooft with insights by others, and popularised the completed theory.[73] In this way, from 1971, interest and acceptance “exploded” [73] and the ideas were quickly absorbed in the mainstream.[71][73]

The resulting electroweak theory and Standard Model have correctly predicted (among other discoveries) weak neutral currents, three bosons, the top and charm quarks, and with great precision, the mass and other properties of some of these.[Note 7] Many of those involved eventually won Nobel Prizes or other renowned awards. A 1974 paper and comprehensive review in Reviews of Modern Physics commented that “while no one doubted the [mathematical] correctness of these arguments, no one quite believed that nature was diabolically clever enough to take advantage of them”,[76]:9 adding that the theory had so far produced meaningful answers that accorded with experiment, but it was unknown whether the theory was actually correct.[76]:9,36(footnote),43–44,47 By 1986 and again in the 1990s it became possible to write that understanding and proving the Higgs sector of the Standard Model was “the central problem today in particle physics.” [77][78]

Summary and impact of the PRL papers[edit]

The three papers written in 1964 were each recognised as milestone papers during Physical Review Letters‘s 50th anniversary celebration.[67] Their six authors were also awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work.[79] (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.[80] ) Two of the three PRL papers (by Higgs and by GHK) contained equations for the hypothetical field that eventually would become known as the Higgs field and its hypothetical quantum, the Higgs boson.[59][60] Higgs’ subsequent 1966 paper showed the decay mechanism of the boson; only a massive boson can decay and the decays can prove the mechanism.[citation needed]

In the paper by Higgs the boson is massive, and in a closing sentence Higgs writes that “an essential feature” of the theory “is the prediction of incomplete multiplets of scalar and vector bosons“.[59] (Frank Close comments that 1960s gauge theorists were focused on the problem of massless vector bosons, and the implied existence of a massive scalar boson was not seen as important; only Higgs directly addressed it.[81]:154, 166, 175) In the paper by GHK the boson is massless and decoupled from the massive states.[60] In reviews dated 2009 and 2011, Guralnik states that in the GHK model the boson is massless only in a lowest-order approximation, but it is not subject to any constraint and acquires mass at higher orders, and adds that the GHK paper was the only one to show that there are no massless Goldstone bosons in the model and to give a complete analysis of the general Higgs mechanism.[50][82] All three reached similar conclusions, despite their very different approaches: Higgs’ paper essentially used classical techniques, Englert and Brout’s involved calculating vacuum polarization in perturbation theory around an assumed symmetry-breaking vacuum state, and GHK used operator formalism and conservation laws to explore in depth the ways in which Goldstone’s theorem may be worked around.[51]

In addition to explaining how mass is acquired by vector bosons, the Higgs mechanism also predicts the ratio between the W boson and Z boson masses as well as their couplings with each other and with the Standard Model quarks and leptons.[citation needed] Subsequently, many of these predictions have been verified by precise measurements performed at the LEP and the SLC colliders, thus overwhelmingly confirming that some kind of Higgs mechanism does take place in nature,[83] but the exact manner by which it happens has not yet been discovered.[citation needed] The results of searching for the Higgs boson are expected to provide evidence about how this is realized in nature.[citation needed]

Theoretical properties[edit]

Main article: Higgs mechanism

Theoretical need for the Higgs[edit]


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

Gauge invariance is an important property of modern particle theories such as the Standard Model, partly due to its success in other areas of fundamental physics such as electromagnetism and the strong interaction (quantum chromodynamics). However, there were great difficulties in developing gauge theories for the weak nuclear force or a possible unified electroweak interaction. Fermions with a mass term would violate gauge symmetry and therefore cannot be gauge invariant. (This can be seen by examining the Dirac Lagrangian for a fermion in terms of left and right handed components; we find none of the spin-half particles could ever flip helicity as required for mass, so they must be massless.[Note 12]) W and Z bosons are observed to have mass, but a boson mass term contains terms, which clearly depend on the choice of gauge and therefore these masses too cannot be gauge invariant. Therefore it seems that none of the standard model fermions or bosons could “begin” with mass as an inbuilt property except by abandoning gauge invariance. If gauge invariance were to be retained, then these particles had to be acquiring their mass by some other mechanism or interaction. Additionally, whatever was giving these particles their mass, had to not “break” gauge invariance as the basis for other parts of the theories where it worked well, and had to not require or predict unexpected massless particles and long-range forces (seemingly an inevitable consequence ofGoldstone’s theorem) which did not actually seem to exist in nature.

A solution to all of these overlapping problems came from the discovery of a previously unnoticed borderline case hidden in the mathematics of Goldstone’s theorem,[Note 10] that under certain conditions it might theoretically be possible for a symmetry to be broken without disrupting gauge invariance and without any new massless particles or forces, and having “sensible” (renormalisable) results mathematically: this became known as the Higgs mechanism.

The Standard Model hypothesizes a field which is responsible for this effect, called the Higgs field (symbol: \phi), which has the unusual property of a non-zero amplitude in its ground state; i.e., a non-zero vacuum expectation value. It can have this effect because of its unusual “Mexican hat” shaped potential whose lowest “point” is not at its “centre”. Below a certain extremely high energy level the existence of this non-zero vacuum expectation spontaneously breakselectroweak gauge symmetry which in turn gives rise to the Higgs mechanism and triggers the acquisition of mass by those particles interacting with the field. This effect occurs because scalar field components of the Higgs field are “absorbed” by the massive bosons as degrees of freedom, and couple to the fermions viaYukawa coupling, thereby producing the expected mass terms. In effect when symmetry breaks under these conditions, the Goldstone bosons that arise interactwith the Higgs field (and with other particles capable of interacting with the Higgs field) instead of becoming new massless particles, the intractable problems of both underlying theories “neutralise” each other, and the residual outcome is that elementary particles acquire a consistent mass based on how strongly they interact with the Higgs field. It is the simplest known process capable of giving mass to the gauge bosons while remaining compatible with gauge theories.[84] Itsquantum would be a scalar boson, known as the Higgs boson.[85]


Summary of interactions between certainparticles described by the Standard Model.

Properties of the Standard Model Higgs[edit]

In the Standard Model, the Higgs field consists of four components, two neutral ones and two charged componentfields. Both of the charged components and one of the neutral fields are Goldstone bosons, which act as the longitudinal third-polarization components of the massive W+, W, and Z bosons. The quantum of the remaining neutral component corresponds to (and is theoretically realised as) the massive Higgs boson.[86] Since the Higgs field is a scalar field (meaning it does not transform under Lorentz transformations), the Higgs boson has no spin. The Higgs boson is also its own antiparticle and is CP-even, and has zero electric and colour charge.[87]

The Minimal Standard Model does not predict the mass of the Higgs boson.[88] If that mass is between 115 and180 GeV/c2, then the Standard Model can be valid at energy scales all the way up to the Planck scale (1019GeV).[89] Many theorists expect new physics beyond the Standard Model to emerge at the TeV-scale, based on unsatisfactory properties of the Standard Model.[90] The highest possible mass scale allowed for the Higgs boson (or some other electroweak symmetry breaking mechanism) is 1.4 TeV; beyond this point, the Standard Model becomes inconsistent without such a mechanism, because unitarity is violated in certain scattering processes.[91]

It is also possible, although experimentally difficult, to estimate the mass of the Higgs boson indirectly. In the Standard Model, the Higgs boson has a number of indirect effects; most notably, Higgs loops result in tiny corrections to masses of W and Z bosons. Precision measurements of electroweak parameters, such as the Fermi constant and masses of W/Z bosons, can be used to calculate constraints on the mass of the Higgs. As of July 2011, the precision electroweak measurements tell us that the mass of the Higgs boson is likely to be less than about 161 GeV/c2 at 95% confidence level (this upper limit would increase to185 GeV/c2 if the lower bound of 114.4 GeV/c2 from the LEP-2 direct search is allowed for[83]). These indirect constraints rely on the assumption that the Standard Model is correct. It may still be possible to discover a Higgs boson above these masses if it is accompanied by other particles beyond those predicted by the Standard Model.[92]


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

If Higgs particle theories are correct, then a Higgs particle can be produced much like other particles that are studied, in a particle collider. This involves accelerating a large number of particles to extremely high energies and extremely close to the speed of light, then allowing them to smash together. Protons and leadions (the bare nuclei of lead atoms) are used at the LHC. In the extreme energies of these collisions, the desired esoteric particles will occasionally be produced and this can be detected and studied; any absence or difference from theoretical expectations can also be used to improve the theory. The relevant particle theory (in this case the Standard Model) will determine the necessary kinds of collisions and detectors. The Standard Model predicts that Higgs bosons could be formed in a number of ways,[93][94][95] although the probability of producing a Higgs boson in any collision is always expected to be very small—for example, only 1 Higgs boson per 10 billion collisions in the Large Hadron Collider.[Note 13] The most common expected processes for Higgs boson production are:

  • Gluon fusion. If the collided particles are hadrons such as the proton or antiproton—as is the case in the LHC and Tevatron—then it is most likely that two of the gluons binding the hadron together collide. The easiest way to produce a Higgs particle is if the two gluons combine to form a loop of virtual quarks. Since the coupling of particles to the Higgs boson is proportional to their mass, this process is more likely for heavy particles. In practice it is enough to consider the contributions of virtual top and bottom quarks (the heaviest quarks). This process is the dominant contribution at the LHC and Tevatron being about ten times more likely than any of the other processes.[93][94]
  • Higgs Strahlung. If an elementary fermion collides with an anti-fermion—e.g., a quark with an anti-quark or an electron with a positron—the two can merge to form a virtual W or Z boson which, if it carries sufficient energy, can then emit a Higgs boson. This process was the dominant production mode at the LEP, where an electron and a positron collided to form a virtual Z boson, and it was the second largest contribution for Higgs production at the Tevatron. At the LHC this process is only the third largest, because the LHC collides protons with protons, making a quark-antiquark collision less likely than at the Tevatron. Higgs Strahlung is also known as associated production.[93][94][95]
  • Weak boson fusion. Another possibility when two (anti-)fermions collide is that the two exchange a virtual W or Z boson, which emits a Higgs boson. The colliding fermions do not need to be the same type. So, for example, an up quark may exchange a Z boson with an anti-down quark. This process is the second most important for the production of Higgs particle at the LHC and LEP.[93][95]
  • 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.[93][94]



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

Quantum mechanics predicts that if it is possible for a particle to decay into a set of lighter particles, then it will eventually do so.[97] This is also true for the Higgs boson. The likelihood with which this happens depends on a variety of factors including: the difference in mass, the strength of the interactions, etc. Most of these factors are fixed by the Standard Model, except for the mass of the Higgs boson itself. For a Higgs boson with a mass of 126 GeV/c2 the SM predicts a mean life time of about 1.6×10−22 s.[Note 2]


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

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

One way that the Higgs can decay is by splitting into a fermion–antifermion pair. As general rule, the Higgs is more likely to decay into heavy fermions than light fermions, because the mass of a fermion is proportional to the strength of its interaction with the Higgs.[99] By this logic the most common decay should be into a top–antitop quark pair. However, such a decay is only possible if the Higgs is heavier than ~346 GeV/c2, twice the mass of the top quark. For a Higgs mass of 126 GeV/c2 the SM predicts that the most common decay is into abottom–antibottom quark pair, which happens 56.1% of the time.[98] The second most common fermion decay at that mass is a tau–antitau pair, which happens only about 6% of the time.[98]

Another possibility is for the Higgs to split into a pair of massive gauge bosons. The most likely possibility is for the Higgs to decay into a pair of W bosons (the light blue line in the plot), which happens about 23.1% of the time for a Higgs boson with a mass of 126 GeV/c2.[98] The W bosons can subsequently decay either into a quark and an antiquark or into a charged lepton and a neutrino. However, the decays of W bosons into quarks are difficult to distinguish from the background, and the decays into leptons cannot be fully reconstructed (because neutrinos are impossible to detect in particle collision experiments). A cleaner signal is given by decay into a pair of Z-bosons (which happens about 2.9% of the time for a Higgs with a mass of126 GeV/c2),[98] if each of the bosons subsequently decays into a pair of easy-to-detect charged leptons (electrons or muons).

Decay into massless gauge bosons (i.e., gluons or photons) is also possible, but requires intermediate loop of virtual heavy quarks (top or bottom) or massive gauge bosons.[99] The most common such process is the decay into a pair of gluons through a loop of virtual heavy quarks. This process, which is the reverse of the gluon fusion process mentioned above, happens approximately 8.5% of the time for a Higgs boson with a mass of 126 GeV/c2.[98] 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.[98] 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.[99]

Alternative models[edit]

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

The key method to distinguish between these different models involves study of the particles’ interactions (“coupling”) and exact decay processes (“branching ratios”), which can be measured and tested experimentally in particle collisions. In the Type-I 2HDM model one Higgs doublet couples to up and down quarks, while the second doublet does not couple to quarks. This model has two interesting limits, in which the lightest Higgs couples to just fermions (“gauge-phobic“) or just gauge bosons (“fermiophobic”), but not both. In the Type-II 2HDM model, one Higgs doublet only couples to up-type quarks, the other only couples to down-type quarks.[100] The heavily researched Minimal Supersymmetric Standard Model (MSSM) includes a Type-II 2HDM Higgs sector, so it could be disproven by evidence of a Type-I 2HDM Higgs.[citation needed]

In other models the Higgs scalar is a composite particle. For example, in technicolor the role of the Higgs field is played by strongly bound pairs of fermions calledtechniquarks. Other models, feature pairs of top quarks (see top quark condensate). In yet other models, there is no Higgs field at all and the electroweak symmetry is broken using extra dimensions.[101][102]


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

Further theoretical issues and hierarchy problem[edit]

The Standard Model leaves the mass of the Higgs boson as a parameter to be measured, rather than a value to be calculated. This is seen as theoretically unsatisfactory, particularly as quantum corrections (related to interactions 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 mass of the order of 100 to 1000 GeV to ensure unitarity (in this case, to unitarise longitudinal vector boson scattering).[103] Reconciling these points appears to require explaining why there is an almost-perfect cancellation resulting in the visible mass of ~ 125 GeV, and it is not clear how to do this. Because the weak force is about 1032 times stronger than gravity, and (linked to this) the Higgs boson’s mass is so much less than thePlanck mass or the grand unification energy, it appears that either there is some underlying connection or reason for these observations which is unknown and not described by the Standard Model, or some unexplained and extremely precise fine-tuning of parameters – however at present neither of these explanations is proven. This is known as a hierarchy problem.[104] More broadly, the hierarchy problem amounts to the worry that a future theory of fundamental particles and interactions should not have excessive fine-tunings or unduly delicate cancellations, and should allow masses of particles such as the Higgs boson to be calculable. The problem is in some ways unique to spin-0 particles (such as the Higgs boson), which can give rise to issues related to quantum corrections that do not affect particles with spin.[103] A number of solutions have been proposed, including supersymmetry, conformal solutions and solutions via extra dimensions such as braneworld models.

Experimental search[edit]

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

Because Higgs boson production in a particle collision is likely to be very rare (1 in 10 billion at the LHC),[Note 13] and many other possible collision events can have similar decay signatures, the data of hundreds of trillions of collisions needs to be analysed and must “show the same picture” before a conclusion about the existence of the Higgs boson can be reached. To conclude that a new particle has been found, particle physicists require that the statistical analysis of two independent particle detectors each indicate that there is lesser than a one-in-a-million chance that the observed decay signatures are due to just background random Standard Model events—i.e., that the observed number of events is more than 5 standard deviations (sigma) different from that expected if there was no new particle. More collision data allows better confirmation of the physical properties of any new particle observed, and allows physicists to decide whether it is indeed a Higgs boson as described by the Standard Model or some other hypothetical new particle.

To find the Higgs boson, a powerful particle accelerator was needed, because Higgs bosons might not be seen in lower-energy experiments. The collider needed to have a high luminosity in order to ensure enough collisions were seen for conclusions to be drawn. Finally, advanced computing facilities were needed to process the vast amount of data (25 petabytes per year as at 2012) produced by the collisions.[105] For the announcement of 4 July 2012, a new collider known as the Large Hadron Collider was constructed at CERN with a planned eventual collision energy of 14 TeV—over seven times any previous collider—and over 300 trillion (3×1014) LHC proton–proton collisions were analysed by the LHC Computing Grid, the world’s largest computing grid (as of 2012), comprising over 170 computing facilities in a worldwide network across 36 countries.[105][106][107]

Search prior to 4 July 2012[edit]

The first extensive search for the Higgs boson was conducted at the Large Electron–Positron Collider (LEP) at CERN in the 1990s. At the end of its service in 2000, LEP had found no conclusive evidence for the Higgs.[Note 14] This implied that if the Higgs boson were to exist it would have to be heavier than114.4 GeV/c2.[108]

The search continued at Fermilab in the United States, where the Tevatron—the collider that discovered the top quark in 1995—had been upgraded for this purpose. There was no guarantee that the Tevatron would be able to find the Higgs, but it was the only supercollider that was operational since the Large Hadron Collider (LHC) was still under construction and the planned Superconducting Super Collider had been cancelled in 1993 and never completed. The Tevatron was only able to exclude further ranges for the Higgs mass, and was shut down on 30 September 2011 because it no longer could keep up with the LHC. The final analysis of the data excluded the possibility of a Higgs boson with a mass between 147 GeV/c2 and 180 GeV/c2. In addition, there was a small (but not significant) excess of events possibly indicating a Higgs boson with a mass between 115 GeV/c2 and 140 GeV/c2.[109]

The Large Hadron Collider at CERN in Switzerland, was designed specifically to be able to either confirm or exclude the existence of the Higgs boson. Built in a 27 km tunnel under the ground near Geneva originally inhabited by LEP, it was designed to collide two beams of protons, initially at energies of 3.5 TeV per beam (7 TeV total), or almost 3.6 times that of the Tevatron, and upgradeable to 2 × 7 TeV (14 TeV total) in future. Theory suggested if the Higgs boson existed, collisions at these energy levels should be able to reveal it. As one of the most complicated scientific instruments ever built, its operational readiness was delayed for 14 months by a magnet quench event nine days after its inaugural tests, caused by a faulty electrical connection that damaged over 50 superconducting magnets and contaminated the vacuum system.[110][111][112]

Data collection at the LHC finally commenced in March 2010.[113] By December 2011 the two main particle detectors at the LHC, ATLAS and CMS, had narrowed down the mass range where the Higgs could exist to around 116-130 GeV (ATLAS) and 115-127 GeV (CMS).[114][115] 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,[116] both experiments had seen among their results, the slow emergence of a small yet consistent excess of gamma and 4-lepton decay signatures and several other particle decays, all hinting at a new particle at a mass around 125 GeV.[116] By around November 2011, the anomalous data at 125 GeV was becoming “too large to ignore” (although still far from conclusive), and the team leaders at both ATLAS and CMS each privately suspected they might have found the Higgs.[116] On November 28, 2011, at an internal meeting of the two team leaders and the director general of CERN, the latest analyses were discussed outside their teams for the first time, suggesting both ATLAS and CMS might be converging on a possible shared result at 125 GeV, and initial preparations commenced in case of a successful finding.[116] While this information was not known publicly at the time, the narrowing of the possible Higgs range to around 115–130 GeV and the repeated observation of small but consistent event excesses across multiple channels at both ATLAS and CMS in the 124-126 GeV region (described as “tantalising hints” of around 2-3 sigma) were public knowledge with “a lot of interest”.[117] 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.[117][118]

Discovery of candidate boson at CERN[edit]

2-photon Higgs decay.svg  4-lepton Higgs decay.svg
Feynman diagrams showing the cleanest channels associated with the low-mass (~125 GeV), Higgs boson candidate observed by ATLAS and CMS at the LHC. The dominant production mechanism at this mass involves two gluons from each proton fusing to a Top-quark Loop, which couples strongly to the Higgs field to produce a Higgs boson.Left: Diphoton channel: Boson subsequently decays into 2 gamma ray photons by virtual interaction with a W boson loop or top quark loop.Right: 4-Lepton “golden channel”: Boson emits 2 Z bosons, which each decay into 2leptons (electrons, muons).

Experimental analysis of these channels reached a significance of 5-sigma.[119][120] The analysis of additional vector boson fusion channels brought the CMS significance to 4.9-sigma.[119][120]

On 22 June 2012 CERN announced an upcoming seminar covering tentative findings for 2012,[121][122] and shortly afterwards (from around 1 July 2012 according to an analysis of the spreading rumour in social media[123]) 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.[124][125]Speculation escalated to a “fevered” pitch when reports emerged that Peter Higgs, who proposed the particle, was to be attending the seminar,[126][127] 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).[128][129])

On 4 July 2012 both of the CERN experiments announced they had independently made the same discovery:[130] CMS of a previously unknown boson with mass 125.3 ± 0.6 GeV/c2[119][120] and ATLAS of a boson with mass 126.0 ± 0.6 GeV/c2.[131][132] Using the combined analysis of two interaction types (known as ‘channels’), both experiments independently reached a local significance of 5-sigma —- less than a one in three-and-a-half million chance of error. When additional channels were taken into account, the CMS significance was reduced to 4.9-sigma.[120]

The two teams had been working ‘blinded’ from each other from around late 2011 or early 2012,[116] meaning they did not discuss their results with each other, providing additional certainty that any common finding was genuine validation of a particle.[105] 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 being due to random background effects) and mass 126.0 ± 0.4 (stat) ± 0.4 (sys) GeV/c2, [132]and CMS improved the significance to 5-sigma and mass 125.3 ± 0.4 (stat) ± 0.5 (sys) GeV/c2.[119]

The new particle tested as a possible Higgs boson[edit]

Following the 2012 discovery, it was still unconfirmed whether or not the 125 GeV/c2 particle was a Higgs boson. On one hand, observations remained consistent with the observed particle being the Standard Model Higgs boson, and the particle decayed into at least some of the predicted channels. Moreover, the production rates and branching ratios for the observed channels broadly matched the predictions by the Standard Model within the experimental uncertainties. However, the experimental uncertainties currently still left room for alternative explanations, meaning an announcement of the discovery of a Higgs boson would have been premature.[99] To allow more opportunity for data collection, the LHC’s proposed 2012 shutdown and 2013–14 upgrade were postponed by 7 weeks into 2013.[133]

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.[134] Physicist Matt Strassler highlighted “considerable” evidence that the new particle is not a pseudoscalar negative parity particle (consistent with this required finding for a Higgs boson), “evaporation” or lack of increased significance for previous hints of non-Standard Model findings, expected Standard Model interactions with W and Z bosons, absence of “significant new implications” for or against supersymmetry, and in general no significant deviations to date from the results expected of a Standard Model Higgs boson.[135]However some kinds of extensions to the Standard Model would also show very similar results;[136] 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.[134][135]

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,[9][11] and scientists did not yet positively say it was the Higgs boson.[137] Despite this, in late 2012, widespread media reports announced (incorrectly) that a Higgs boson had been confirmed during the year.[143]

In January 2013, CERN director-general Rolf-Dieter Heuer stated that based on data analysis to date, an answer could be possible ‘towards’ mid-2013,[144] and the deputy chair of physics at Brookhaven National Laboratory stated in February 2013 that a “definitive” answer might require “another few years” after thecollider’s 2015 restart.[145] 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.[146]

Confirmation of new particle as a Higgs boson, and current status[edit]

On 14 March 2013 CERN confirmed that:

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

This also makes the particle the first elementary scalar particle to be discovered in nature.[12]

Examples of tests used to validate whether the 125 GeV particle is a Higgs boson:[135][147]

Requirement How tested / explanation Current status (March 2013)
Zero spin Examining decay patterns. Spin-1 had been ruled out at the time of initial discovery by the observed decay to two photons (γ γ), leaving spin-0 and spin-2 as remaining candidates. Spin-0 tentatively confirmed.[1][148][149] Spin-0 tentatively confirmed.[148][149] The spin-2 hypothesis is excluded with a confidence level exceeding 99.9%.[149]
+ and not  parity Studying the angles at which decay products fly apart. Negative parity was also disfavoured if spin-0 was confirmed.[150] Positive parity tentatively confirmed.[1][148][149] The spin-0 negative parity hypothesis is excluded with a confidence level exceeding 99.9%.[148]
Decay channels (outcomes of particle decaying) are as predicted The Standard Model predicts the decay patterns of a 125–126 GeV Higgs boson. Are these all being seen, and at the right rates?Particularly significant, we should observe decays into pairs of photons (γ γ), W and Z bosons (WW and ZZ), bottom quarks (bb), and tau leptons (τ τ), among the possible outcomes. γ γ, τ τ,[151] WW and ZZ observed; bb not yet confirmed. Some branching levels (decay rates) are a little higher than expected in preliminary results, in particular H → γ γ, which gives a peak at ATLASa little higher than that seen in 4-lepton decays and at CMS.[152]
Couples to mass
(i.e., interacts with particles that have mass)
Particle physicist Adam Falkowski states that the essential qualities of a Higgs boson are that it is a spin-0 (scalar) particle which also couples to mass (W and Z bosons); proving spin-0 alone is insufficient.[147] Couplings to mass strongly evidenced (“At 95% confidence level cV is within 15% of the standard model value cV=1″).[147]
Higher energy results remain consistent After the LHC’s 2015 restart at the LHC’s full planned energies of 13 – 14 TeV, searches for multiple Higgs particles (as predicted in some theories) and tests targeting other versions of particle theory will take place. These higher energy results must continue to give results consistent with Higgs theories To be studied following LHC upgrade

Public discussion[edit]


Names used by physicists[edit]

The name most strongly associated with the particle and field is the Higgs boson[81]:168 and Higgs field. For some time the particle was known by a combination of its PRL author names (including at times Anderson), for example the Brout–Englert–Higgs particle, the Anderson-Higgs particle, or the Englert–Brout–Higgs–Guralnik–Hagen–Kibble mechanism,[Note 15] and these are still used at times.[51][154] Fueled in part by the issue of recognition and a potential shared Nobel Prize,[154][155] the most appropriate name is still occasionally a topic of debate as at 2012.[154] (Higgs himself prefers to call the particle either by an acronym of all those involved, or “the scalar boson”, or “the so-called Higgs particle”.[155])

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

Reason Basis of explanation
Higgs undertook a step which was either unique, clearer or more explicit in his paper, in formally predicting and examining the particle. Of the PRL papers’ authors, only the paper by Higgs explicitly offered as a prediction, that a massive particle would exist, and calculated some of its properties;[81]:167[156] he was therefore “the first to postulate the existence of a massive particle” according to Nature.[154] Physicist and author Frank Closeand physicist-blogger Peter Woit both comment that the paper by GHK was also completed after Higgs and Brout–Englert were submitted to Physical Review Letters.[81]:167[157] and that Higgs alone had drawn attention to a predicted massive scalar boson, while all others had focused on the massive vectorbosons;[81]:154, 166, 175[157] In this way, Higgs’ contribution also provided experimentalists with a crucial “concrete target” needed to test the theory.[158]However in Higgs’ view, Brout and Englert did not explicitly mention the boson since its existence is plainly obvious in their work,[55]:6 while according to Guralnik the GHK paper was a complete analysis of the entire symmetry breaking mechanism whose mathematical rigour is absent from the other two papers, and a massive particle may exist in some solutions.[82]:9 Higgs’ paper also provided an “especially sharp” statement of the challenge and its solution according to science historian David Kaiser.[155]
The name was popularised in the 1970s due to its use as a convenient shorthand or because of a mistake in citing. Many accounts (including Higgs’ own[55]:7) credit the “Higgs” name to physicist Benjamin Lee (in Korean: Lee Whi-soh). Lee was a significant populist for the theory in its early stages, and habitually attached the name “Higgs” as a “convenient shorthand” for its components from 1972[13][154][159][160][161] and in at least one instance from as early as 1966.[163][81]:167 Although Lee clarified in his footnotes that “‘Higgs’ is an abbreviation for Higgs, Kibble, Guralnik, Hagen, Brout, Englert”,[161] his use of the term (and perhaps also Steven Weinberg’s mistaken cite of Higgs’ paper as the first in his seminal 1967 paper[81][162][163]) meant that by around 1975–76 others had also begun to use the name ‘Higgs’ exclusively as a shorthand.[164]


The Higgs boson is often referred to as the “God particle” in popular media outside the scientific community. The nickname comes from the title of a 1993 book on the Higgs boson and particle physics by Nobel Physics prizewinner and Fermilab director Leon Lederman.[17] Lederman wrote it in the context of failing US government support for the Superconducting Super Collider,[165] a part-constructed titanic[166][167] competitor to the Large Hadron Collider with planned collision energies of 2 × 20 TeV that was championed by Lederman since its 1983 inception[165][168][169] 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.[170]

While media use of this term may have contributed to wider awareness and interest,[171] many scientists feel the name is inappropriate[13][14][172] since it is sensational hyperbole and misleads readers;[173] the particle also has nothing to do with God,[173] leaves open numerous questions in fundamental physics, and does not explain the ultimate origin of the universe. Higgs, an atheist, was reported to be displeased and stated in a 2008 interview that he found it “embarrassing” because it was “the kind of misuse… which I think might offend some people”.[173][174][175] Science writer Ian Sample stated in his 2010 book on the search that the nickname is “universally hate[d]” by physicists and perhaps the “worst derided” in the history of physics, but that (according to Lederman) the publisher rejected all titles mentioning “Higgs” as unimaginative and too unknown.[176]

Lederman begins with a review of the long human search for knowledge, and explains that his tongue-in-cheek title draws an analogy between the impact of the Higgs field on the fundamental symmetries at the Big Bang, and the apparent chaos of structures, particles, forces and interactions that resulted and shaped our present universe, with the biblical story of Babel in which the primordial single language of early Genesis was fragmented into many disparate languages and cultures.[177]

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

—Leon M. Lederman and Dick Teresi, The God Particle: If the Universe is the Answer, What is the Question[17] p. 22

Lederman whimsically 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”.[178]

Other proposals[edit]

A renaming competition by British newspaper The Guardian in 2009 resulted in their science correspondent choosing the name “the champagne bottle boson” as the best submission: “The bottom of a champagne bottle is in the shape of the Higgs potential and is often used as an illustration in physics lectures. So it’s not an embarrassingly grandiose name, it is memorable, and [it] has some physics connection too.”[179] The name Higgson was suggested as well, in an opinion piece in the Institute of Physics‘ online publication[180]

Media explanations and analogies[edit]

There has been considerable public discussion of analogies and explanations for the Higgs particle and how the field creates mass,[181][182] including coverage of explanatory attempts in their own right and a competition in 1993 for the best popular explanation by then-UK Minister for Science Sir William Waldegrave[183] and articles in newspapers worldwide.


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

An educational collaboration involving an LHC physicist and a High School Teachers at CERN educator suggests thatdispersion of light – responsible for the rainbow and dispersive prism – is a useful analogy for the Higgs field’s symmetry breaking and mass-causing effect.[184]

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

Matt Strassler uses electric fields as an analogy:[185]

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

A similar explanation was offered by The Guardian:[186]

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

The Higgs field’s effect on particles was famously described by physicist David Miller as akin to a room full of political party workers spread evenly throughout a room: the crowd gravitates to and slows down famous people but does not slow down others.[Note 16] He also drew attention to well-known effects in solid state physics where an electron’s effective mass can be much greater than usual in the presence of a crystal lattice.[187]

Analogies based on drag effects, including analogies of “syrup” or “molasses” are also well known, but can be somewhat misleading since they may be understood (incorrectly) as saying that the Higgs field simply resists some particles’ motion but not others’ – a simple resistive effect could also conflict withNewton’s third law.[189]

Recognition and awards[edit]

There has been considerable discussion of how to allocate the credit if the Higgs boson is proven, made more pointed as a Nobel prize had been expected, and the very wide basis of people entitled to consideration. These include a range of theoreticians who made the Higgs mechanism theory possible, the theoreticians of the 1964 PRL papers (including Higgs himself), the theoreticians who derived from these, a working electroweak theory and the Standard Model itself, and also the experimentalists at CERN and other institutions who made possible the proof of the Higgs field and boson in reality. The Nobel prize has a limit of 3 persons to share an award, and some possible winners are already prize holders for other work, or are deceased (the prize is only awarded to persons in their lifetime). Existing prizes for works relating to the Higgs field, boson, or mechanism include:

  • Nobel Prize in Physics (1979) – Glashow, Salam, and Weinberg, for contributions to the theory of the unified weak and electromagnetic interaction between elementary particles [190]
  • Nobel Prize in Physics (1999) – ‘t Hooft and Veltman, for elucidating the quantum structure of electroweak interactions in physics [191]
  • Nobel Prize in Physics (2008) – Nambu (shared), for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics [53]
  • 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 [79] (for the 1964 papers described above)
  • Wolf Prize (2004) – Englert, Brout, and Higgs
  • Nobel Prize in Physics (2013) – Peter Higgs and François Englert, for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider [192]

Additionally Physical Review Letters‘ 50-year review (2008) recognized the 1964 PRL symmetry breaking papers and Weinberg’s 1967 paper A model of Leptons(the most cited paper in particle physics, as of 2012) “milestone Letters”.[75]

Following reported observation of the Higgs-like particle in July 2012, several Indian 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[193][194] (although physicists have described Bose’s connection to the discovery as tenuous).[195]

Technical aspects and mathematical formulation[edit]

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

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

while the field has charge +1/2 under the weak hypercharge U(1) symmetry (in the convention where the electric charge, Q, the weak isospin, I3, and the weak hypercharge, Y, are related by Q = I3 + Y).[196]


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

The Higgs part of the Lagrangian is[196]

\mathcal{L}_H = \left|\left(\partial_\mu -i g W_\mu^a \tau^a -i\frac{g'}{2} B_\mu\right)\phi\right|^2 + \mu^2 \phi^\dagger\phi-\lambda (\phi^\dagger\phi)^2,

where W_\mu^a and B_\mu are the gauge bosons of the SU(2) and U(1) symmetries, g and g' their respective coupling constants, \tau^a=\sigma^a/2 (where \sigma^a are the Pauli matrices) a complete set generators of the SU(2) symmetry, and \lambda>0 and \mu^{2}>0, so that the ground state breaks the SU(2) symmetry (see figure). The ground state of the Higgs field (the bottom of the potential) is degenerate with different ground states related to each other by a SU(2) gauge transformation. It is always possible to pick a gauge such that in the ground state \phi^1=\phi^2=\phi^3=0. The expectation value of \phi^0 in the ground state (the vacuum expectation value or vev) is then \langle\phi^0\rangle = v, where v = \tfrac{|\mu|}{\sqrt{\lambda}}. The measured value of this parameter is ~246 GeV/c2.[99] It has units of mass, and is the only free parameter of the Standard Model that is not a dimensionless number. Quadratic terms in W_{\mu} and B_{\mu} arise, which give masses to the Wand Z bosons:[196]

M_W = \frac{v|g|}2,

with their ratio determining the Weinberg angle, \cos \theta_W = \frac{M_W}{M_Z} = \frac{|g|}{\sqrt{g^2+{g'}^2}}, and leave a massless U(1) photon, \gamma.

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

\begin{align}\mathcal{L}_{Y} =<br />
&-\lambda_u^{ij}\frac{\phi^0-i\phi^3}{\sqrt{2}}\overline u_L^i  u_R^j<br />
+\lambda_u^{ij}\frac{\phi^1-i\phi^2}{\sqrt{2}}\overline d_L^i  u_R^j\\<br />
&-\lambda_d^{ij}\frac{\phi^0+i\phi^3}{\sqrt{2}}\overline d_L^i  d_R^j<br />
-\lambda_d^{ij}\frac{\phi^1+i\phi^2}{\sqrt{2}}\overline u_L^i  d_R^j\\<br />
&-\lambda_e^{ij}\frac{\phi^0+i\phi^3}{\sqrt{2}}\overline e_L^i  e_R^j<br />
-\lambda_e^{ij}\frac{\phi^1+i\phi^2}{\sqrt{2}}\overline \nu_L^i  e_R^j<br />
+ \textrm{h.c.},\end{align}

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

\mathcal{L}_{m} = -m_u^i\overline u_L^i  u_R^i -m_d^i\overline d_L^i  d_R^i -m_e^i\overline e_L^i  e_R^i+ \textrm{h.c.},

where the masses of the fermions are  m_{u,d,e}^i = \lambda_{u,d,e}^i v/\sqrt{2}, and  \lambda_{u,d,e}^i denote the eigenvalues of the Yukawa matrices.[196]

See also[edit]

Standard Model


  1. Jump up^ Note that such events also occur due to other processes. Detection involves astatistically significant excess of such events at specific energies.
  2. ^ Jump up to:a b In the Standard Model, the total decay width of a Higgs boson with a mass of 126 GeV/c2 is predicted to be 4.21×10−3 GeV.[98] The mean lifetime is given by \tau = \hbar/\Gamma.
  3. ^ Jump up to:a b The range of a force is inversely proportional to the mass of the particles transmitting it.[16] In the Standard Model, forces are carried by virtual particles. These particles’ movement and interactions with each other are limited by theenergy–time uncertainty principle. As a result, the more massive a single virtual particle is, the greater its energy, and therefore the shorter the distance it can travel. A particle’s mass therefore determines the maximum distance at which it can interact with other particles and on any force it mediates. By the same token, the reverse is also true: massless and near-massless particles can carry long distance forces. (See also: Compton wavelength and Static forces and virtual-particle exchange) Since experiments have shown that the weak force acts over only a very short range, this implies that there must exist massive gauge bosons. And indeed, their masses have since been confirmed by measurement.
  4. Jump up^ It is quite common for a law of physics to hold true only if certain assumptions held true or only under certain conditions. For example, Newton’s laws of motionapply only at speeds where relativistic effects are negligible; and laws related to conductivity, gases, and classical physics (as opposed to quantum mechanics) may apply only within certain ranges of size, temperature, pressure, or other conditions.
  5. Jump up^ Electroweak symmetry is broken by the Higgs field in its lowest energy state, called its “ground state“. At high energy levels this does not happen, and the gauge bosons of the weak force would therefore be expected to be massless.
  6. Jump up^ 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 far from fanciful. Against this, once the entire model was developed around 1972, no better theory yet existed, and its predictions and solutions were so accurate, that it became the preferred theory anyway. It then became crucial to science, to know whether it was correct.
  7. ^ Jump up to:a b c The success of the Higgs based electroweak theory and Standard Model is illustrated by their predictions of the mass of two particles later detected: the W boson (predicted mass: 80.390 ± 0.018 GeV, experimental measurement: 80.387 ± 0.019 GeV), and the Z boson (predicted mass: 91.1874 ± 0.0021, experimental measurement: 91.1876 ± 0.0021 GeV). The existence of the Z boson was itself another prediction. Other correct predictions included the weak neutral current, the gluon, and the top and charm quarks, all later proven to exist as the theory said.
  8. Jump up^ The bubble’s effects would be expected to propagate across the universe at the speed of light from wherever it occurred. However space is vast – with even the nearest galaxy being over 2 million lightyears from us, and others being many billions of lightyears distant, so the effect of such an event would be unlikely to arise here for billions of years after first occurring.[35][36]
  9. Jump up^ If the Standard Model is correct, then the particles and forces we observe in our universe exist as they do, because of underlying quantum fields. Quantum fields can have states of differing stability, including ‘stable’, ‘unstable’ and ‘metastable‘ states (the latter remain stable unless sufficiently perturbed). If a more stable vacuum state were able to arise, then existing particles and forces would no longer arise as they presently do. Different particles or forces would arise from (and be shaped by) whatever new quantum states arose. The world we know depends upon these particles and forces, so if this happened, everything around us, from subatomic particles to galaxies, and all fundamental forces, would be reconstituted into new fundamental particles and forces and structures. The universe would potentially lose all of its present structures and become inhabited by new ones (depending upon the exact states involved) based upon the same quantum fields.
  10. ^ Jump up to:a b Goldstone’s theorem only applies to gauges having manifest Lorentz covariance, a condition that took time to become questioned. But the process ofquantisation requires a gauge to be fixed and at this point it becomes possible to choose a gauge such as the ‘radiation’ gauge which is not invariant over time, so that these problems can be avoided. According to Bernstein (1974, p.8):
    “the “radiation gauge” condition ∇⋅A(x) = 0 is clearly noncovariant, which means that if we wish to maintain transversality of the photon in all Lorentz frames, the photon field Aμ(x) cannot transform like a four-vector. This is no catastrophe, since the photon field is not an observable, and one can readily show that the S-matrix elements, which are observable have covariant structures …. in gauge theories one might arrange things so that one had a symmetry breakdown because of the noninvariance of the vacuum; but, because the Goldstone et al. proof breaks down, the zero mass Goldstone mesons need not appear.” [Emphasis in original]

    Bernstein (1974) contains an accessible and comprehensive background and review of this area, see external links

  11. Jump up^ A field with the “Mexican hat” potential V(\phi)= \mu^2\phi^2 + \lambda\phi^4 and \mu^2 < 0 has a minimum not at zero but at some non-zero value \phi_0. By expressing the action in terms of the field \tilde \phi = \phi-\phi_0 (where \phi_0 is a constant independent of position), we find the Yukawa term has a component g\phi_0 \bar\psi\psi. Since both g and \phi_0 are constants, this looks exactly like the mass term for a fermion of mass g\phi_0. The field \tilde\phi is then the Higgs field.
  12. Jump up^ In the Standard Model, the mass term arising from the Dirac Lagrangian for any fermion \psi is -m\bar{\psi}\psi. This is not invariant under the electroweak symmetry, as can be seen by writing \psi in terms of left and right handed components:

    i.e., contributions from \bar{\psi}_L\psi_L and \bar{\psi}_R\psi_R terms do not appear. We see that the mass-generating interaction is achieved by constant flipping of particlechirality. Since the spin-half particles have no right/left helicity pair with the sameSU(2) and SU(3) representation and the same weak hypercharge, then assuming these gauge charges are conserved in the vacuum, none of the spin-half particles could ever swap helicity. Therefore in the absence of some other cause, all fermions must be massless.

  13. ^ Jump up to:a b The example is based on the production rate at the LHC operating at 7 TeV. The total cross-section for producing a Higgs boson at the LHC is about 10picobarn,[93] while the total cross-section for a proton–proton collision is 110millibarn.[96]
  14. Jump up^ 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.
  15. Jump up^ Other names have included: the “Anderson–Higgs” mechanism,[153] “Higgs–Kibble” mechanism (by Abdus Salam)[81] and “ABEGHHK’tH” mechanism [for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble and ‘t Hooft] (by Peter Higgs).[81]
  16. Jump up^ 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.[187][188]


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  2. ^ Jump up to:a b Bryner, J. (14 March 2013). “Particle confirmed as Higgs boson”. NBC News. Retrieved 2013-03-14.
  3. ^ Jump up to:a b Heilprin, J. (14 March 2013). “Higgs Boson Discovery Confirmed After Physicists Review Large Hadron Collider Data at CERN”. The Huffington Post. Retrieved 2013-03-14.
  4. Jump up^ CMS collaboration (2014). Precise determination of the mass of the Higgs boson and studies of the compatibility of its couplings with the standard model(Technical report). CMS-PAS-HIG-14-009. CERN. Retrieved 10 July 2014.
  5. Jump up^ ATLAS collaboration (9 September 2014). “Measurement of the Higgs boson mass from the H → γγ and H → ZZ* → 4l channels in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector”. Phys. Rev. D(American Physical Society) 90 (5): 052004.doi:10.1103/PhysRevD.90.052004. Retrieved 15 September 2014.
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  7. ^ Jump up to:a b c Strassler, M. (12 October 2012). “The Higgs FAQ 2.0” Retrieved 2013-01-08. “[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 Higgs field, because it is so important. [emphasis in original]”
  8. Jump up^ Strassler, M. (8 October 2011). “The Known Particles – If The Higgs Field Were Zero”. Retrieved 13 November 2012. “The Higgs field: so important it merited an entire experimental facility, the Large Hadron Collider, dedicated to understanding it.”
  9. ^ Jump up to:a b c Biever, C. (6 July 2012). “It’s a boson! But we need to know if it’s the Higgs”. New Scientist. Retrieved 2013-01-09. “‘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?’ 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?’ As there could be many different kinds of Higgs bosons, there’s no straight answer.
    [emphasis in original]”
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  25. Jump up^ M. Stone (1976). “Lifetime and decay of excited vacuum states”. Phys. Rev. D14 (12): 3568–3573. Bibcode:1976PhRvD..14.3568S.doi:10.1103/PhysRevD.14.3568.
  26. Jump up^ P.H. Frampton (1976). “Vacuum Instability and Higgs Scalar Mass”. Phys. Rev. Lett. 37 (21): 1378–1380. Bibcode:1976PhRvL..37.1378F.doi:10.1103/PhysRevLett.37.1378.
  27. Jump up^ P.H. Frampton (1977). “Consequences of Vacuum Instability in Quantum Field Theory”. Phys. Rev. D15 (10): 2922–28. Bibcode:1977PhRvD..15.2922F.doi:10.1103/PhysRevD.15.2922.
  28. Jump up^ Ellis, Espinosa, Giudice, Hoecker, & Riotto, J.; Espinosa, J.R.; Giudice, G.F.; Hoecker, A.; Riotto, A. (2009). “The Probable Fate of the Standard Model”. Phys. Lett. B 679 (4): 369–375. arXiv:0906.0954. Bibcode:2009PhLB..679..369E.doi:10.1016/j.physletb.2009.07.054.
  29. Jump up^ Masina, Isabella (2013-02-12). “Higgs boson and top quark masses as tests of electroweak vacuum stability”. Phys. Rev. D 87 (5): 53001. arXiv:1209.0393.Bibcode:2013PhRvD..87e3001M. doi:10.1103/PhysRevD.87.053001.
  30. Jump up^ Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia (2013-07-12).“Investigating the near-criticality of the Higgs boson”. JHEP 1312 (2013) 089.arXiv:1307.3536. Bibcode:2013JHEP…12..089B.doi:10.1007/JHEP12(2013)089.
  31. Jump up^ Irene Klotz (editing by David Adams and Todd Eastham) (2013-02-18).“Universe Has Finite Lifespan, Higgs Boson Calculations Suggest”. Huffington Post. Reuters. Retrieved 21 February 2013. “Earth will likely be long gone before any Higgs boson particles set off an apocalyptic assault on the universe”
  32. Jump up^ Hoffman, Mark (2013-02-19). “Higgs Boson Will Destroy The Universe Eventually”. ScienceWorldReport. Retrieved 21 February 2013.
  33. Jump up^ “Higgs boson will aid in creation of the universe – and how it will end”.Catholic Online/NEWS CONSORTIUM. 2013-02-20. Retrieved 21 February 2013. “[T]he Earth will likely be long gone before any Higgs boson particles set off an apocalyptic assault on the universe”
  34. Jump up^ For example, Huffington Post/Reuters[31] and others[32][33]
  35. ^ Jump up to:a b c Boyle, Alan (2013-02-19). “Will our universe end in a ‘big slurp’? Higgs-like particle suggests it might”. NBC News’ Cosmic log. Retrieved 21 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 quotes Fermilab‘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 in Nature that “without warning, a bubble of true vacuum could nucleate somewhere in the universe and move outwards…”
  36. Jump up^ Peralta, Eyder (2013-02-19). “If Higgs Boson Calculations Are Right, A Catastrophic ‘Bubble’ Could End Universe”. npr – two way. Retrieved 21 February 2013. Article cites Fermilab‘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.”
  37. Jump up^ Bezrukov; Shaposhnikov (2007-10-19). “The Standard Model Higgs boson as the inflaton”. Phys.Lett. B659 (2008) 703-706.
  38. Jump up^ Salvio, Alberto (2013-08-09). “Higgs Inflation at NNLO after the Boson Discovery”. Phys.Lett. B727 (2013) 234-239. arXiv:1308.2244.Bibcode:2013PhLB..727..234S. doi:10.1016/j.physletb.2013.10.042.
  39. Jump up^ Cole, K. (2000-12-14). “One Thing Is Perfectly Clear: Nothingness Is Perfect”. Los Angeles Times. p. ‘Science File’. Retrieved 17 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.”
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  44. Jump up^ Examples of Great Discoveries in the Fundamental Forces – Gravity probe BFAQ, Stanford University website, 2012
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  47. Jump up^ Sean Carroll (13 November 2012). The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World. Penguin Group US. ISBN 978-1-101-60970-5.
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  53. ^ Jump up to:a b The Nobel Prize in Physics 2008 – official Nobel Prize website.
  54. Jump up^ List of Anderson 1958–1959 papers referencing ‘symmetry’, at APS Journals
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  56. Jump up^ Anderson, P. (1963). “Plasmons, gauge invariance and mass”. Physical Review130: 439. Bibcode:1963PhRv..130..439A. doi:10.1103/PhysRev.130.439.
  57. Jump up^ Klein, A.; Lee, B. (1964). “Does Spontaneous Breakdown of Symmetry Imply Zero-Mass Particles?”. Physical Review Letters 12 (10): 266.Bibcode:1964PhRvL..12..266K. doi:10.1103/PhysRevLett.12.266.
  58. Jump up^ Englert, François; Brout, Robert (1964). “Broken Symmetry and the Mass of Gauge Vector Mesons”. Physical Review Letters 13 (9): 321–23.Bibcode:1964PhRvL..13..321E. doi:10.1103/PhysRevLett.13.321.
  59. ^ Jump up to:a b c Higgs, Peter (1964). “Broken Symmetries and the Masses of Gauge Bosons”. Physical Review Letters 13 (16): 508–509.Bibcode:1964PhRvL..13..508H. doi:10.1103/PhysRevLett.13.508.
  60. ^ Jump up to:a b c Guralnik, Gerald; Hagen, C. R.; Kibble, T. W. B. (1964). “Global Conservation Laws and Massless Particles”. Physical Review Letters 13 (20): 585–587. Bibcode:1964PhRvL..13..585G. doi:10.1103/PhysRevLett.13.585.
  61. Jump up^ Higgs, Peter (1964). “Broken symmetries, massless particles and gauge fields”.Physics Letters 12 (2): 132–133. Bibcode:1964PhL….12..132H.doi:10.1016/0031-9163(64)91136-9.
  62. Jump up^ Higgs, Peter (2010-11-24). “My Life as a Boson”. Talk given by Peter Higgs at Kings College, London, Nov 24 2010. Retrieved 17 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.”
  63. Jump up^ G.S. Guralnik (2011). “Gauge invariance and the Goldstone theorem – 1965 Feldafing talk”. Modern Physics Letters A 26 (19): 1381–1392.arXiv:1107.4592. Bibcode:2011MPLA…26.1381G.doi:10.1142/S0217732311036188.
  64. Jump up^ Higgs, Peter (1966). “Spontaneous Symmetry Breakdown without Massless Bosons”. Physical Review 145 (4): 1156–1163.Bibcode:1966PhRv..145.1156H. doi:10.1103/PhysRev.145.1156.
  65. Jump up^ Kibble, Tom (1967). “Symmetry Breaking in Non-Abelian Gauge Theories”.Physical Review 155 (5): 1554–1561. Bibcode:1967PhRv..155.1554K.doi:10.1103/PhysRev.155.1554.
  66. Jump up^ Guralnik, G. S.; Hagen, C. R.; Kibble, T. W. B. (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics 2.
  67. ^ Jump up to:a b Physical Review Letters – 50th Anniversary Milestone Papers. Physical Review Letters.
  68. Jump up^ S. Weinberg (1967). “A Model of Leptons”. Physical Review Letters 19 (21): 1264–1266. Bibcode:1967PhRvL..19.1264W.doi:10.1103/PhysRevLett.19.1264.
  69. Jump up^ A. Salam (1968). N. Svartholm, ed. “Elementary Particle Physics: Relativistic Groups and Analyticity”. Eighth Nobel Symposium. Stockholm: Almquvist and Wiksell. p. 367.
  70. Jump up^ S.L. Glashow (1961). “Partial-symmetries of weak interactions”. Nuclear Physics 22 (4): 579–588. Bibcode:1961NucPh..22..579G. doi:10.1016/0029-5582(61)90469-2.
  71. ^ Jump up to:a b c Ellis, John; Gaillard, Mary K.; Nanopoulos, Dimitri V. (2012). “A Historical Profile of the Higgs Boson”. arXiv:1201.6045 [hep-ph].
  72. Jump up^ “Martin Veltman Nobel Lecture, December 12, 1999, p.391” (PDF). Retrieved 2013-10-09.
  73. ^ Jump up to:a b c d e f Politzer, David. “The Dilemma of Attribution”. Nobel Prize lecture, 2004. Nobel Prize. Retrieved 22 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.”
  74. Jump up^ Coleman, Sidney (1979-12-14). “The 1979 Nobel Prize in Physics”. Science206 (4424): 1290–1292. Bibcode:1979Sci…206.1290C.doi:10.1126/science.206.4424.1290. Retrieved 22 January 2013. – discussed by David Politzer in his 2004 Nobel speech.[73]
  75. ^ Jump up to:a b Letters from the Past – A PRL Retrospective (50 year celebration, 2008)
  76. ^ Jump up to:a b Jeremy Bernstein (January 1974). “Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that”. Reviews of Modern Physics 46(1): 7. Bibcode:1974RvMP…46….7B. doi:10.1103/RevModPhys.46.7. Retrieved 2012-12-10.
  77. Jump up^ José Luis Lucio and Arnulfo Zepeda (1987). Proceedings of the II Mexican School of Particles and Fields, Cuernavaca-Morelos, 1986. World Scientific. p. 29. ISBN 9971504340.
  78. Jump up^ Gunion, Dawson, Kane, and Haber (199). The Higgs Hunter’s Guide (1st ed.). pp. 11 (?). ISBN 9780786743186. – quoted as being in the first (1990) edition of the book by Peter Higgs in his talk “My Life as a Boson”, 2001, ref#25.
  79. ^ Jump up to:a b American Physical Society – “J. J. Sakurai Prize for Theoretical Particle Physics”.
  80. Jump up^ Merali, Zeeya (4 August 2010). “Physicists get political over Higgs”. Nature Magazine. Retrieved 28 December 2011.
  81. ^ Jump up to:a b c d e f g h i j Close, Frank (2011). The Infinity Puzzle: Quantum Field Theory and the Hunt for an Orderly Universe. Oxford: Oxford University Press. ISBN 978-0-19-959350-7.
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  86. Jump up^ Gunion, John (2000). The Higgs Hunter’s Guide (illustrated, reprint ed.). Westview Press. pp. 1–3. ISBN 9780738203058.
  87. Jump up^ Flatow, Ira (6 July 2012). “At Long Last, The Higgs Particle… Maybe”. NPR. Retrieved 10 July 2012.
  88. Jump up^ “Explanatory Figures for the Higgs Boson Exclusion Plots”. ATLAS News. CERN. Retrieved 6 July 2012.
  89. Jump up^ Bernardi, G.; Carena, M.; Junk, T. (2012). “Higgs Bosons: Theory and Searches”. p. 7.
  90. Jump up^ Lykken, Joseph D. (2009). “Beyond the Standard Model”. Proceedings of the 2009 European School of High-Energy Physics, Bautzen, Germany, 14 – 27 June 2009. arXiv:1005.1676.
  91. Jump up^ Plehn, Tilman (2012). Lectures on LHC Physics. Lecture Notes is Physics 844. Springer. Sec. 1.2.2. arXiv:0910.4122. ISBN 3642240399.
  92. Jump up^ Peskin, Michael E.; Wells, James D. (2001). “How Can a Heavy Higgs Boson be Consistent with the Precision Electroweak Measurements?”. Physical Review D 64 (9): 093003. arXiv:hep-ph/0101342. Bibcode:2001PhRvD..64i3003P.doi:10.1103/PhysRevD.64.093003.
  93. ^ Jump up to:a b c d e f Baglio, Julien; Djouadi, Abdelhak (2011). “Higgs production at the lHC”. Journal of High Energy Physics 1103 (3): 055. arXiv:1012.0530.Bibcode:2011JHEP…03..055B. doi:10.1007/JHEP03(2011)055.
  94. ^ Jump up to:a b c d Baglio, Julien; Djouadi, Abdelhak (2010). “Predictions for Higgs production at the Tevatron and the associated uncertainties”. Journal of High Energy Physics 1010 (10): 063. arXiv:1003.4266.Bibcode:2010JHEP…10..064B. doi:10.1007/JHEP10(2010)064.
  95. ^ Jump up to:a b c Teixeira-Dias (LEP Higgs working group), P. (2008). “Higgs boson searches at LEP”. Journal of.Physics: Conference Series 110 (4): 042030.arXiv:0804.4146. Bibcode:2008JPhCS.110d2030T. doi:10.1088/1742-6596/110/4/042030.
  96. Jump up^ “Collisions”. LHC Machine Outreach. CERN. Retrieved 26 July 2012.
  97. Jump up^ Asquith, Lily (22 June 2012). “Why does the Higgs decay?”. Life and Physics(London: The Guardian). Retrieved 14 August 2012.
  98. ^ Jump up to:a b c d e f g LHC Higgs Cross Section Working Group; Dittmaier; Mariotti; Passarino; Tanaka; Alekhin; Alwall; Bagnaschi; Banfi (2012). “Handbook of LHC Higgs Cross Sections: 2. Differential Distributions”. CERN Report 2 (Tables A.1 – A.20) 1201: 3084. arXiv:1201.3084. Bibcode:2012arXiv1201.3084L.
  99. ^ Jump up to:a b c d e “Higgs bosons: theory and searches”. PDGLive. Particle Data Group. 12 July 2012. Retrieved 15 August 2012.
  100. Jump up^ Branco, G. C.; Ferreira, P.M.; Lavoura, L.; Rebelo, M.N.; Sher, Marc; Silva, João P. (July 2012). “Theory and phenomenology of two-Higgs-doublet models”.Physics Reports (Elsevier) 516 (1): 1–102. arXiv:1106.0034.Bibcode:2012PhR…516….1B. doi:10.1016/j.physrep.2012.02.002.
  101. Jump up^ Csaki, C.; Grojean, C.; Pilo, L.; Terning, J. (2004). “Towards a realistic model of Higgsless electroweak symmetry breaking”. Physical Review Letters 92 (10): 101802. arXiv:hep-ph/0308038. Bibcode:2004PhRvL..92j1802C.doi:10.1103/PhysRevLett.92.101802. PMID 15089195.
  102. Jump up^ Csaki, C.; Grojean, C.; Pilo, L.; Terning, J.; Terning, John (2004). “Gauge theories on an interval: Unitarity without a Higgs”. Physical Review D 69 (5): 055006. arXiv:hep-ph/0305237. Bibcode:2004PhRvD..69e5006C.doi:10.1103/PhysRevD.69.055006.
  103. ^ Jump up to:a b “The Hierarchy Problem: why the Higgs has a snowball’s chance in hell”. Quantum Diaries. 2012-07-01. Retrieved 19 March 2013.
  104. Jump up^ “The Hierarchy Problem | Of Particular Significance”. Retrieved 2013-10-09.
  105. ^ Jump up to:a b c “Hunt for Higgs boson hits key decision point”. MSNBC. 2012-12-06. Retrieved 2013-01-19.
  106. Jump up^ Worldwide LHC Computing Grid main page 14 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”
  107. Jump up^ What is the Worldwide LHC Computing Grid? (Public ‘About’ page) 14 November 2012: “Currently WLCG is made up of more than 170 computing centers in 36 countries…The WLCG is now the world’s largest computing grid”
  108. Jump up^ W.-M. Yao et al. (2006). Searches for Higgs Bosons “Review of Particle Physics”. Journal of Physics G 33: 1. arXiv:astro-ph/0601168.Bibcode:2006JPhG…33….1Y. doi:10.1088/0954-3899/33/1/001.
  109. Jump up^ 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 to 10.0 fb−1 of Data”.arXiv:1207.0449 [hep-ex].
  110. Jump up^ “Interim Summary Report on the Analysis of the 19 September 2008 Incident at the LHC” (PDF). CERN. 15 October 2008. EDMS 973073. Retrieved 28 September 2009.
  111. Jump up^ “CERN releases analysis of LHC incident” (Press release). CERN Press Office. 16 October 2008. Retrieved 28 September 2009.
  112. Jump up^ “LHC to restart in 2009” (Press release). CERN Press Office. 5 December 2008. Retrieved 8 December 2008.
  113. Jump up^ “LHC progress report”. The Bulletin. CERN. 3 May 2010. Retrieved 7 December 2011.
  114. Jump up^ “ATLAS experiment presents latest Higgs search status”. ATLAS homepage. CERN. 13 December 2011. Retrieved 13 December 2011.
  115. Jump up^ Taylor, Lucas (13 December 2011). “CMS search for the Standard Model Higgs Boson in LHC data from 2010 and 2011”. CMS public website. CERN. Retrieved 13 December 2011.
  116. ^ Jump up to:a b c d e Overbye, D. (5 March 2013). “Chasing The Higgs Boson”. The New York Times. Retrieved 2013-03-05.
  117. ^ Jump up to:a b “ATLAS and CMS experiments present Higgs search status” (Press release). CERN Press Office. 13 December 2011. Retrieved 14 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”
  118. Jump up^ “WLCG Public Website”. CERN. Retrieved 29 October 2012.
  119. ^ Jump up to:a b c d CMS collaboration (2012). “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC”. Physics Letters B 716 (1): 30–61.arXiv:1207.7235. Bibcode:2012PhLB..716…30C.doi:10.1016/j.physletb.2012.08.021.
  120. ^ Jump up to:a b c d Taylor, Lucas (4 July 2012). “Observation of a New Particle with a Mass of 125 GeV”. CMS Public Website. CERN. Retrieved 4 July 2012.
  121. Jump up^ “Press Conference: Update on the search for the Higgs boson at CERN on 4 July 2012”. 22 June 2012. Retrieved 4 July 2012.
  122. Jump up^ “CERN to give update on Higgs search”. CERN. 22 June 2012. Retrieved 2 July 2011.
  123. Jump up^ “Scientists analyse global Twitter gossip around Higgs boson discovery” (from arXiv). 2013-01-23. Retrieved 6 February 2013. – stated to be ” the first time scientists have been able to analyse the dynamics of social media on a global scale before, during and after the announcement of a major scientific discovery.” For the paper itself see: De Domenico, M.; Lima, A.; Mougel, P.; Musolesi, M. (2013). The Anatomy of a Scientific Gossip. arXiv:1301.2952.Bibcode:2013NatSR…3E2980D. doi:10.1038/srep02980.
  124. Jump up^ “Higgs boson particle results could be a quantum leap”. Times LIVE. 28 June 2012. Retrieved 4 July 2012.
  125. Jump up^ CERN prepares to deliver Higgs particle findings, Australian Broadcasting Corporation. Retrieved 4 July 2012.
  126. Jump up^ “God Particle Finally Discovered? Higgs Boson News At Cern Will Even Feature Scientist It’s Named After”. Retrieved 2013-01-19.
  127. Jump up^ Our Bureau (2012-07-04). “Higgs on way, theories thicken”. Calcutta, India: Retrieved 2013-01-19.
  128. Jump up^ Thornhill, Ted (2013-07-03). “God Particle Finally Discovered? Higgs Boson News At Cern Will Even Feature Scientist It’s Named After”. Huffington Post. Retrieved 23 July 2013.
  129. Jump up^ Cooper, Rob (2013-07-01 (updated subsequently)). “God particle is ‘found’: Scientists at Cern expected to announce on Wednesday Higgs boson particle has been discovered”. Daily Mail (London). Retrieved 23 July 2013. – States that ““Five leading theoretical physicists have been invited to the event on Wednesday – sparking speculation that the particle has been discovered.”, including Higgs and Englert, and that Kibble – who was invited but unable to attend – “told the Sunday Times: ‘My guess is that is must be a pretty positive result for them to be asking us out there’.”
  130. Jump up^ Adrian Cho (13 July 2012). “Higgs Boson Makes Its Debut After Decades-Long Search”. Science 337 (6091): 141–143. doi:10.1126/science.337.6091.141.PMID 22798574.
  131. Jump up^ “Latest Results from ATLAS Higgs Search”. ATLAS News. CERN. 4 July 2012. Retrieved 4 July 2012.
  132. ^ Jump up to:a b ATLAS collaboration (2012). “Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC”.Physics Letters B 716 (1): 1–29. arXiv:1207.7214.Bibcode:2012PhLB..716….1A. doi:10.1016/j.physletb.2012.08.020.
  133. Jump up^ Gillies, James (23 July 2012). “LHC 2012 proton run extended by seven weeks”. CERN bulletin. Retrieved 29 August 2012.
  134. ^ Jump up to:a b “Higgs boson behaving as expected”. 3 News NZ. 15 November 2012.
  135. ^ Jump up to:a b c Strassler, Matt (2012-11-14). “Higgs Results at Kyoto”. Of Particular Significance: Conversations About Science with Theoretical Physicist Matt Strassler. Prof. Matt Strassler’s personal particle physics website. Retrieved 10 January 2013. “ATLAS and CMS only just co-discovered this particle in July … We will not know after today whether it is a Higgs at all, whether it is a Standard Model Higgs or not, or whether any particular speculative idea…is now excluded. […] Knowledge about nature does not come easy. We discovered the top quark in 1995, and we are still learning about its properties today… we will still be learning important things about the Higgs during the coming few decades. We’ve no choice but to be patient.”
  136. Jump up^ Sample, Ian (14 November 2012). “Higgs particle looks like a bog Standard Model boson, say scientists”. The Guardian (London). Retrieved 15 November 2012.
  137. Jump up^ “CERN experiments observe particle consistent with long-sought Higgs boson”. CERN press release. 4 July 2012. Retrieved 4 July 2012.
  138. Jump up^ “Person Of The Year 2012”. Time. 19 December 2012.
  139. Jump up^ “Higgs Boson Discovery Has Been Confirmed”. Forbes. Retrieved 2013-10-09.
  140. Jump up^ Staff, Slate V (2012-09-11). “Higgs Boson Confirmed; CERN Discovery Passes Test”. Retrieved 2013-10-09.
  141. Jump up^ “The Year Of The Higgs, And Other Tiny Advances In Science”. NPR. 2013-01-01. Retrieved 2013-10-09.
  142. Jump up^ “Confirmed: the Higgs boson does exist”. The Sydney Morning Herald. 4 July 2012.
  143. Jump up^ Time,[138] Forbes,[139] Slate,[140] NPR,[141] and others[142]
  144. Jump up^ “AP CERN chief: Higgs boson quest could wrap up by midyear”. MSNBC. Associated Press. 2013-01-27. Retrieved 20 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 Jan 2013.
  145. Jump up^ Boyle, Alan (2013-02-16). “Will our universe end in a ‘big slurp’? Higgs-like particle suggests it might”. – cosmic log. Retrieved 20 February 2013. “‘it’s going to take another few years’ after the collider is restarted to confirm definitively that the newfound particle is the Higgs boson.”
  146. Jump up^ Gillies, James (2013-03-06). “A question of spin for the new boson”. CERN. Retrieved 7 March 2013.
  147. ^ Jump up to:a b c Adam Falkowski (writing as ‘Jester’) (2013-02-27). “When shall we call it Higgs?”. Résonaances particle physics blog. Retrieved 7 March 2013.
  148. ^ Jump up to:a b c d CMS Collaboration (February 2013). “Study of the Mass and Spin-Parity of the Higgs Boson Candidate via Its Decays to Z Boson Pairs”. Phys. Rev. Lett. (American Physical Society) 110 (8): 081803.doi:10.1103/PhysRevLett.110.081803. Retrieved 15 September 2014.
  149. ^ Jump up to:a b c d ATLAS Collaboration (7 October 2013). “Evidence for the spin-0 nature of the Higgs boson using ATLAS data”. Phys. Lett. B (American Physical Society) 726 (1-3): 120–144. doi:10.1016/j.physletb.2013.08.026. Retrieved 15 September 2014.
  150. Jump up^ “Higgs-like Particle in a Mirror”. American Physical Society. Retrieved 26 February 2013.
  151. Jump up^ The CMS Collaboration (2014/06/22/online). “Evidence for the direct decay of the 125 GeV Higgs boson to fermions”. Nature Publishing Group doi= 10.1038/nphys3005.
  152. Jump up^ Adam Falkowski (writing as ‘Jester’) (2012-12-13). “Twin Peaks in ATLAS”. Résonaances particle physics blog. Retrieved 24 February 2013.
  153. Jump up^ Liu, G. Z.; Cheng, G. (2002). “Extension of the Anderson-Higgs mechanism”.Physical Review B 65 (13). arXiv:cond-mat/0106070.Bibcode:2002PhRvB..65m2513L. doi:10.1103/PhysRevB.65.132513.
  154. ^ Jump up to:a b c d e Editorial (2012-03-21). “Mass appeal: As physicists close in on the Higgs boson, they should resist calls to change its name”. Nature. 483, 374 (7390): 374. Bibcode:2012Natur.483..374.. doi:10.1038/483374a. Retrieved 21 January 2013.
  155. ^ Jump up to:a b c Becker, Kate (2012-03-29). “A Higgs by Any Other Name”. “NOVA” (PBS) physics. Retrieved 21 January 2013.
  156. Jump up^ “Frequently Asked Questions: The Higgs!”. The Bulletin. CERN. Retrieved 18 July 2012.
  157. ^ Jump up to:a b Woit’s physics blog “Not Even Wrong”: Anderson on Anderson-Higgs2013-04-13
  158. Jump up^ Sample, Ian (2012-07-04). “Higgs boson’s many great minds cause a Nobel prize headache”. The Guardian (London). Retrieved 23 July 2013.
  159. Jump up^ “Rochester’s Hagen Sakurai Prize Announcement” (Press release). University of Rochester. 2010.[dead link]
  160. Jump up^ C.R. Hagen Sakurai Prize Talk (YouTube). 2010.
  161. ^ Jump up to:a b Peskin, M. (July 2012). “40 Years of the Higgs Boson”. Presentation at SSI 2012. Standford/SSI 2012. pp. 3–5. Retrieved 21 January 2013. “quoting Lee’s ICHEP 1972 presentation at Fermilab: “…which is known as the Higgs mechanism…” and “Lee’s locution” – his footnoted explanation of this shorthand”
  162. ^ Jump up to:a b Weinberg, Steven (2012-05-10). “The Crisis of Big Science”. The New York Review of Books (footnote 1). Retrieved 12 February 2013.
  163. ^ Jump up to:a b Cho, A (2012-09-14). “Particle physics. Why the ‘Higgs’?”. Science 337(6100): 1287. doi:10.1126/science.337.6100.1287. PMID 22984044. Retrieved 12 February 2013. “Lee … apparently used the term ‘Higgs Boson’ as early as 1966… but what may have made the term stick is a seminal paper Steven Weinberg…published in 1967…Weinberg acknowledged the mix-up in an essay in the New York Review of Books in May 2012.”[dead link] (See also original article in New York Review of Books[162] and Frank Close’s 2011 book The Infinity Puzzle[81]:372 (Book extract) which identified the error)
  164. Jump up^ Examples of early papers using the term “Higgs boson” include ‘A phenomenological profile of the Higgs boson’ (Ellis, Gaillard and Nanopoulos, 1976), ‘Weak interaction theory and neutral currents’ (Bjorken, 1977), and ‘Mass of the Higgs boson’ (Wienberg, received 1975)
  165. ^ Jump up to:a b ASCHENBACH, JOY (1993-12-05). “No Resurrection in Sight for Moribund Super Collider : Science: Global financial partnerships could be the only way to salvage such a project. Some feel that Congress delivered a fatal blow”. Los Angeles Times. Retrieved 16 January 2013. “‘We have to keep the momentum and optimism and start thinking about international collaboration,’ said Leon M. Lederman, the Nobel Prize-winning physicist who was the architect of the super collider plan”
  166. Jump up^ “A Supercompetition For Illinois”. Chicago Tribune. 1986-10-31. Retrieved 16 January 2013. “The SSC, proposed by the U.S. Department of Energy in 1983, is a mind-bending project … this gigantic laboratory … this titanic project”
  167. Jump up^ Diaz, Jesus (2012-12-15). “This Is [The] World’s Largest Super Collider That Never Was”. Gizmodo. Retrieved 16 January 2013. “…this titanic complex…”
  168. Jump up^ Abbott, Charles (June 1987). “Illinois Issues journal, June 1987”. p. 18. “Lederman, who considers himself an unofficial propagandist for the super collider, said the SSC could reverse the physics brain drain in which bright young physicists have left America to work in Europe and elsewhere.”
  169. Jump up^ Kevles, Dan. “Good-bye to the SSC: On the Life and Death of the Superconducting Super Collider”. California Institute of Technology: “Engineering & Science”. 58 no. 2 (Winter 1995): 16–25. Retrieved 16 January 2013. “Lederman, one of the principal spokesmen for the SSC, was an accomplished high-energy experimentalist who had made Nobel Prize-winning contributions to the development of the Standard Model during the 1960s (although the prize itself did not come until 1988). He was a fixture at congressional hearings on the collider, an unbridled advocate of its merits.”
  170. Jump up^ Calder, Nigel (2005). Magic Universe:A Grand Tour of Modern Science. pp. 369–370. ISBN 9780191622359. “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”
  171. Jump up^ Alister McGrath, Higgs boson: the particle of faith, The Daily Telegraph, Published 15 December 2011. Retrieved 15 December 2011.
  172. Jump up^ Sample, Ian (3 March 2009). “Father of the God particle: Portrait of Peter Higgs unveiled”. London: The Guardian. Retrieved 24 June 2009.
  173. ^ Jump up to:a b c Chivers, Tom (2011-12-13). “How the ‘God particle’ got its name”. The Telegraph (London). Retrieved 2012-12-03.
  174. Jump up^ Key scientist sure “God particle” will be found soon Reuters news story. 7 April 2008.
  175. Jump up^ Interview: the man behind the ‘God particle’“, New Scientist 13 September 2008, pp. 44–5 (original interview in the Guardian: Father of the ‘God Particle’, June 30, 2008)
  176. Jump up^ Sample, Ian (2010). Massive: The Hunt for the God Particle. pp. 148–149 and 278–279. ISBN 9781905264957.
  177. Jump up^ Cole, K. (2000-12-14). “One Thing Is Perfectly Clear: Nothingness Is Perfect”. Los Angeles Times. p. ‘Science File’. Retrieved 17 January 2013. “Consider the early universe–a state of pure, perfect nothingness; a formless fog of undifferentiated stuff … ‘perfect symmetry’ … What shattered this primordial perfection? One likely culprit is the so-called Higgs field … Physicist Leon Lederman compares the way the Higgs operates to the biblical story of Babel [whose citizens] all spoke the same language … Like God, says Lederman, the Higgs differentiated the perfect sameness, confusing everyone (physicists included) … [Nobel Prizewinner Richard] Feynman wondered why the universe we live in was so obviously askew … Perhaps, he speculated, total perfection would have been unacceptable to God. And so, just as God shattered the perfection of Babel, ‘God made the laws only nearly symmetrical'”
  178. Jump up^ Lederman, p. 22 et seq:
    “Something we cannot yet detect and which, one might say, has been put there to test and confuse us … The issue is whether physicists will be confounded by this puzzle or whether, in contrast to the unhappy Babylonians, we will continue to build the tower and, as Einstein put it, ‘know the mind of God’.”
    “And the Lord said, Behold the people are un-confounding my confounding. And the Lord sighed and said, Go to, let us go down, and there give them the God Particle so that they may see how beautiful is the universe I have made”.
  179. Jump up^ Sample, Ian (12 June 2009). “Higgs competition: Crack open the bubbly, the God particle is dead”. The Guardian (London). Retrieved 4 May 2010.
  180. Jump up^ Gordon, Fraser (5 July 2012). “Introducing the higgson”. Retrieved 25 August 2012.
  181. Jump up^ Wolchover, Natalie (2012-07-03). “Higgs Boson Explained: How ‘God Particle’ Gives Things Mass”. Huffington Post. Retrieved 21 January 2013.
  182. Jump up^ Oliver, Laura (2012-07-04). “Higgs boson: how would you explain it to a seven-year-old?”. The Guardian (London). Retrieved 21 January 2013.
  183. Jump up^ Zimmer, Ben (2012-07-15). “Higgs boson metaphors as clear as molasses”.The Boston Globe. Retrieved 21 January 2013.
  184. Jump up^ “The Higgs particle: an analogy for Physics classroom (section)”. (a collaboration website of LHCb physicist Xabier Vidal and High School Teachers at CERN educator Ramon Manzano). Retrieved 2013-01-09.
  185. Jump up^ Flam, Faye (2012-07-12). “Finally – A Higgs Boson Story Anyone Can Understand”. The Philadelphia Inquirer ( Retrieved 21 January 2013.
  186. Jump up^ Sample, Ian (2011-04-28). “How will we know when the Higgs particle has been detected?”. The Guardian (London). Retrieved 21 January 2013.
  187. ^ Jump up to:a b Miller, David. “A quasi-political Explanation of the Higgs Boson; for Mr Waldegrave, UK Science Minister 1993”. Retrieved 10 July 2012.
  188. Jump up^ Kathryn Grim. “Ten things you may not know about the Higgs boson”. Symmetry Magazine. Retrieved 10 July 2012.
  189. Jump up^ David Goldberg, Associate Professor of Physics, Drexel University (2010-10-17). “What’s the Matter with the Higgs Boson?”. “Ask a physicist”. Retrieved 21 January 2013.
  190. Jump up^ The Nobel Prize in Physics 1979 – official Nobel Prize website.
  191. Jump up^ The Nobel Prize in Physics 1999 – official Nobel Prize website.
  192. Jump up^ [1] – official Nobel Prize website.
  193. Jump up^ Daigle, Katy (10 July 2012). “India: Enough about Higgs, let’s discuss the boson”. AP News. Retrieved 10 July 2012.
  194. Jump up^ Bal, Hartosh Singh (19 September 2012). “The Bose in the Boson”. New York Times. Retrieved 21 September 2012.
  195. Jump up^ Alikhan, Anvar (16 July 2012). “The Spark In A Crowded Field”. Outlook India. Retrieved 10 July 2012.
  196. ^ Jump up to:a b c d Peskin & Schroeder 1995, Chapter 20

Further reading[edit]

External links[edit]

Popular science, mass media, and general coverage[edit]

Significant papers and other[edit]

Introductions to the field[edit]



Anthony Garrett Lisi:  unveiled a helix that wraps around 48 times revealing the fabric and infra-structure of everything sub-atomic and unending.  This defines the reason that all of us everywhere are inter-connected.  There is neither separation in space nor in matter.  There is more dark matter that is not visible and cannot be touched.  We live in a constantly changing universe.  impermanent, expansive and constant.


Antony Garrett Lisi

From Wikipedia, the free encyclopedia
Antony Garrett Lisi
Garrett Lisi interview.jpg

Antony Garrett Lisi being interviewed in Los Angeles
Born January 24, 1968 (age 46)
Nationality American
Fields Theoretical physics
Institutions Theiss Research
Alma mater UCLA
Known for An Exceptionally Simple Theory of Everything

Antony Garrett Lisi (born January 24, 1968), known as Garrett Lisi,[1] is an American theoretical physicist andadventure sports enthusiast. Lisi works as an independent researcher without an academic position. He is a strong proponent of balance in life, in his case between scientific research and enjoyment of the outdoors.[2][3][4]

Lisi is known for “An Exceptionally Simple Theory of Everything,” a paper proposing a unified field theory based on the E8 Lie group, combining particle physics with Einstein’s theory of gravitation. The theory is incomplete and not widely accepted by the physics community.


Early life[edit]

Born in Los Angeles and raised in San Diego, California,[5] Lisi graduated the Cate School (south of Santa Barbara, California) in 1986. He learned to surf in San Diego, where he traveled between surf breaks in an oldVW Bus.[6] Lisi went on to receive two B.S. degrees with highest honors in physics and mathematics from theUniversity of California, Los Angeles, in 1991. Lisi received a Ph.D. in physics from the University of California, San Diego, in 1999.[7]

After the Ph.D.[edit]

After getting his Ph.D., Lisi left academia and moved to Maui — expressing his dissatisfaction with the state of theoretical physics:

I got my PhD and looked at my options. I love differential geometry, general relativity, and particle physics. But the only options available then for a postdoc in those combined areas were in string theory, and I thought string theory was overly speculative. There are many really impressive aspects of strings — anomaly cancelation in particular — but there are other things that just seem wild and physically unsubstantiated. I had gotten lucky by investing my graduate stipend in a little company many thought was going out of business (AAPL), so I decided to go to Maui, learn to windsurf, and work on physics on my own.[8]

On Maui, Lisi volunteered as a staff member at a local Sudbury school, and split his time between working on his own physics research and surfing.[9]

While living in a customized van with his girlfriend, Crystal Baranyk, Lisi taught physics classes at University of Hawaii – Maui College.[9] After two years on Maui, Lisi says he was offered a tenure track teaching position at the local college, but turned it down (even though he was nearly broke) because it wouldn’t have given him enough time for his physics research.[1] At the same time, he submitted a grant application to the newly formed Foundational Questions Institute (FQXi). Lisi says the decision to turn down the job offer and hope for FQXi funding was “a hell of a gamble.”[1][10]

Academic reentry[edit]

On July 31, 2006, Lisi was awarded an FQXi grant to develop his research in quantum mechanics and unification.[11] The grant allowed Lisi to devote his full attention to physics and create his personal research wiki, Deferential Geometry.[12] On June 9, 2007, Lisi realized that the algebraic structure he had constructed to unify the standard model of particle physics with general relativity partially matched part of the algebraic structure of the E8 Lie group.[13][14]

On July 21, 2007, Lisi traveled to the inaugural FQXi conference in Reykjavík, Iceland. He was invited to give several academic talks.[9] On invitation from Lee Smolin, Lisi visited the Perimeter Institute for Theoretical Physics in October, and posted his paper, “An Exceptionally Simple Theory of Everything,”[15] to thearXiv on November 6, 2007. Discussions of Lisi’s theory developed rapidly over most major physics blogs,[6] and the story of Lisi’s theory and personal history was reported by many online and traditional media sources around the world.[16][17][18]

Lisi presented at the TED Conference on February 28, 2008,[19] and has since presented several academic talks and colloquia.[20]

On July 8, 2009, at a FQXi conference in the Azores, Lisi made a public bet with Frank Wilczek that superparticles would not be detected by July 8, 2015.[21]

In July 2010, mathematicians and physicists met with Lisi at the Banff International Research Station in Alberta, Canada, for a week to discuss his theory.[22]

Physics research[edit]

Work on quantum mechanics[edit]

On May 8, 2006, in an arXiv preprint, “Quantum mechanics from a universal action reservoir,”[23] Lisi proposes that the path integral formulation of quantum mechanics can be derived from information theory and the existence of a universal action reservoir.[24]

Deferential geometry[edit]

Lisi is an early practitioner of open notebook science.[25] Lisi created his “personal wiki notebook in theoretical physics” — the Deferential Geometry website — by using TiddlyWiki and jsMath.[12] Lisi uses this wiki to organize his research notes in theoretical physics, referring to this as “open source physics.”[11][26]

An Exceptionally Simple Theory of Everything[edit]

Lisi’s main work in theoretical physics is his Exceptionally Simple Theory of Everything, which proposes a unified field theory combining a grand unification theoryof particle physics with Albert Einstein‘s general relativistic description of gravitation, using the largest simple exceptional Lie algebra, E8. In a paper posted to the physics arXiv on November 6, 2007,[15] and in a popular article published in Scientific American in December, 2010,[27] Lisi describes his proposal that gravity, thestandard model bosons and fermions can be unified as parts of an E8 superconnection. This unified field theory attempts to describe all fundamental interactionsobserved in nature, as a possible theory of everything, unifying Albert Einstein‘s general relativity with the standard model of particle physics. The theory, calledE8 Theory, also predicts the existence of many new particles.[28]

Lisi designed a web application, the Elementary Particle Explorer,[29] for visualizing the charge structure of the elementary particles in the standard model, in grand unified theories, and in E8 Theory.

Lisi’s theory has been applauded but also criticized in the scientific community.[30][31][32][33] He has addressed the criticism, while acknowledging that the theory is incomplete. In a Scientific American post, Garrett himself states:

(the 3 generation) … issue remains the most significant problem, and until it is solved the theory is not complete and cannot be considered much more than a speculative proposal. Without fully describing how the three generations of fermions work, the theory and all predictions from it remain tenuous.[34]

Adventure sports[edit]

Garrett Lisi is an adventure sports enthusiast — surfing, snowboarding, and kitesurfing at the expert level as well as participating in many other adventure sports.[2][6][35] In an interview for Wired News, Lisi says:

Surfing and snowboarding are what I do for fun – to get out and play in nature. We live in a beautiful universe, and I wish to enjoy it and understand it as best I can. And I try to live a balanced life. Surfing is simply the most fun I know how to have on this planet. And physics, and science in general, is the best way of understanding how everything works. So this is what I spend my time doing. I do what I love, and follow my interests. Shouldn’t everyone?[36]


Garrett Lisi surfingHo’okipa, Maui, on January 13, 2012

Lisi brings some of his physics to his sports activities.[37] During graduate school and years in Maui, most of Lisi’s surfboards were adorned with the wave equation as decorative art.[2][38] And when riding an extra-long carving board, for alpine snowboarding, in Colorado and Tahoe, Lisi always wears a long white lab coat.[2][6][39][40] He has also become a sponsored team rider for anOregon surfboard manufacturer, 42 Surfboards.[36]

Although concentrating on surfing, kitesurfing and snowboarding, Lisi participates in a wide variety of adventure sports.[41] On his online journal, Lisi describes his experiences surfing, snowboarding, windsurfing, sailing, kitesurfing, mountain biking,skateboarding, motorcycling, cliff diving, rock climbing, hang gliding, paragliding, backpacking, water skiing, wakeboarding, flying,sky diving, and scuba diving.[9] Lisi is working on a film about young scientists who combine cutting-edge research with adventure sports.[42]

Science hostel[edit]

Lisi proposes the creation of a more casual kind of science institute— a science hostel —which he says “would essentially be large houses in beautiful locations where theorists could live and work.”[39] Citing his experience living in Maui and the mountains of Tahoe and Colorado, Lisi says that for theoretical research it is good to have opportunities for hiking and things to do outside in attractive environments.[43][44] Describing the idea more formally, Lisi says:

The physical requirements for conducting scholarly research have changed dramatically with the rise of the internet. It is now viable for researchers with laptop computers to work autonomously – with access to current articles and communication channels on par with the resources available at large universities. These new circumstances motivate the creation of a new kind of research enterprise: a Science Hostel. By providing places to live and work with other researchers, in beautiful locations, a Science Hostel could increase creative productivity and overall quality of life for scholars in the internet age.[45]

Invention USA[edit]

Main article: Invention USA

In December 2011, Lisi began starring, with Reichart Von Wolfsheild, in Invention USA, a History channel documentary television series.[46]


  1. ^ Jump up to:a b c A. G. Lisi (2008-07-05). “A.”. Archived from the original on 23 May 2008. Retrieved 2008-07-05.
  2. ^ Jump up to:a b c d Evan Ratliff (2008-05-01). “Has A Surfer/Snowboarder Who Lives In A Van Rewritten Physics? Maybe.”. Outside Magazine. Retrieved 2008-07-02.
  3. Jump up^ Brad Melekian (2007-12-03). “Physicist balances waves with world of science”. The San Diego Union Tribune. Retrieved 2008-07-02.
  4. Jump up^ Benjamin Wallace-Wells (2008-07-21). “Surfing the Universe”. The New Yorker.
  5. Jump up^ Jim Patton (2007-11-15). “‘Physics is Beautiful’ And a few other thoughts from Garrett Lisi”. Fox News. Retrieved 2008-07-02.
  6. ^ Jump up to:a b c d James Owen Weatherall (2008-06-01). “No Strings Attached”. Men’s Journal.
  7. Jump up^ A. G. Lisi (2008-07-05). “A. Garrett Lisi’s C.V.”. Retrieved 2008-07-05.
  8. Jump up^ Sean Carroll (2008-07-06). “Garrett Lisi’s Theory of Everything!”. Cosmic Variance. Archived from the original on 23 June 2008. Retrieved 2008-07-06.
  9. ^ Jump up to:a b c d Antony Garrett Lisi (1999-10-13). “The Mauitian Chronicles”. The Mauitian Chronicles. Archived from the original on 20 July 2008. Retrieved 2008-07-02.
  10. Jump up^ Jacob Shafer (2011). “Physicist Garrett Lisi And His Theory of Everything”.Maui Time Weekly.
  11. ^ Jump up to:a b “FQXi awards: A. Garrett Lisi”. FQXi. 2006-07-31. Archived from the original on 6 July 2008. Retrieved 2008-07-05.
  12. ^ Jump up to:a b Antony Garrett Lisi (2008-07-05). “Deferential Geometry”. Deferential Geometry. Archived from the original on 31 May 2008. Retrieved 2008-07-05.
  13. Jump up^ Zeeya Merali (2007-11-15). “Is mathematical pattern the theory of everything?”. New Scientist. Archived from the original on 12 May 2008. Retrieved 2008-06-15.
  14. Jump up^ Roger Highfield (2007-11-14). “Surfer dude stuns physicists with theory of everything”. The Daily Telegraph. Archived from the original on 2008-05-20. Retrieved 2008-06-15.
  15. ^ Jump up to:a b Garrett Lisi, A. (2007). “An Exceptionally Simple Theory of Everything”.arXiv:0711.0770 [hep-th].
  16. Jump up^ Mitch Porter (2010-01-30). “Surfer inspires comparisons to Albert Einstein”.Toronto Star. Retrieved 2011-01-13.
  17. Jump up^ “Geometry is all”. The Economist. 2007-11-22. Retrieved 2008-06-15.
  18. Jump up^ “Could the Next Einstein Be a Surfer Dude?”. Discover Magazine. 2008-02-26. Archived from the original on 9 May 2008. Retrieved 2008-06-15.
  19. Jump up^ A. G. Lisi (2008-02-28). “Garrett Lisi profile”. TED talks. Archived from the original on 18 October 2008. Retrieved 2008-10-17.
  20. Jump up^ Greg Boustead (2008-11-17). “Garrett Lisi’s Exceptional Approach to Everything”. SEED Magazine.
  21. Jump up^ A. G. Lisi (2009-08-08). “Science Pond”. Science Pond. Retrieved 2009-12-13.
  22. Jump up^ Merali, Zeeya (September 2010). “Rummaging for a Final Theory: Can a 1960s Approach Unify Gravity with the Rest of Physics?”. Scientific American. Retrieved 2011-01-15.
  23. Jump up^ Garrett Lisi, A. (2006). “Quantum mechanics from a universal action reservoir”.arXiv:physics/0605068 [physics.pop-ph].
  24. Jump up^ John Reilly (2007-11-17). “This could end the String Theory industry”. The Long View. Retrieved 2008-07-06.
  25. Jump up^ Dave Bacon (2008-06-26). “Pseudo Open Notebook Science?”. The Quantum Pontiff. Retrieved 2008-07-06.
  26. Jump up^ Timothy M. O’Brien (2008-09-25). “A. Garrett Lisi on Using Wikis to Support Open Source Science”. O’Reilly. Archived from the original on 6 January 2010. Retrieved 2009-12-13.
  27. Jump up^ A. G. Lisi; James Owen Weatherall (2010). “A Geometric Theory of Everything”. Scientific American 303 (6): 30–37.doi:10.1038/scientificamerican1210-54. PMID 21141358.
  28. Jump up^ “Ten Quick Questions With… Garrett Lisi”. Science Channel. 2008-03-01.Archived from the original on 5 June 2008. Retrieved 2008-07-02.
  29. Jump up^ Troy Gardner (2008-08-09). “Elementary Particle Explorer”. Deferential Geometry. Archived from the original on 17 September 2008. Retrieved 2008-09-04.
  30. Jump up^ “Surfer makes waves with scientific ‘theory of everything'”. CBC News. 2007-11-16. Archived from the original on 11 June 2008. Retrieved 2008-07-02.
  31. Jump up^ Collins, Graham P. (March 2008). “Wipeout?”. Scientific American: 30–32. Retrieved 2008-06-18.
  32. Jump up^ J. Distler; S. Garibaldi (2010). “There is No “Theory of Everything” Inside E8“.Communications in Mathematical Physics 298 (2): 419–436. arXiv:0905.2658.Bibcode:2010CMaPh.298..419D. doi:10.1007/s00220-010-1006-y.
  33. Jump up^ Amber Dance (2008-04-01). “Outsider Science”. Symmetry Magazine.Archived from the original on 5 July 2008. Retrieved 2008-06-15.
  34. Jump up^ Garrett Lisi (2011-5-4) Scientific American retrieved 2011-6-2
  35. Jump up^ Steve Farrar (2007-11-18). “Einstein on a snowboard”. The Sunday Times(London). Archived from the original on 7 August 2008. Retrieved 2008-07-02.
  36. ^ Jump up to:a b Kim Zetter (2008-02-27). “Surfer-Physicist’s Unified Theory Leads to Fame, Backlash”. Wired Magazine. Archived from the original on 20 June 2008. Retrieved 2008-06-15.
  37. Jump up^ Scott Bass (2007-12-01). “MOST INTERESTING SURFERS OF 2007: The Top Ten”. Surfer Magazine. Retrieved 2008-07-02.
  38. Jump up^ “Wave Mechanic”. User Friendly. 2007-11-18. Retrieved 2008-07-02.
  39. ^ Jump up to:a b Scott Dodd (2007-10-26). “Surfing the Folds of Spacetime” (PDF). FQXi article. Retrieved 2008-06-15.
  40. Jump up^ Roger Highfield (2007-11-21). “Surfer Dude’s Theory of Everything – The Movie”. The Daily Telegraph. Archived from the original on 2008-06-12. Retrieved 2008-07-02.
  41. Jump up^ Jay DiMartino (2009-04-10). “Garrett Lisi: Dropping in and Dropping Science”. Retrieved 2009-12-13.
  42. Jump up^ Roger Highfield (2009-11-10). “Surfer dude’s theory of everything: the magic of Garrett Lisi”. The Daily Telegraph. Archived from the original on 13 November 2009. Retrieved 2009-12-12.
  43. Jump up^ Sabine Hossenfelder (2007-08-06). “Garrett Lisi’s Inspiration”. Backreaction. Retrieved 2008-06-15.
  44. Jump up^ John Horgan (2008-09-20). “Surfing Einstein’s Really Revolutionary Idea”.The Center for Science Writings. Retrieved 2009-12-13.
  45. Jump up^ Antony Garrett Lisi (2008-07-06). “Science Hostel”. Science Hostel.Archived from the original on 25 July 2008. Retrieved 2008-07-06.
  46. Jump up^ ‘Invention USA,’ a chance to dream, Media Life Magazine, Tom Conroy, 8 December 2011 (retrieved 20 December 2011)

External links[edit]


An Exceptionally Simple Theory of Everything

From Wikipedia, the free encyclopedia

“An Exceptionally Simple Theory of Everything”[1] is a physics preprint proposing a basis for a unified field theory, very often referred to as “E8 Theory,”[2]which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything. The paper was posted to the physicsarXiv by Antony Garrett Lisi on November 6, 2007, and was not submitted to a peer-reviewed scientific journal.[3] The title is a pun on the algebra used, the Lie algebra of the largest “simple“, “exceptionalLie group, E8. The paper’s goal is to describe how the combined structure and dynamics of all gravitational andStandard Model particle fields, including fermions, are part of the E8 Lie algebra.[2] In the paper, Lisi states that all three generations of fermions do not directly embed in E8 with correct quantum numbers and spins, but that they might be described via a triality transformation, noting that the theory is incomplete and that a correct description of the relationship between triality and generations, if it exists, awaits a better understanding.

The theory received accolades from a few physicists[citation needed] amid a flurry of media coverage, but also met with widespread skepticism.[4] Scientific Americanreported in March 2008 that the theory was being “largely but not entirely ignored” by the mainstream physics community, with a few physicists picking up the work to develop it further.[5]

In a follow-up paper, Lee Smolin proposes a spontaneous symmetry breaking mechanism for obtaining the classical action in Lisi’s model, and speculates on the path to its quantization.[6]

In July 2009 Jacques Distler and Skip Garibaldi published a critical paper in Communications in Mathematical Physics called “There is no ‘Theory of Everything’ inside E8,”[7] arguing that Lisi’s theory, and a large class of related models, cannot work. They offer a direct proof that it is impossible to embed all three generations of fermions in E8, or to obtain even the one-generation Standard Model without the presence of an antigeneration. In response to Distler and Garibaldi’s paper, Lisi argues, in a new paper “An Explicit Embedding of Gravity and the Standard Model in E8,”[8] peer reviewed and published in a conference proceedings, that some assumptions about fermion embeddings are unnecessary and that the antigeneration is not per se a problem sufficient to rule out the one-generation Standard Model.[8][9] In December 2010 and May 2011 Lisi wrote in the popular magazine Scientific American a feature article on the E8 Theory of Everything and an entry in the blog section of the magazine addressing some of the criticism of his theory and how it has progressed, noting that the theory is still incomplete and makes only tenuous predictions, with the three generation issue remaining as a significant problem.[9]


Lisi’s model is a variant and extension of a Grand Unification Theory (a “GUT”, describing electromagnetism, theweak interaction and the strong interaction) to include gravitation, a Higgs boson and fermions in an attempt to describe all fields of the Standard Model and gravity as different parts of one field over four-dimensional spacetime. More specifically, Lisi combines the left-right symmetric Pati–Salam GUT with a MacDowell–Mansouri description of gravity, using the spin connection and gravitational frame combined with a Higgs boson, necessitating acosmological constant. The model is formulated as a gauge theory, using a modified BF action, with E8 as the Lie group. Mathematically, this is an E8 principal bundle, with connection, over a four-dimensional base manifold. Lisi’s embedding of the Standard Model gauge group in E8 leads him to predict the existence of 22 new bosonic particles at an undetermined mass scale.

Lisi states that the fermions enter via an unconventional use of the BRST technique, as Grassmann number fields valued in part of the E8 Lie algebra. The bosons are combined with these fermions as one-form and Grassmann number parts of a kind of superconnection, each valued in separate parts of the E8 Lie algebra. The curvature of this superconnection is calculated, producing the Riemann curvature, gauge field curvature, gravitational torsion,covariant derivative of the Higgs, and the covariant Dirac derivative of the fermions. This curvature is used to build the modified BF action by hand, in an attempt to match the dynamics of the Standard Model and gravity.

In the paper, Lisi describes several deficiencies in this model. The most important deficiency is noted as an incorrect, or “poorly understood”, inclusion of the second and third generations of fermions in E8, relying on triality. This deficiency, and the incomplete nature of the model, precludes the prediction of masses for new or existing particles. Also, Lisi notes the use of explicit symmetry breaking in building his action, rather than offering a more desirable spontaneous symmetry breaking mechanism. And, no attempt is made to provide a quantum description of the theory—this being left for future work. About it, Lee Smolin proposed a spontaneous symmetry breaking mechanism for obtaining the action in Lisi’s model, and speculates on the path to its quantization as a spin foam.[6]

Non-technical overview[edit]


Levels of magnification:
1. Macroscopic level – Matter
2. Molecular level
3. Atomic level – Protons, neutrons, and electrons
4. Subatomic level – Electron
5. Subatomic level – Quarks
6. Lie group geometrical representation level

In modern particle physics, the most common approach to describe elementary particles and their interactions is usually through a gauge theory based on a Lie group. A Lie group is a mathematical structure with many complex symmetries, which can be described as an object with a complex geometry. In the corresponding quantum field theory, there is a particle associated with each of these symmetries, and these particles can interact with each other according to the geometry of the group and how the particles are related to the group representation.

In Lisi’s model, the Lie group used is E8, a group with 248 parameters.[10]

In general, in each gauge theory based on a Yang–Mills action, the symmetries of the Lie group are associated to a specific kind of particles known as gauge bosons (like photons, W and Z bosons, and gluons in the Standard Model; in models involving supersymmetry this is a little more complicated). These gauge bosons can interact with each other and with fermions according to the geometry of the group and its fundamental representations. One of Lisi’s challenges is that his theory identifies fermions with the symmetries that are usually associated only with gauge bosons. Generally this is considered not possible and this aspect of the theory still needs to be completed. Another aspect different from the common approaches is that Lisi’s theory includes also gravity in the Lie Group E8. While this aspect has been proven to be possible in supersymmetric theories and impossible in a large class of theories (Coleman-Mandula theorem), it is sometimes attempted in other theories and models that do not strictly belong to those classes. It is still not clear if this feature is achievable in Lisi’s theory.[11]

In general, a unified theory has a Lie group large enough to contain the Standard Model symmetries. There are many such theories, some of which have used E8 for a long time (like string theory). In Lisi’s specific model, as introduced above, each of the 248 symmetries of E8 corresponds to a different elementary particle: Standard Model gauge bosons, gravitons and Standard Model fermions, which can all interact (as usual in this kind of theories) according to the geometry of the group, in this case E8. Lisi states that: “E8 reproduc[es] all known fields and dynamics through pure geometry.”[1]

The complicated geometry of Lie groups, E8 amongst them, is described graphically using group representationtheory. Using this mathematical description, each symmetry of a group—and so each kind of elementary particle—can be associated with a point in a weight diagram. The coordinates of these points are the quantum numbers—thecharges—of elementary particles, which are conserved in interactions.

In order to form a theory of everything, Lisi’s model must eventually predict the exact number of fundamental particles, all of their properties, masses, forces between them, the nature of spacetime, and the cosmological constant. Much of this work is still in the conceptual stage—in particular, quantization and predictions of particle masses have not been done and the model at the moment cannot reproduce all the known particles.

Lisi himself acknowledges it as a work-in-progress: “The theory is very young, and still in development,”[12] and the three generation “issue remains the most significant problem, and until it is solved the theory is not complete and cannot be considered much more than a speculative proposal. Without fully describing how the three generations of fermions work, the theory and all predictions from it remain tenuous.”[9]

Algebraic breakdown[edit]

Lisi proposes a decomposition of e8, the 248 dimensional Lie algebra of E8, into parts accommodating the gravitational and standard model fields according to the following schema:[1][13][14][15]

\mathrm{so}(7,1) \,
strong B-L
\mathrm{so}(1,7) \,
3 \times (8 \times 8)
\mathrm{so}(3,1) \,
4 \times (2 + \overline{2}) \,
\mathrm{su}(2)_L+\mathrm{su}(2)_R \,
\mathrm{su}(3) \,
\mathrm{u}(1)_{B-L} \,
new bosons
\mathrm{u}(1)+3 \times 6 \,
gen 1
8_{S+} \times 8_{S+} \,
gen 2*
8_{S-} \times 8_{S-} \,
gen 3*
8_{V} \times 8_{V} \,

∗ These two generations are only formally identified as second and third generations, this being a problematic aspect of the theory,[9] as explained above.


By matching 226 known standard model particles to some of the 248 symmetries of E8, the theory is able to predict the existence and quantum numbers of 22 new particles.[1] Three of these are the same new \mathrm{su}(2)_R \, and \mathrm{u}(1)_{B-L} \, gauge bosons as predicted in the Pati–Salam model, the W’ and Z’ bosons. Another is a new \mathrm{u}(1) \, gauge boson, with a corresponding new quantum number. And the remaining 18 new bosons predicted are new colored fields, interacting with the strong force. Lisi states that some of these 22 particles might be seen at the Large Hadron Collider.[16]

Since Lisi does not specify masses for these particles their prediction is not falsifiable by non-discovery in any given experiment, because the masses could exceed the experiment’s reach. However, the discovery of new particles that do not fit in Lisi’s classification, such as superpartners, would fall outside the model, and falsify Lisi’s match to E8. Also, because the theory at the moment fails to predict all the known particles and the matching of the three fermion generations is tentative and problematic in the model, Lisi places a low confidence in these predictions.

Q and A[edit]

Q: How does time arise from symmetry breaking in E8?

Lisi: It’s not precisely clear yet, but there are four time-like directions in E8 that mix to give the direction of time in spacetime.

Chronology and reaction[edit]

Three previous arXiv preprints by Lisi deal with mathematical physics related to the theory. “Clifford Geometrodynamics,”[17] in 2002, endeavors to describe fermions geometrically as BRST ghosts. “Clifford bundle formulation of BF gravity generalized to the standard model,”[18] in 2005, describes the algebra of gravitational and Standard Model fields acting on a generation of fermions, but does not mention E8. “Quantum mechanics from a universal action reservoir,”[19] in 2006, attempts to derive quantum mechanics using information theory.

Before writing his 2007 paper, Lisi discussed his work on an Foundational Questions Institute (FQXi) forum,[20] at an FQXi conference,[21] and for an FQXi article.[22] Lisi gave his first talk on E8 Theory at the Loops ’07 conference in Morelia, Mexico,[23] soon followed by a talk at the Perimeter Institute.[24] John Baezcommented on Lisi’s work in “This Week’s Finds in Mathematical Physics (Week 253)”,[25] and Lisi was interviewed on Sabine Hossenfelder’s “Backreaction” blog.[26] Lisi’s arXiv preprint, “An Exceptionally Simple Theory of Everything”, appeared on November 6, 2007, and immediately attracted a great deal of attention. Lisi made a further presentation for the International Loop Quantum Gravity Seminar on November 13, 2007,[27] and responded to press inquiries on an FQXi forum.[28] He presented his work at the TED Conference on February 28, 2008.[29]

Numerous news sites from all over the world reported on the new theory in 2007 and 2008, noting Lisi’s personal history and the controversy in the physics community. The first mainstream and scientific press coverage began with articles in The Daily Telegraph[12] and New Scientist,[30] with articles soon following in many other newspapers and magazines.

Lisi’s paper spawned a variety of reactions and debates across various physics blogs and online discussion groups. The first to comment was Sabine Hossenfelder, summarizing the paper and noting the lack of a dynamical symmetry breaking mechanism.[31] Luboš Motl offered a colorful critique, objecting to the addition of bosons and fermions in Lisi’s superconnection, and to the violation of the Coleman-Mandula theorem.[32] In the presentation “What’s new at the arXiv?” on May 20, 2008, Simeon Warner stated that Lisi’s paper is the most downloaded article on the arXiv.[33][34] Among the physicists early to comment on E8 Theory, Sabine Hossenfelder, Peter Woit and Lee Smolin were generally supportive, while Luboš Motl and Jacques Distler were critical.

On his blog, Musings, Jacques Distler offered one of the strongest criticisms of Lisi’s approach, claiming to demonstrate that, unlike in the Standard Model, Lisi’s model is nonchiral — consisting of a generation and an anti-generation — and to prove that any alternative embedding in E8 must be similarly nonchiral.[15][35][36]These arguments were distilled in a paper written jointly with Skip Garibaldi, “There is no ‘Theory of Everything’ inside E8,”[7] published in Communications in Mathematical Physics. In this paper, Distler and Garibaldi offer a proof that it is impossible to embed all three generations of fermions in E8, or to obtain even the one-generation Standard Model. In a press release from his university, “Rock climber takes on surfer’s theory,”[37][38] Garibaldi states that his article with Distler is a rebuttal of Lisi’s theory. In response, Lisi argues that Distler and Garibaldi made unnecessary assumptions about how the embedding needs to happen.[9]Addressing the one generation case, in June 2010 Lisi posted a new paper on E8 Theory, “An Explicit Embedding of Gravity and the Standard Model in E8,”[8]peer reviewed and published in a conference proceedings, describing how the algebra of gravity and the Standard Model with one generation of fermions embeds in the E8 Lie algebra explicitly using matrix representations. When this embedding is done, Lisi agrees that there is an antigeneration of fermions (also known as “mirror fermions”) remaining in E8; but while Distler and Garibaldi state that these mirror fermions make the theory nonchiral, Lisi states that these mirror fermions might have high masses, making the theory chiral, or that they might be related to the other generations. Addressing the three generation case, Lisi agrees that three generations of fermions cannot be directly embedded in E8, but suggests that a gauge transformation related to triality might be used to relate the 64 mirror fermions and 64 other E8 generators to two other generations of 64 fermions.[9]

The group blog, The n-Category Cafe, provides some of the more technical discussions, with posts by Lisi, Urs Schreiber,[13] Kea,[39] and Jacques Distler.[39]

Sixteen arXiv preprints have cited Lisi’s work. Lee Smolin‘s “The Plebanski action extended to a unification of gravity and Yang–Mills theory”, December 6, 2007, proposes a symmetry breaking mechanism to go from an E8 symmetric action to Lisi’s action for the Standard Model and gravity.[6] Roberto Percacci’s “Mixing internal and spacetime transformations: some examples and counterexamples”[11] addresses a general loophole in the Coleman-Mandula theorem also thought to work in E8 Theory.[9] Percacci and Fabrizio Nesti’s “Chirality in unified theories of gravity”[40] confirms the embedding of the algebra of gravitational and Standard Model forces acting on a generation of fermions in so(3,11) \oplus 64, mentioning that Lisi’s “ambitious attempt to unify all known fields into a single representation of E8 stumbled into chirality issues.”[40] Mathematician Bertram Kostant discussed Lisi’s work in a colloquium presentation at UC Riverside.[41] In a joint paper with Lee Smolin and Simone Speziale,[42] published in Journal of Physics A, Lisi proposes a new action and symmetry breaking mechanism. In “An Explicit Embedding of Gravity and the Standard Model in E8,”[8] Lisi describes E8 Theory using explicit matrix representations.

On August 4, 2008, FQXi awarded Lisi a grant for further development of E8 Theory.[43][44]

In September 2010 Scientific American reported on a conference inspired by Lisi’s work.[45]

In October 2010, Lisi, Smolin and Simone Speziale published a partially related paper on unification, in a peer-reviewed journal, proposing an action and symmetry breaking mechanism, and using an alternative treatment of fermions.[42] In December 2010 Scientific American published a feature article on E8 Theory, “A Geometric Theory of Everything”,[2] written by Lisi and James Owen Weatherall.

In December 2011, in his paper, “String and M-theory: answering the critics,”[46] for a Special Issue of Foundations of Physics: “Forty Years Of String Theory: Reflecting On the Foundations”, Michael Duff argues against Lisi’s theory and the attention it has received in the popular press.[47] Duff states that Lisi’s paper was incorrect, citing Distler and Garibaldi’s proof, and criticizes the press for giving too much positive attention to an “outsider” scientist and theory.’


  1. ^ Jump up to:a b c d A. G. Lisi (2007). “An Exceptionally Simple Theory of Everything”.arXiv:0711.0770 [hep-th].
  2. ^ Jump up to:a b c A. G. Lisi; J. O. Weatherall (2010). “A Geometric Theory of Everything”.Scientific American 303 (6): 54–61. doi:10.1038/scientificamerican1210-54.PMID 21141358.
  3. Jump up^ Greg Boustead (2008-11-17). “Garrett Lisi’s Exceptional Approach to Everything”. SEED Magazine.
  4. Jump up^ Amber Dance (2008-04-01). “Outsider Science”. Symmetry Magazine.Archived from the original on 5 July 2008. Retrieved 2008-06-15.
  5. Jump up^ Collins, Graham P. (March 2008). “Wipeout?”. Scientific American: 30–32. Retrieved 2008-06-18.
  6. ^ Jump up to:a b c Lee Smolin (2007). “The Plebanski action extended to a unification of gravity and Yang-Mills theory”. arXiv:0712.0977 [hep-th].
  7. ^ Jump up to:a b Jacques Distler; Skip Garibaldi (2009). “There is no ‘Theory of Everything’ inside E8”. arXiv:0905.2658 [math.RT].
  8. ^ Jump up to:a b c d A. G. Lisi (2010). “An Explicit Embedding of Gravity and the Standard Model in E8”. arXiv:1006.4908 [gr-qc].
  9. ^ Jump up to:a b c d e f g A G Lisi (2011-05-11). “Garrett Lisi Responds to Criticism of his Proposed Unified Theory of Physics”. Scientific American. Archived from the original on 2 July 2011. Retrieved 2011-07-30.
  10. Jump up^ “Mathematicians Map E8. AIM. Archived from the original on 29 December 2007. Retrieved 2007-12-30.
  11. ^ Jump up to:a b Roberto Percacci (2008). “Mixing internal and spacetime transformations: some examples and counterexamples”. arXiv:0803.0303 [hep-th].
  12. ^ Jump up to:a b Roger Highfield (2007-11-14). “Surfer dude stuns physicists with theory of everything”. The Daily Telegraph. Archived from the original on 19 June 2008. Retrieved 2008-06-15.
  13. ^ Jump up to:a b Urs Schreiber (2008-05-10). “E8 Quillen Superconnection”. The n-Category Cafe. Archived from the original on 19 June 2008. Retrieved 2008-06-15.
  14. Jump up^ Jacques Distler (2007-12-09). “A Little More Group Theory”. Musings. Retrieved 2008-08-30.
  15. ^ Jump up to:a b Jacques Distler (2007-11-21). “A Little Group Theory”. Musings.Archived from the original on 12 May 2008. Retrieved 2008-06-15.
  16. Jump up^ “The Big Bang: what will we find?”. The Daily Telegraph. 2008-03-25. Retrieved 2008-06-15.
  17. Jump up^ A. G. Lisi (2002). “Clifford Geometrodynamics”. arXiv:gr-qc/0212041 [gr-qc].
  18. Jump up^ A. G. Lisi (2005). “Clifford bundle formulation of BF gravity generalized to the standard model”. arXiv:gr-qc/0511120 [gr-qc].
  19. Jump up^ A. G. Lisi (2006). “Quantum mechanics from a universal action reservoir”.arXiv:physics/0605068 [physics.pop-ph].
  20. Jump up^ A. G. Lisi (2007-06-09). “Pieces of E8”. FQXi forum. Archived from the original on 2 June 2008. Retrieved 2008-06-15.
  21. Jump up^ A. G. Lisi (2007-07-21). “Standard model and gravity”. inaugural FQXiconference. Retrieved 2008-06-15.
  22. Jump up^ Scott Dodd (2007-10-26). “Surfing the Folds of Spacetime” (PDF). FQXi article. Retrieved 2008-06-15.
  23. Jump up^ A. G. Lisi (2007-06-25). “Deferential Geometry”. Loops ’07 conference. Retrieved 2008-06-15.
  24. Jump up^ A. G. Lisi (2007-10-04). “An Exceptionally Simple Theory of Everything”.Perimeter Institute talk. Retrieved 2008-06-15.
  25. Jump up^ John Baez (2007-06-27). “This Week’s Finds in Mathematical Physics (Week 253)”. Archived from the original on 30 June 2008. Retrieved 2008-06-15.
  26. Jump up^ Sabine Hossenfelder (2007-08-06). “Garrett Lisi’s Inspiration”. Backreaction. Retrieved 2008-06-15.
  27. Jump up^ A. G. Lisi (2007-11-13). “A Connection With Everything”. International Loop Quantum Gravity Seminar. Archived from the original on 22 May 2008. Retrieved 2008-06-15.
  28. Jump up^ A. G. Lisi (2007-11-20). “An Exceptionally Simple FAQ”. FQXi forum.Archived from the original on 2 June 2008. Retrieved 2008-06-15.
  29. Jump up^ A. G. Lisi (2008-02-28). “Garrett Lisi: A beautiful new theory of everything”.TED talks. Archived from the original on 18 October 2008. Retrieved 2008-10-17.
  30. Jump up^ Zeeya Merali (2007-11-15). “Is mathematical pattern the theory of everything?”. New Scientist. Archived from the original on 12 May 2008. Retrieved 2008-06-15.
  31. Jump up^ Sabine Hossenfelder (2007-11-06). “A Theoretically Simple Exception of Everything”. Backreaction. Archived from the original on 26 May 2008. Retrieved 2008-06-15.
  32. Jump up^ Luboš Motl (2007-11-07). “Garrett Lisi: An exceptionally simple theory of everything”. The Reference Frame. Retrieved 2008-06-15.
  33. Jump up^ Peter Woit (2008-05-28). “INSPIRE”. Not Even Wrong. Retrieved 2008-08-05.
  34. Jump up^ Simeon Warner (2008-05-20). “What’s new at the arXiv?”. HEP Information Resource Summit. Retrieved 2008-07-22. (The slide containing this statement was subsequently removed from the presentation file.)
  35. Jump up^ Jacques Distler (2007-12-09). “A Little More Group Theory”. Musings. Retrieved 2008-11-15.
  36. Jump up^ Jacques Distler (2008-09-14). “My Dinner with Garrett”. Musings. Archivedfrom the original on 19 November 2008. Retrieved 2008-11-15.
  37. Jump up^ Carol Clark (2010-03-18). “Rock climber takes on surfer’s theory”.esciencecommons. Retrieved 2011-07-30.
  38. Jump up^ “No ‘Simple Theory of Everything’ Inside the Enigmatic E8, Researcher Says”. ScienceDaily. 2010-03-26. Retrieved 2011-07-30.
  39. ^ Jump up to:a b
  40. ^ Jump up to:a b R. Percacci; F. Nesti (2009). “Chirality in unified theories of gravity”.arXiv:0909.4537 [hep-th].
  41. Jump up^ Bertram Kostant (2008-02-12). “On Some Mathematics in Garrett Lisi’s ‘E8 Theory of Everything'”. UC Riverside mathematics colloquium. Archivedfrom the original on 28 June 2008. Retrieved 2008-06-15.
  42. ^ Jump up to:a b A. G. Lisi; Lee Smolin; Simone Speziale (2010). “Unification of gravity, gauge fields, and Higgs bosons”. arXiv:1004.4866 [gr-qc].
  43. Jump up^ “E8 Theory”. FQXi. 2008-08-04. Archived from the original on 9 August 2008. Retrieved 2008-08-05.
  44. Jump up^ “FQXi Grants”. FQXi. Archived from the original on 3 July 2008. Retrieved 2008-08-08.
  45. Jump up^ Merali, Zeeya (September 2010). “Rummaging for a Final Theory”. Scientific American. Retrieved 2010-08-25.
  46. Jump up^ M. J. Duff (2011). “String and M-theory: answering the critics”.arXiv:1112.0788v1.
  47. Jump up^ Peter Woit (2011-12-07). “String and M-theory: answering the critics”. Not Even Wrong. Retrieved 2011-12-21.

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