Quantum Cosmology

The physical laws that govern the universe prescribe how an initial state evolves with time. In classical physics, if the initial state of a system is specified exactly then the subsequent motion will be completely predictable. In quantum physics, specifying the initial state of a system allows one to calculate the probability that it will be found in any other state at a later time. Cosmology attempts to describe the behaviour of the entire universe using these physical laws. In applying these laws to the universe one immediately encounters a problem. What is the initial state that the laws should be applied to? In practice, cosmologists tend to work backwards by using the observed properties of the universe now to understand what it was like at earlier times. This approach has proved very successful. However it has led cosmologists back to the question of the initial conditions.
Inflation (a period of accelerating expansion in the very early universe) is now accepted as the standard explanation of several cosmological problems. In order for inflation to have occurred, the universe must have been formed containing some matter in a highly excited state. Inflationary theory does not address the question of why this matter was in such an excited state. Answering this demands a theory of the pre-inflationary initial conditions. There are two serious candidates for such a theory. The first, proposed by Andrei Linde of Stanford University, is called chaotic inflation. According to chaotic inflation, the universe starts off in a completely random state. In some regions matter will be more energetic than in others and inflation could ensue, producing the observable universe.

The second contender for a theory of initial conditions is quantum cosmology, the application of quantum theory to the entire universe. At first this sounds absurd because typically large systems (such as the universe) obey classical, not quantum, laws. Einstein's theory of general relativity is a classical theory that accurately describes the evolution of the universe from the first fraction of a second of its existence to now. However it is known that general relativity is inconsistent with the principles of quantum theory and is therefore not an appropriate description of physical processes that occur at very small length scales or over very short times. To describe such processes one requires a theory of quantum gravity.

In non-gravitational physics the approach to quantum theory that has proved most successful involves mathematical objects known as path integrals. Path integrals were introduced by the Nobel prizewinner Richard Feynman, of CalTech. In the path integral approach, the probability that a system in an initial state A will evolve to a final state B is given by adding up a contribution from every possible history of the system that starts in A and ends in B. For this reason a path integral is often referred to as a `sum over histories'. For large systems, contributions from similar histories cancel each other in the sum and only one history is important. This history is the history that classical physics would predict.

For mathematical reasons, path integrals are formulated in a background with four spatial dimensions rather than three spatial dimensions and one time dimension. There is a procedure known as `analytic continuation' which can be used to convert results expressed in terms of four spatial dimensions into results expressed in terms of three spatial dimensions and one time dimension. This effectively converts one of the spatial dimensions into the time dimension. This spatial dimension is sometimes referred to as `imaginary' time because it involves the use of so-called imaginary numbers, which are well defined mathematical objects used every day by electrical engineers.

The success of path integrals in describing non-gravitational physics naturally led to attempts to describe gravity using path integrals. Gravity is rather different from the other physical forces, whose classical description involves fields (e.g. electric or magnetic fields) propagating in spacetime. The classical description of gravity is given by general relativity, which says that the gravitational force is related to the curvature of spacetime itself i.e. to its geometry. Unlike for non-gravitational physics, spacetime is not just the arena in which physical processes take place but it is a dynamical field. Therefore a sum over histories of the gravitational field in quantum gravity is really a sum over possible geometries for spacetime.

The gravitational field at a fixed time can be described by the geometry of the three spatial dimensions at that time. The history of the gravitational field is described by the four dimensional spacetime that these three spatial dimensions sweep out in time. Therefore the path integral is a sum over all four dimensional spacetime geometries that interpolate between the initial and final three dimensional geometries. In other words it is a sum over all four dimensional spacetimes with two three dimensional boundaries which match the initial and final conditions. Once again, mathematical subtleties require that the path integral be formulated in four spatial dimensions rather than three spatial dimensions and one time dimension.

The path integral formulation of quantum gravity has many mathematical problems. It is also not clear how it relates to more modern attempts at constructing a theory of quantum gravity such as string/M-theory. However it can be used to correctly calculate quantities that can be calculated independently in other ways e.g. black hole temperatures and entropies.

We can now return to cosmology. At any moment, the universe is described by the geometry of the three spatial dimensions as well as by any matter fields that may be present. Given this data one can, in principle, use the path integral to calculate the probability of evolving to any other prescribed state at a later time. However this still requires a knowledge of the initial state, it does not explain it.

Quantum cosmology is a possible solution to this problem. In 1983, Stephen Hawking and James Hartle developed a theory of quantum cosmology which has become known as the `No Boundary Proposal'. Recall that the path integral involves a sum over four dimensional geometries that have boundaries matching onto the initial and final three geometries. The Hartle-Hawking proposal is to simply do away with the initial three geometry i.e. to only include four dimensional geometries that match onto the final three geometry. The path integral is interpreted as giving the probability of a universe with certain properties (i.e. those of the boundary three geometry) being created from nothing.

In practice, calculating probabilities in quantum cosmology using the full path integral is formidably difficult and an approximation has to be used. This is known as the semiclassical approximation because its validity lies somewhere between that of classical and quantum physics. In the semiclassical approximation one argues that most of the four dimensional geometries occuring in the path integral will give very small contributions to the path integral and hence these can be neglected. The path integral can be calculated by just considering a few geometries that give a particularly large contribution. These are known as instantons. Instantons don't exist for all choices of boundary three geometry; however those three geometries that do admit the existence of instantons are more probable than those that don't. Therefore attention is usually restricted to three geometries close to these.

Remember that the path integral is a sum over geometries with four spatial dimensions. Therefore an instanton has four spatial dimensions and a boundary that matches the three geometry whose probability we wish to compute. Typical instantons resemble (four dimensional) surfaces of spheres with the three geometry slicing the sphere in half. They can be used to calculate the quantum process of universe creation, which cannot be described using classical general relativity. They only usually exist for small three geometries, corresponding to the creation of a small universe. Note that the concept of time does not arise in this process. Universe creation is not something that takes place inside some bigger spacetime arena - the instanton describes the spontaneous appearance of a universe from literally nothing. Once the universe exists, quantum cosmology can be approximated by general relativity so time appears.

People have found different types of instantons that can provide the initial conditions for realistic universes. The first attempt to find an instanton that describes the creation of a universe within the context of the `no boundary' proposal was made by Stephen Hawking and Ian Moss. The Hawking-Moss instanton describes the creation of an eternally inflating universe with `closed' spatial three-geometries.

It is presently an unsolved question whether our universe contains closed, flat or open spatial three-geometries. In a flat universe, the large-scale spatial geometry looks like the ordinary three-dimensional space we experience around us. In contrast to this, the spatial sections of a realistic closed universe would look like three-dimensional (surfaces of) spheres with a very large but finite radius. An open geometry would look like an infinite hyperboloid. Only a closed universe would therefore be finite. There is, however, nowadays strong evidence from cosmological observations in favour of an infinite open universe. It is therefore an important question whether there exist instantons that describe the creation of open universes.

The idea behind the Coleman-De Luccia instanton, discovered in 1987, is that the matter in the early universe is initially in a state known as a false vacuum. A false vacuum is a classically stable excited state which is quantum mechanically unstable. In the quantum theory, matter which is in a false vacuum may `tunnel' to its true vacuum state. The quantum tunnelling of the matter in the early universe was described by Coleman and De Luccia. They showed that false vacuum decay proceeds via the nucleation of bubbles in the false vacuum. Inside each bubble the matter has tunnelled. Surprisingly, the interior of such a bubble is an infinite open universe in which inflation may occur. The cosmological instanton describing the creation of an open universe via this bubble nucleation is known as a Coleman-De Luccia instanton.

The Coleman-De Luccia Instanton
Remember that this scenario requires the existence of a false vacuum for the matter in the early universe. Moreover, the condition for inflation to occur once the universe has been created strongly constrains the way the matter decays to its true vacuum. Therefore the creation of open inflating universes appears to be rather contrived in the absence of any explanation of these specific pre-inflationary initial conditions.

Recently, Stephen Hawking and Neil Turok have proposed a bold solution to this problem. They constructed a class of instantons that give rise to open universes in a similar way to the instantons of Coleman and De Luccia. However, they did not require the existence of a false vacuum or other very specific properties of the excited matter state. The price they pay for this is that their instantons have singularities: places where the curvature becomes infinite. Since singularities are usually regarded as places where the theory breaks down and must be replaced by a more fundamental theory, this is a quite controversial feature of their work.

The Hawking-Turok Instanton
The question of course arises which of these instantons describes correctly the creation of our own universe. The way one might hope to distinguish between different theories of quantum cosmology is by considering quantum fluctuations about these instantons. The Heisenberg uncertainty principle in quantum mechanics implies that vacuum fluctuations are present in every quantum theory. In the full quantum picture therefore, an instanton provides us just with a background geometry in the path integral with respect to which quantum fluctuations need to be considered.

During inflation, these quantum mechanical vacuum fluctuations are amplified and due to the accelerating expansion of the universe they are stretched to macroscopic length scales. Later on, when the universe has cooled, they seed the growth of large scale structures (e.g. galaxies) like those we see today. One sees the imprint of these primordial fluctuations as small temperature perturbations in the cosmic microwave background radiation.

Since different types of instantons predict slightly different fluctuation spectra, the temperature perturbations in the cosmic microwave background radiation will depend on the instanton from which the universe was created. In the next decade the satellites MAP and PLANCK will be launched to measure the temperature of the microwave background radiation in different directions on the sky to a very high accuracy. The observations will not only provide us with a very important test of inflation itself but may also be the first possibility to observationally distinguish between different theories for quantum cosmology.

The observations made by MAP and PLANCK will therefore turn the `no boundary' proposal and instanton cosmology into real testable science!

Higgs boson

From Wikipedia, the free encyclopedia

Higgs boson

Candidate Higgs boson events from collisions between protons in the LHC. The top event in the CMS experiment shows a decay into two photons (dashed yellow lines and green towers). The lower event in the ATLAS experiment shows a decay into 4 muons (red tracks).[Note 1]
Composition	Elementary particle
Statistics	Bosonic
Status	A Higgs boson of mass ≈125 GeV 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
Colour 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 allows scientists to explore the Higgs field^[6][7] – a fundamental field first suspected to exist in the 1960s that unlike the more familiar electromagnetic field cannot be "turned off", but instead takes a non-zero constant value almost everywhere. The presence of this field - now believed to be confirmed - explains why some fundamental particles have mass even though the symmetries controlling their interactions should require them to be massless, and also answers several other long-standing puzzles in physics, such as the reason the weak force has a much shorter range than the electromagnetic force, and validating whether the last unverified area of the Standard Model was correct or not.

Despite being present everywhere, the existence of the Higgs field has been very hard to confirm. It can be detected through its excitations (i.e. Higgs particles), but these are extremely hard to produce and detect. The importance of this fundamental question led to a 40 year search for this elusive particle, and the construction of one of the world's most expensive and complex experimental facilities to date, CERN's 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 and 127 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 mechanism that 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 inappropriate sensationalism.^[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-researcher Robert Brout had died in 2011 and the Nobel Prize is not ordinarily given posthumously.

In the Standard Model, the Higgs particle is a boson with no spin, electric charge, or colour charge. It is also very unstable, decaying into other particles almost immediately. It is a quantum excitation of one of the four components of the Higgs field. The latter constitutes a scalar field, with two neutral and two electrically charged components, 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 as fermions (via Yukawa couplings), causing these to acquire mass as well. Some versions of the theory predict more than one kind of Higgs fields and bosons. Alternative "Higgsless" models would have been considered if the Higgs boson was not discovered.

10. A non-technical summary

    "Higgs" terminology

    [hide]A simple explanation – what are the Higgs mechanism, field and boson?
    Symmetries and 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 called W and Z bosons).[Note 3] Their very short range – a result of their mass – makes structures like atoms 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 mathematical model devised by three groups of researchers in 1964 that explains why and how gauge bosons could still be massive despite their governing symmetry. It showed that the conditions for the symmetry would be 'broken' if an unusual type of field 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 electrons and 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 confirmed 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 confirmed 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]

    Overview

    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 evidence 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 disciplines. If not, then other more complicated theories would need to be explored. The simplest solution to whether 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 confirmed, but revealing the exact cause has been difficult .
    
    Various analogies have also been invented to describe the Higgs field and boson, including analogies with well-known symmetry breaking effects such as the rainbow and prism, electric fields, ripples, and resistance of macro objects moving through media, like people moving through crowds or some objects moving through syrup or molasses. However, analogies based on simple resistance to motion are inaccurate as the Higgs field does not work by resisting motion.
    

    Significance

    Scientific impact

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

    Validating[citation needed] the Standard Model, or choosing between extensions and alternatives	Does the Higgs field exist, which fundamentally validates[citation needed] 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 how symmetry breaking happens within the electroweak interaction	Below an extremely high temperature, electroweak symmetry breaking causes the electroweak interaction to manifest in part as the short-ranged weak force, which is carried by massive gauge bosons. Without this, the universe we see around us could not exist, because atoms and other structures could not form, and reactions in stars such as our Sun would not occur. But it is not clear how this actually happens in nature. Is the Standard Model correct in its approach, and can it be made more exact with actual experimental measurements? If not the Higgs field, then what is breaking symmetry in its place?
    Finding how certain particles acquire mass	Electroweak symmetry breaking (due to a Higgs field or otherwise) is believed proven responsible for the masses of fundamental particles such as elementary fermions (including electrons and quarks) and the massive W and Z gauge bosons. Finding how this happens is pivotal to particle physics. It is worth noting that the Higgs field does not 'create' mass out of nothing (which would violate the law of conservation of energy). Nor is the Higgs field responsible for the mass of all particles. For example, about 99% of the mass of baryons (composite particles such as the proton and neutron) is due instead to 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 into cosmic inflation	There has been considerable scientific research on possible links between the Higgs field and the inflaton – a hypothetical field suggested as the explanation for the expansion of space during the first fraction of a second of the universe (known as the "inflationary epoch"). Some theories suggest that a fundamental scalar field might be responsible for this phenomenon; the Higgs field is such a field and therefore has led to papers analysing whether it could also be the inflaton responsible for this exponential expansion of the universe during the Big Bang. Such theories are highly tentative and face significant problems related to unitarity, but may be viable if combined with additional features such as large non-minimal coupling, a Brans–Dicke scalar, or other "new" physics, and have received treatments suggesting that Higgs inflation models are still of interest theoretically.
    Insight into the nature of the universe, and its possible fates	Diagram showing the Higgs boson and top quark masses, which could indicate whether our universe is stable, or a long-lived 'bubble'. As of 2012, the 2σ ellipse based on Tevatron and LHC data still allows for both possibilities.[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]). A 125 – 127 GeV Higgs mass seems to be extremely close to the boundary for stability (estimated in 2012 as 123.8 – 135.0 GeV[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 Bang caused the universe to be a kind of featureless symmetry of undifferentiated extremely high energy. In this kind of speculation, the single unified field of a Grand Unified Theory is identified as (or modeled upon) the Higgs field, and it is through successive symmetry breakings of the Higgs field or some similar field at phase transitions that the present universe's known forces and fields arise.[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 major unanswered problem in physics. Further information: Zero-point energy and Vacuum state

    "Real world" impact

    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 and computers, 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 and magnetism; 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]
    

    History

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

    
    Nobel Prize Laureate Peter Higgs in Stockholm, December 2013
    
    Particle physicists study matter made from fundamental particles whose interactions are mediated by exchange particles - gauge bosons - acting as force carriers. At the beginning of the 1960s a number of these particles had been discovered or proposed, along with theories suggesting how they relate to each other, some of which had already been reformulated as field theories in which the objects of study are not particles and forces, but quantum fields and their symmetries.^[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 the renormalization 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

    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

    Theoretical need for the Higgs

    
    "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" symmetry inevitably becomes broken since eventually the ball must at random roll one way or another.
    
    Gauge invariance is an important property of modern particle theories such as the Standard Model, partly due to its success in other areas of fundamental physics such as electromagnetism and the strong interaction (quantum chromodynamics). However, there were great difficulties in developing gauge theories for the weak nuclear force or a possible unified electroweak interaction. Fermions with a mass term would violate gauge symmetry and therefore cannot be gauge invariant. (This can be seen by examining the Dirac Lagrangian for a fermion in terms of left and right handed components; we find none of the spin-half particles could ever flip helicity as required for mass, so they must be massless.^{[Note 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 of Goldstone's theorem) which did not actually seem to exist in nature.
    
    A solution to all of these overlapping problems came from the discovery of a previously unnoticed borderline case hidden in the mathematics of Goldstone's theorem,^{[Note 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: ), which has the unusual property of a non-zero amplitude in its ground state; i.e., a non-zero vacuum expectation value. It can have this effect because of its unusual "Mexican hat" shaped potential whose lowest "point" is not at its "centre". Below a certain extremely high energy level the existence of this non-zero vacuum expectation spontaneously breaks electroweak gauge symmetry which in turn gives rise to the Higgs mechanism and triggers the acquisition of mass by those particles interacting with the field. This effect occurs because scalar field components of the Higgs field are "absorbed" by the massive bosons as degrees of freedom, and couple to the fermions via Yukawa coupling, thereby producing the expected mass terms. In effect when symmetry breaks under these conditions, the Goldstone bosons that arise interact with the Higgs field (and with other particles capable of interacting with the Higgs field) instead of becoming new massless particles, the intractable problems of both underlying theories "neutralise" each other, and the residual outcome is that elementary particles acquire a consistent mass based on how strongly they interact with the Higgs field. It is the simplest known process capable of giving mass to the gauge bosons while remaining compatible with gauge theories.^[84] Its quantum would be a scalar boson, known as the Higgs boson.^[85]
    
    
    
    Summary of interactions between certain particles described by the Standard Model.

    Properties of the Standard Model Higgs

    In the Standard Model, the Higgs field consists of four components, two neutral ones and two charged component fields. Both of the charged components and one of the neutral fields are Goldstone bosons, which act as the longitudinal third-polarization components of the massive W⁺, W^–, and Z bosons. The quantum of the remaining neutral component corresponds to (and is theoretically realised as) the massive Higgs boson.^[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 and 180 GeV/c², then the Standard Model can be valid at energy scales all the way up to the Planck scale (10¹⁹ GeV).^[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 to 185 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]
    

    Production

    Feynman diagrams for Higgs production

    Gluon fusion	Higgs Strahlung
    Vector boson fusion	Top fusion

    If Higgs particle theories are correct, then a Higgs particle can be produced much like other particles that are studied, in a particle collider. This involves accelerating a large number of particles to extremely high energies and extremely close to the speed of light, then allowing them to smash together. Protons and lead ions (the bare nuclei of lead atoms) are used at the LHC. In the extreme energies of these collisions, the desired esoteric particles will occasionally be produced and this can be detected and studied; any absence or difference from theoretical expectations can also be used to improve the theory. The relevant particle theory (in this case the Standard Model) will determine the necessary kinds of collisions and detectors. The Standard Model predicts that Higgs bosons could be formed in a number of ways,^[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]

    Decay

    
    The Standard Model prediction for the decay width of the Higgs particle depends on the value of its mass.
    
    Quantum mechanics predicts that if it is possible for a particle to decay into a set of lighter particles, then it will eventually do so.^[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 a bottom–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 of 126 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

    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 called techniquarks. Other models, feature pairs of top quarks (see top quark condensate). In yet other models, there is no Higgs field at all and the electroweak symmetry is broken using extra dimensions.^[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

    The Standard Model leaves the mass of the Higgs boson as a parameter to be measured, rather than a value to be calculated. This is seen as theoretically unsatisfactory, particularly as quantum corrections (related to interactions with virtual particles) should apparently cause the Higgs particle to have a mass immensely higher than that observed, but at the same time the Standard Model requires a mass of the order of 100 to 1000 GeV to ensure unitarity (in this case, to unitarise longitudinal vector boson scattering).^[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 the Planck mass or the grand unification energy, it appears that either there is some underlying connection or reason for these observations which is unknown and not described by the Standard Model, or some unexplained and extremely precise fine-tuning of parameters – however at present neither of these explanations is proven. This is known as a hierarchy problem.^[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.
    There are also issues of Quantum triviality, which suggests that it may not be possible to create a consistent quantum field theory involving elementary scalar particles.
    

    Experimental search

    To produce Higgs bosons, two beams of particles are accelerated to very high energies and allowed to collide within a particle detector. Occasionally, although rarely, a Higgs boson will be created fleetingly as part of the collision byproducts. Because the Higgs boson decays very quickly, particle detectors cannot detect it directly. Instead the detectors register all the decay products (the decay signature) and from the data the decay process is reconstructed. If the observed decay products match a possible decay process (known as a decay channel) of a Higgs boson, this indicates that a Higgs boson may have been created. In practice, many processes may produce similar decay signatures. Fortunately, the Standard Model precisely predicts the likelihood of each of these, and each known process, occurring. So, if the detector detects more decay signatures consistently matching a Higgs boson than would otherwise be expected if Higgs bosons did not exist, then this would be strong evidence that the Higgs boson exists.
    Because Higgs boson production in a particle collision is likely to be very rare (1 in 10 billion at the LHC),^{[Note 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

    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 than 114.4 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

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

    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 the collider'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

    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] 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 ATLAS a 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

    Naming

    Names used by physicists

    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 Close and physicist-blogger Peter Woit both comment that the paper by GHK was also completed after Higgs and Brout–Englert were submitted to Physical Review Letters.[81]:167[157] and that Higgs alone had drawn attention to a predicted massive scalar boson, while all others had focused on the massive vector bosons;[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]

    Nickname

    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 the 1993 book on the Higgs boson and particle physics - The God Particle: If the Universe Is the Answer, What Is the Question? by Nobel Physics prizewinner and Fermilab director Leon Lederman.^[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

    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 physicsworld.com.^[180]
    

    Media explanations and analogies

    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 because photons are not all affected to the same degree by the dispersive material of the prism.
    
    An educational collaboration involving an LHC physicist and a High School Teachers at CERN educator suggests that dispersion of light – responsible for the rainbow and dispersive prism – is a useful analogy for the Higgs field's symmetry breaking and mass-causing effect.^[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 with Newton's third law.^[189]
    

    Recognition and awards

    There has been considerable discussion of how to allocate the credit if the Higgs boson is proven, made more pointed as a Nobel prize had been expected, and the very wide basis of people entitled to consideration. These include a range of theoreticians who made the Higgs mechanism theory possible, the theoreticians of the 1964 PRL papers (including Higgs himself), the theoreticians who derived from these, a working electroweak theory and the Standard Model itself, and also the experimentalists at CERN and other institutions who made possible the proof of the Higgs field and boson in reality. The Nobel prize has a limit of 3 persons to share an award, and some possible winners are already prize holders for other work, or are deceased (the prize is only awarded to persons in their lifetime). Existing prizes for works relating to the Higgs field, boson, or mechanism include:
    
    
    • Nobel Prize in Physics (1979) – Glashow, Salam, and Weinberg, for contributions to the theory of the unified weak and electromagnetic interaction between elementary particles ^[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 physicist Satyendra 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]