Standard Model

The Standard Model of particle physics is the theory describing three of the four known fundamental forces (the electromagnetic, weak, and strong interactions, and not including the gravitational force) in the universe, as well as classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists around the world,[1] with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, confirmation of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.

Although the Standard Model is believed to be theoretically self-consistent[2] and has demonstrated huge successes in providing experimental predictions, it leaves some phenomena unexplained and falls short of being a complete theory of fundamental interactions. It does not fully explain baryon asymmetry, incorporate the full theory of gravitation[3] as described by general relativity, or account for the accelerating expansion of the Universe as possibly described by dark energy. The model does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations and their non-zero masses.

The development of the Standard Model was driven by theoretical and experimental particle physicists alike. For theorists, the Standard Model is a paradigm of a quantum field theory, which exhibits a wide range of physics including spontaneous symmetry breaking, anomalies and non-perturbative behavior. It is used as a basis for building more exotic models that incorporate hypothetical particles, extra dimensions, and elaborate symmetries (such as supersymmetry) in an attempt to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations.

Standard Model of Elementary Particles
Elementary particles included in the Standard Model

Historical background

In 1954, Chen Ning Yang and Robert Mills extended the concept of gauge theory for abelian groups, e.g. quantum electrodynamics, to nonabelian groups to provide an explanation for strong interactions.[4] In 1961, Sheldon Glashow combined the electromagnetic and weak interactions.[5] In 1967 Steven Weinberg[6] and Abdus Salam[7] incorporated the Higgs mechanism[8][9][10] into Glashow's electroweak interaction, giving it its modern form.

The Higgs mechanism is believed to give rise to the masses of all the elementary particles in the Standard Model. This includes the masses of the W and Z bosons, and the masses of the fermions, i.e. the quarks and leptons.

After the neutral weak currents caused by Z boson exchange were discovered at CERN in 1973,[11][12][13][14] the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 Nobel Prize in Physics for discovering it. The W± and Z0 bosons were discovered experimentally in 1983; and the ratio of their masses was found to be as the Standard Model predicted.

The theory of the strong interaction (i.e. quantum chromodynamics, QCD), to which many contributed, acquired its modern form in 1973–74 when asymptotic freedom was proposed[15][16] (a development which made QCD the main focus of theoretical research)[17] and experiments confirmed that the hadrons were composed of fractionally charged quarks.[18][19]

The term "Standard Model" was first coined by Abraham Pais and Sam Treiman in 1975, with reference to the electroweak theory with four quarks.[20]

Overview

At present, matter and energy are best understood in terms of the kinematics and interactions of elementary particles. To date, physics has reduced the laws governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. A major goal of physics is to find the "common ground" that would unite all of these theories into one integrated theory of everything, of which all the other known laws would be special cases, and from which the behavior of all matter and energy could be derived (at least in principle).[21]

Particle content

The Standard Model includes members of several classes of elementary particles, which in turn can be distinguished by other characteristics, such as color charge.

All particles can be summarized as follows:

Elementary particles
Elementary fermionsHalf-integer spinObey the Fermi–Dirac statisticsElementary bosonsInteger spinObey the Bose–Einstein statistics
Quarks and antiquarksSpin = 1/2Have color chargeParticipate in strong interactionsLeptons and antileptonsSpin = 1/2No color chargeElectroweak interactionsGauge bosonsSpin = 1Force carriersScalar bosonsSpin = 0
Generations
  1. Up (u), Down (d)
  2. Charm (c), Strange (s)
  3. Top (t), Bottom (b)
Generations
  1. Electron (
    e
    )1, Electron neutrino (
    ν
    e
    )
  2. Muon (
    μ
    ), Muon neutrino (
    ν
    μ
    )
  3. Tau (
    τ
    ), Tau neutrino (
    ν
    τ
    )
Four kinds (four fundamental interactions)
  1. Photon (
    γ
    , electromagnetic interaction)
  2. W and Z bosons (
    W+
    ,
    W
    ,
    Z
    , weak interaction)
  3. Eight types of gluons (
    g
    , strong interaction)
  4. Graviton (
    G
    , gravity, hypothetical)2
Higgs boson (H0)

Notes:
1. The antielectron (
e+
) is traditionally called positron.
2. The known force carrier bosons all have spin = 1 and are therefore vector bosons. The hypothetical graviton has spin = 2 and is a tensor boson; whether it is a gauge boson as well, is unknown.

Fermions

Elementary particle interactions in the Standard Model
Summary of interactions between particles described by the Standard Model

The Standard Model includes 12 elementary particles of spin12, known as fermions. According to the spin–statistics theorem, fermions respect the Pauli exclusion principle. Each fermion has a corresponding antiparticle.

The fermions of the Standard Model are classified according to how they interact (or equivalently, by what charges they carry). There are six quarks (up, down, charm, strange, top, bottom), and six leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino). Pairs from each classification are grouped together to form a generation, with corresponding particles exhibiting similar physical behavior (see table).

The defining property of the quarks is that they carry color charge, and hence interact via the strong interaction. A phenomenon called color confinement results in quarks being very strongly bound to one another, forming color-neutral composite particles (hadrons) containing either a quark and an antiquark (mesons) or three quarks (baryons). The familiar proton and neutron are the two baryons having the smallest mass. Quarks also carry electric charge and weak isospin. Hence they interact with other fermions both electromagnetically and via the weak interaction. The remaining six fermions do not carry color charge and are called leptons. The three neutrinos do not carry electric charge either, so their motion is directly influenced only by the weak nuclear force, which makes them notoriously difficult to detect. However, by virtue of carrying an electric charge, the electron, muon, and tau all interact electromagnetically.

Each member of a generation has greater mass than the corresponding particles of lower generations. The first-generation charged particles do not decay, hence all ordinary (baryonic) matter is made of such particles. Specifically, all atoms consist of electrons orbiting around atomic nuclei, ultimately constituted of up and down quarks. Second- and third-generation charged particles, on the other hand, decay with very short half-lives and are observed only in very high-energy environments. Neutrinos of all generations also do not decay and pervade the universe, but rarely interact with baryonic matter.

Gauge bosons

Standard Model Feynman Diagram Vertices
The above interactions form the basis of the standard model. Feynman diagrams in the standard model are built from these vertices. Modifications involving Higgs boson interactions and neutrino oscillations are omitted. The charge of the W bosons is dictated by the fermions they interact with; the conjugate of each listed vertex (i.e. reversing the direction of arrows) is also allowed.

In the Standard Model, gauge bosons are defined as force carriers that mediate the strong, weak, and electromagnetic fundamental interactions.

Interactions in physics are the ways that particles influence other particles. At a macroscopic level, electromagnetism allows particles to interact with one another via electric and magnetic fields, and gravitation allows particles with mass to attract one another in accordance with Einstein's theory of general relativity. The Standard Model explains such forces as resulting from matter particles exchanging other particles, generally referred to as force mediating particles. When a force-mediating particle is exchanged, at a macroscopic level the effect is equivalent to a force influencing both of them, and the particle is therefore said to have mediated (i.e., been the agent of) that force. The Feynman diagram calculations, which are a graphical representation of the perturbation theory approximation, invoke "force mediating particles", and when applied to analyze high-energy scattering experiments are in reasonable agreement with the data. However, perturbation theory (and with it the concept of a "force-mediating particle") fails in other situations. These include low-energy quantum chromodynamics, bound states, and solitons.

The gauge bosons of the Standard Model all have spin (as do matter particles). The value of the spin is 1, making them bosons. As a result, they do not follow the Pauli exclusion principle that constrains fermions: thus bosons (e.g. photons) do not have a theoretical limit on their spatial density (number per volume). The different types of gauge bosons are described below.

  • Photons mediate the electromagnetic force between electrically charged particles. The photon is massless and is well-described by the theory of quantum electrodynamics.
  • The
    W+
    ,
    W
    , and
    Z
    gauge bosons mediate the weak interactions between particles of different flavors (all quarks and leptons). They are massive, with the
    Z
    being more massive than the
    W±
    . The weak interactions involving the
    W±
    exclusively act on left-handed particles and right-handed antiparticles. Furthermore, the
    W±
    carries an electric charge of +1 and −1 and couples to the electromagnetic interaction. The electrically neutral
    Z
    boson interacts with both left-handed particles and antiparticles. These three gauge bosons along with the photons are grouped together, as collectively mediating the electroweak interaction.
  • The eight gluons mediate the strong interactions between color charged particles (the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled by a combination of color and anticolor charge (e.g. red–antigreen).[note 1] Because the gluons have an effective color charge, they can also interact among themselves. The gluons and their interactions are described by the theory of quantum chromodynamics.

The interactions between all the particles described by the Standard Model are summarized by the diagrams on the right of this section.

Higgs boson

The Higgs particle is a massive scalar elementary particle theorized by Peter Higgs in 1964, when he showed that Goldstone's 1962 theorem (generic continuous symmetry, which is spontaneously broken) provides a third polarisation of a massive vector field. Hence, Goldstone's original scalar doublet, the massive spin-zero particle, was proposed as the Higgs boson. (see 1964 PRL symmetry breaking papers) and is a key building block in the Standard Model.[8][9][10][22] It has no intrinsic spin, and for that reason is classified as a boson (like the gauge bosons, which have integer spin).

The Higgs boson plays a unique role in the Standard Model, by explaining why the other elementary particles, except the photon and gluon, are massive. In particular, the Higgs boson explains why the photon has no mass, while the W and Z bosons are very heavy. Elementary-particle masses, and the differences between electromagnetism (mediated by the photon) and the weak force (mediated by the W and Z bosons), are critical to many aspects of the structure of microscopic (and hence macroscopic) matter. In electroweak theory, the Higgs boson generates the masses of the leptons (electron, muon, and tau) and quarks. As the Higgs boson is massive, it must interact with itself.

Because the Higgs boson is a very massive particle and also decays almost immediately when created, only a very high-energy particle accelerator can observe and record it. Experiments to confirm and determine the nature of the Higgs boson using the Large Hadron Collider (LHC) at CERN began in early 2010 and were performed at Fermilab's Tevatron until its closure in late 2011. Mathematical consistency of the Standard Model requires that any mechanism capable of generating the masses of elementary particles becomes visible at energies above 1.4 TeV;[23] therefore, the LHC (designed to collide two 7 TeV proton beams) was built to answer the question of whether the Higgs boson actually exists.[24]

On 4 July 2012, two of the experiments at the LHC (ATLAS and CMS) both reported independently that they found a new particle with a mass of about 125 GeV/c2 (about 133 proton masses, on the order of 10×10−25 kg), which is "consistent with the Higgs boson".[25][26][27][28][29][30] It was later confirmed to be the searched-for Higgs boson.[31]

Theoretical aspects

Construction of the Standard Model Lagrangian

Technically, quantum field theory provides the mathematical framework for the Standard Model, in which a Lagrangian controls the dynamics and kinematics of the theory. Each kind of particle is described in terms of a dynamical field that pervades space-time. The construction of the Standard Model proceeds following the modern method of constructing most field theories: by first postulating a set of symmetries of the system, and then by writing down the most general renormalizable Lagrangian from its particle (field) content that observes these symmetries.

The global Poincaré symmetry is postulated for all relativistic quantum field theories. It consists of the familiar translational symmetry, rotational symmetry and the inertial reference frame invariance central to the theory of special relativity. The local SU(3)×SU(2)×U(1) gauge symmetry is an internal symmetry that essentially defines the Standard Model. Roughly, the three factors of the gauge symmetry give rise to the three fundamental interactions. The fields fall into different representations of the various symmetry groups of the Standard Model (see table). Upon writing the most general Lagrangian, one finds that the dynamics depends on 19 parameters, whose numerical values are established by experiment. The parameters are summarized in the table (made visible by clicking "show") above (note: the Higgs mass is at 125 GeV, the Higgs self-coupling strength λ ~ ​18).

Quantum chromodynamics sector

The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, with SU(3) symmetry, generated by Ta. Since leptons do not interact with gluons, they are not affected by this sector. The Dirac Lagrangian of the quarks coupled to the gluon fields is given by

where

ψ
i
is the Dirac spinor of the quark field, where i = {r, g, b} represents color,
γμ are the Dirac matrices,
Ga
μ
is the 8-component () SU(3) gauge field,
Ta
ij
are the 3 × 3 Gell-Mann matrices, generators of the SU(3) color group,
Ga
μν
represents the gluon field strength tensor,
gs is the strong coupling constant.

Electroweak sector

The electroweak sector is a Yang–Mills gauge theory with the symmetry group U(1) × SU(2)L,

where

Bμ is the U(1) gauge field,
YW is the weak hypercharge – the generator of the U(1) group,
Wμ is the 3-component SU(2) gauge field,
τL are the Pauli matrices – infinitesimal generators of the SU(2) group – with subscript L to indicate that they only act on left-chiral fermions,
g' and g are the U(1) and SU(2) coupling constants respectively,
() and are the field strength tensors for the weak isospin and weak hypercharge fields.

Notice that the addition of fermion mass terms into the electroweak lagrangian is forbidden, since terms of the form do not respect U(1) × SU(2)L gauge invariance. Neither is it possible to add explicit mass terms for the U(1) and SU(2) gauge fields. The Higgs mechanism is responsible for the generation of the gauge boson masses, and the fermion masses result from Yukawa-type interactions with the Higgs field.

Higgs sector

In the Standard Model, the Higgs field is a complex scalar of the group SU(2)L:

where the superscripts + and 0 indicate the electric charge (Q) of the components. The weak hypercharge (YW) of both components is 1.

Before symmetry breaking, the Higgs Lagrangian is

which can also be written as

Yukawa sector

The Yukawa interaction terms are

where Gu,d are 3 × 3 matrices of Yukawa couplings, with the ij term giving the coupling of the generations i and j.

Fundamental forces

The Standard Model describes three of the four fundamental forces in nature; only gravity remains unexplained. In the Standard Model, a force is described as an exchange of bosons between the objects affected, such as a photon for the electromagnetic force and a gluon for the strong interaction. Those particles are called force carriers or messenger particles.[32]

The four fundamental interactions of nature[33]
Property/Interaction Gravitation Weak Electromagnetic Strong
(Electroweak) Fundamental Residual
Mediating particles Not yet observed
(Graviton hypothesised)
W+, W and Z0 γ (photon) Gluons π, ρ and ω mesons
Affected particles All particles Left-handed fermions Electrically charged Quarks, Gluons Hadrons
Acts on Mass, Energy Flavor Electric charge Color charge
Bound states formed Planets, Stars, Solar systems, Galaxies n/a Atoms, Molecules Hadrons Atomic nuclei
Strength at the scale of quarks
(relative to electromagnetism)
10−41(predicted) 10−4 1 60 Not applicable
to quarks
Strength at the scale of
protons/neutrons
(relative to electromagnetism)
10−36(predicted) 10−7 1 Not applicable
to hadrons
20

Tests and predictions

The Standard Model (SM) predicted the existence of the W and Z bosons, gluon, and the top and charm quarks and predicted many of their properties before these particles were observed. The predictions were experimentally confirmed with good precision.[34]

The SM also predicted the existence of the Higgs boson, found in 2012 at the Large Hadron Collider, as the last particle of the SM.[35]

Challenges

Question, Web Fundamentals.svg Unsolved problem in physics:
  • What gives rise to the Standard Model of particle physics?
  • Why do particle masses and coupling constants have the values that we measure?
  • Why are there three generations of particles?
  • Why is there more matter than antimatter in the universe?
  • Where does Dark Matter fit into the model? Does it even consist of one or more new particles?
(more unsolved problems in physics)

Self-consistency of the Standard Model (currently formulated as a non-abelian gauge theory quantized through path-integrals) has not been mathematically proven. While regularized versions useful for approximate computations (for example lattice gauge theory) exist, it is not known whether they converge (in the sense of S-matrix elements) in the limit that the regulator is removed. A key question related to the consistency is the Yang–Mills existence and mass gap problem.

Experiments indicate that neutrinos have mass, which the classic Standard Model did not allow.[36] To accommodate this finding, the classic Standard Model can be modified to include neutrino mass.

If one insists on using only Standard Model particles, this can be achieved by adding a non-renormalizable interaction of leptons with the Higgs boson.[37] On a fundamental level, such an interaction emerges in the seesaw mechanism where heavy right-handed neutrinos are added to the theory. This is natural in the left-right symmetric extension of the Standard Model[38][39] and in certain grand unified theories.[40] As long as new physics appears below or around 1014 GeV, the neutrino masses can be of the right order of magnitude.

Theoretical and experimental research has attempted to extend the Standard Model into a Unified field theory or a Theory of everything, a complete theory explaining all physical phenomena including constants. Inadequacies of the Standard Model that motivate such research include:

  • The model does not explain gravitation, although physical confirmation of a theoretical particle known as a graviton would account for it to a degree. Though it addresses strong and electroweak interactions, the Standard Model does not consistently explain the canonical theory of gravitation, general relativity, in terms of quantum field theory. The reason for this is, among other things, that quantum field theories of gravity generally break down before reaching the Planck scale. As a consequence, we have no reliable theory for the very early universe.
  • Some physicists consider it to be ad hoc and inelegant, requiring 19 numerical constants whose values are unrelated and arbitrary.[41] Although the Standard Model, as it now stands, can explain why neutrinos have masses, the specifics of neutrino mass are still unclear. It is believed that explaining neutrino mass will require an additional 7 or 8 constants, which are also arbitrary parameters.
  • The Higgs mechanism gives rise to the hierarchy problem if some new physics (coupled to the Higgs) is present at high energy scales. In these cases, in order for the weak scale to be much smaller than the Planck scale, severe fine tuning of the parameters is required; there are, however, other scenarios that include quantum gravity in which such fine tuning can be avoided.[42] 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.[43]
  • The model is inconsistent with the emerging Lambda-CDM model of cosmology. Contentions include the absence of an explanation in the Standard Model of particle physics for the observed amount of cold dark matter (CDM) and its contributions to dark energy, which are many orders of magnitude too large. It is also difficult to accommodate the observed predominance of matter over antimatter (matter/antimatter asymmetry). The isotropy and homogeneity of the visible universe over large distances seems to require a mechanism like cosmic inflation, which would also constitute an extension of the Standard Model.

Currently, no proposed Theory of Everything has been widely accepted or verified.

See also

Notes

  1. ^ Technically, there are nine such color–anticolor combinations. However, there is one color-symmetric combination that can be constructed out of a linear superposition of the nine combinations, reducing the count to eight.

References

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Further reading

Introductory textbooks
  • I. Aitchison; A. Hey (2003). Gauge Theories in Particle Physics: A Practical Introduction. Institute of Physics. ISBN 978-0-585-44550-2.
  • W. Greiner; B. Müller (2000). Gauge Theory of Weak Interactions. Springer. ISBN 978-3-540-67672-0.
  • G.D. Coughlan; J.E. Dodd; B.M. Gripaios (2006). The Ideas of Particle Physics: An Introduction for Scientists. Cambridge University Press.
  • D.J. Griffiths (1987). Introduction to Elementary Particles. John Wiley & Sons. ISBN 978-0-471-60386-3.
  • G.L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 978-0-201-11749-3.
Advanced textbooks
Journal articles

External links

Boson

In quantum mechanics, a boson (, ) is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions. The name boson was coined by Paul Dirac to commemorate the contribution of Indian physicist and professor of physics at University of Calcutta and at University of Dhaka, Satyendra Nath Bose in developing, with Albert Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles.Examples of bosons include fundamental particles such as photons, gluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the recently discovered Higgs boson, and the hypothetical graviton of quantum gravity. Some composite particles are also bosons, such as mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, atomic mass number = 2), helium-4, or lead-208; as well as some quasiparticles (e.g. Cooper pairs, plasmons, and phonons).An important characteristic of bosons is that their statistics do not restrict the number of them that occupy the same quantum state. This property is exemplified by helium-4 when it is cooled to become a superfluid. Unlike bosons, two identical fermions cannot occupy the same quantum space. Whereas the elementary particles that make up matter (i.e. leptons and quarks) are fermions, the elementary bosons are force carriers that function as the 'glue' holding matter together. This property holds for all particles with integer spin (s = 0, 1, 2, etc.) as a consequence of the spin–statistics theorem.

When a gas of Bose particles is cooled down to temperatures very close to absolute zero, then the kinetic energy of the particles decreases to a negligible amount, and they condense into the lowest energy level state. This state is called a Bose-Einstein condensate. It is believed that this property is the explanation of superfluidity.

CP violation

In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C symmetry) while its spatial coordinates are inverted ("mirror" or P symmetry). The discovery of CP violation in 1964 in the decays of neutral kaons resulted in the Nobel Prize in Physics in 1980 for its discoverers James Cronin and Val Fitch.

It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present Universe, and in the study of weak interactions in particle physics.

Elementary particle

In particle physics, an elementary particle or fundamental particle is a subatomic particle with no sub structure, thus not composed of other particles. Particles currently thought to be elementary include the fundamental fermions (quarks, leptons, antiquarks, and antileptons), which generally are "matter particles" and "antimatter particles", as well as the fundamental bosons (gauge bosons and the Higgs boson), which generally are "force particles" that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle.

Everyday matter is composed of atoms, once presumed to be matter's elementary particles—atom meaning "unable to cut" in Greek—although the atom's existence remained controversial until about 1910, as some leading physicists regarded molecules as mathematical illusions, and matter as ultimately composed of energy. Soon, subatomic constituents of the atom were identified. As the 1930s opened, the electron and the proton had been observed, along with the photon, the particle of electromagnetic radiation. At that time, the recent advent of quantum mechanics was radically altering the conception of particles, as a single particle could seemingly span a field as would a wave, a paradox still eluding satisfactory explanation.Via quantum theory, protons and neutrons were found to contain quarks—up quarks and down quarks—now considered elementary particles. And within a molecule, the electron's three degrees of freedom (charge, spin, orbital) can separate via the wavefunction into three quasiparticles (holon, spinon, orbiton). Yet a free electron—which is not orbiting an atomic nucleus and lacks orbital motion—appears unsplittable and remains regarded as an elementary particle.Around 1980, an elementary particle's status as indeed elementary—an ultimate constituent of substance—was mostly discarded for a more practical outlook, embodied in particle physics' Standard Model, what's known as science's most experimentally successful theory. Many elaborations upon and theories beyond the Standard Model, including the popular supersymmetry, double the number of elementary particles by hypothesizing that each known particle associates with a "shadow" partner far more massive, although all such superpartners remain undiscovered. Meanwhile, an elementary boson mediating gravitation—the graviton—remains hypothetical.

Fundamental interaction

In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electromagnetic interactions, which produce significant long-range forces whose effects can be seen directly in everyday life, and the strong and weak interactions, which produce forces at minuscule, subatomic distances and govern nuclear interactions. Some scientists hypothesize that a fifth force might exist, but the hypotheses remain speculative.

Each of the known fundamental interactions can be described mathematically as a field. The gravitational force is attributed to the curvature of spacetime, described by Einstein's general theory of relativity. The other three are discrete quantum fields, and their interactions are mediated by elementary particles described by the Standard Model of particle physics.

Within the Standard Model, the strong interaction is carried by a particle called the gluon, and is responsible for quarks binding together to form hadrons, such as protons and neutrons. As a residual effect, it creates the nuclear force that binds the latter particles to form atomic nuclei. The weak interaction is carried by particles called W and Z bosons, and also acts on the nucleus of atoms, mediating radioactive decay. The electromagnetic force, carried by the photon, creates electric and magnetic fields, which are responsible for the attraction between orbital electrons and atomic nuclei which holds atoms together, as well as chemical bonding and electromagnetic waves, including visible light, and forms the basis for electrical technology. Although the electromagnetic force is far stronger than gravity, it tends to cancel itself out within large objects, so over large distances (on the scale of planets and galaxies), gravity tends to be the dominant force.

All four fundamental forces are believed to be related, and to unite into a single force at high energies on a minuscule scale, the Planck scale, but particle accelerators cannot produce the enormous energies required to experimentally probe this. Efforts to devise a common theoretical framework that would explain the relation between the forces are perhaps the greatest goal of today's theoretical physicists. The weak and electromagnetic forces have already been unified with the electroweak theory of Sheldon Glashow, Abdus Salam, and Steven Weinberg for which they received the 1979 Nobel Prize in physics. Progress is currently being made in uniting the electroweak and strong fields within a Grand Unified Theory (GUT). A bigger challenge is to find a way to quantize the gravitational field, resulting in a theory of quantum gravity (QG) which would unite gravity in a common theoretical framework with the other three forces. Some theories, notably string theory, seek both QG and GUT within one framework, unifying all four fundamental interactions along with mass generation within a theory of everything (ToE).

Gauge boson

In particle physics, a gauge boson is a force carrier, a bosonic particle that carries any of the fundamental interactions of nature, commonly called forces. Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons—usually as virtual particles.

All known gauge bosons have a spin of 1. Therefore, all known gauge bosons are vector bosons.

Gauge bosons are different from the other kinds of bosons: first, fundamental scalar bosons (the Higgs boson); second, mesons, which are composite bosons, made of quarks; third, larger composite, non-force-carrying bosons, such as certain atoms.

Grand Unified Theory

A Grand Unified Theory (GUT) is a model in particle physics in which, at high energy, the three gauge interactions of the Standard Model that define the electromagnetic, weak, and strong interactions, or forces, are merged into a single force. Although this unified force has not been directly observed, the many GUT models theorize its existence. If unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.

Experiments have confirmed that at high energy, the electromagnetic interaction and weak interaction unify into a single electroweak interaction. GUT models predict that at even higher energy, the strong interaction and the electroweak interaction will unify into a single electronuclear interaction. This interaction is characterized by one larger gauge symmetry and thus several force carriers, but one unified coupling constant. Unifying gravity with the electronuclear interaction would provide a theory of everything (TOE) rather than a GUT. GUTs are often seen as an intermediate step towards a TOE.

The novel particles predicted by GUT models are expected to have extremely low masses around the GUT scale—just a few orders of magnitude below the Planck scale—and so are well beyond the reach of any foreseen particle collider experiments. Therefore, the particles predicted by GUT models will be unable to be observed directly and instead the effects of grand unification might be detected through indirect observations such as proton decay, electric dipole moments of elementary particles, or the properties of neutrinos. Some GUTs, such as the Pati-Salam model, predict the existence of magnetic monopoles.

GUT models which aim to be completely realistic are quite complicated, even compared to the Standard Model, because they need to introduce additional fields and interactions, or even additional dimensions of space. The main reason for this complexity lies in the difficulty of reproducing the observed fermion masses and mixing angles which may be related to an existence of some additional family symmetries beyond the conventional GUT models. Due to this difficulty, and due to the lack of any observed effect of grand unification so far, there is no generally accepted GUT model.

Models that do not unify the three interactions using one simple group as the gauge symmetry, but do so using semisimple groups, can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well.

Higgs boson

The Higgs boson is an elementary particle in the Standard Model of particle physics, produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. It is named after physicist Peter Higgs, who in 1964, along with five other scientists, proposed the mechanism which suggested the existence of such a particle. Its existence was confirmed in 2012 by the ATLAS and CMS collaborations based on collisions in the LHC at CERN.

On December 10, 2013, two of the physicists, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their theoretical predictions. Although Higgs's name has come to be associated with this theory (the Higgs mechanism), several researchers between about 1960 and 1972 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, although the nickname is strongly disliked by many physicists, including Higgs himself, who regard it as sensationalism.

Higgs mechanism

In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered massless, but measurements show that the W+, W−, and Z bosons actually have relatively large masses of around 80 GeV/c2. The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field (the Higgs field) that permeates all space to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. In the Standard Model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W±, and Z weak gauge bosons through electroweak symmetry breaking. The Large Hadron Collider at CERN announced results consistent with the Higgs particle on 14 March 2013, making it extremely likely that the field, or one like it, exists, and explaining how the Higgs mechanism takes place in nature.

The mechanism was proposed in 1962 by Philip Warren Anderson, following work in the late 1950s on symmetry breaking in superconductivity and a 1960 paper by Yoichiro Nambu that discussed its application within particle physics.

A theory able to finally explain mass generation without "breaking" gauge theory was published almost simultaneously by three independent groups in 1964: by Robert Brout and François Englert; by Peter Higgs; and by Gerald Guralnik, C. R. Hagen, and Tom Kibble. The Higgs mechanism is therefore also called the Brout-Englert-Higgs mechanism, or Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism, Anderson-Higgs mechanism, Anderson-Higgs-Kibble mechanism, Higgs-Kibble mechanism by Abdus Salam and ABEGHHK'tH mechanism [for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, and 't Hooft] by Peter Higgs.On 8 October 2013, following the discovery at CERN's Large Hadron Collider of a new particle that appeared to be the long-sought Higgs boson predicted by the theory, it was announced that Peter Higgs and François Englert had been awarded the 2013 Nobel Prize in Physics.

Lambda-CDM model

The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parametrization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda (Greek Λ) and associated with dark energy; second, the postulated cold dark matter (abbreviated CDM); and third, ordinary matter. It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:

the existence and structure of the cosmic microwave background

the large-scale structure in the distribution of galaxies

the abundances of hydrogen (including deuterium), helium, and lithium

the accelerating expansion of the universe observed in the light from distant galaxies and supernovaeThe model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.

The ΛCDM model can be extended by adding cosmological inflation, quintessence and other elements that are current areas of speculation and research in cosmology.

Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics, entropic gravity, modified gravity, theories of large-scale variations in the matter density of the universe, bimetric gravity, and scale invariance of empty space.

Large Hadron Collider

The Large Hadron Collider (LHC) is the world's largest and most powerful particle collider and the largest machine in the world. It was built by the European Organization for Nuclear Research (CERN) between 1998 and 2008 in collaboration with over 10,000 scientists and hundreds of universities and laboratories, as well as more than 100 countries. It lies in a tunnel 27 kilometres (17 mi) in circumference and as deep as 175 metres (574 ft) beneath the France–Switzerland border near Geneva.

First collisions were achieved in 2010 at an energy of 3.5 teraelectronvolts (TeV) per beam, about four times the previous world record. After upgrades it reached 6.5 TeV per beam (13 TeV total collision energy, the present world record). At the end of 2018, it entered a two-year shutdown period for further upgrades.

The collider has four crossing points, around which are positioned seven detectors, each designed for certain kinds of research. The LHC primarily collides proton beams, but it can also use beams of heavy ions: Lead–lead collisions and proton-lead collisions are typically done for one month per year. The aim of the LHC's detectors is to allow physicists to test the predictions of different theories of particle physics, including measuring the properties of the Higgs boson and searching for the large family of new particles predicted by supersymmetric theories, as well as other unsolved questions of physics.

Mathematical formulation of the Standard Model

This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as containing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs particle.

The Standard Model is renormalizable and mathematically self-consistent, however despite having huge and continued successes in providing experimental predictions it does leave some unexplained phenomena. In particular, although the physics of special relativity is incorporated, general relativity is not, and the Standard Model will fail at energies or distances where the graviton is expected to emerge. Therefore, in a modern field theory context, it is seen as an effective field theory.

This article requires some background in physics and mathematics, but is designed as both an introduction and a reference.

Minimal Supersymmetric Standard Model

The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers only "the [minimum] number of new particle states and new interactions consistent with phenomenology". Supersymmetry pairs bosons with fermions, so every Standard Model particle has a superpartner yet undiscovered. If we find these superparticles, it equates to discovering such particles as dark matter, could provide evidence for grand unification, and provide hints as to whether string theory describes nature. The failure to find evidence for supersymmetry using the Large Hadron Collider suggests a leaning to abandon it.

Particle physics

Particle physics (also known as high energy physics) is a branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word particle can refer to various types of very small objects (e.g. protons, gas particles, or even household dust), particle physics usually investigates the irreducibly smallest detectable particles and the fundamental interactions necessary to explain their behaviour. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "known" particle, the Higgs boson, or even to the oldest known force field, gravity.

Physics beyond the Standard Model

Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the Standard Model itself: the Standard Model is inconsistent with that of general relativity, to the point where one or both theories break down under certain conditions (for example within known spacetime singularities like the Big Bang and black hole event horizons).

Theories that lie beyond the Standard Model include various extensions of the standard model through supersymmetry, such as the Minimal Supersymmetric Standard Model (MSSM) and Next-to-Minimal Supersymmetric Standard Model (NMSSM), and entirely novel explanations, such as string theory, M-theory, and extra dimensions. As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the "best step" towards a Theory of Everything, can only be settled via experiments, and is one of the most active areas of research in both theoretical and experimental physics.

Preon

In particle physics, preons are point particles, conceived of as subcomponents of quarks and leptons. The word was coined by Jogesh Pati and Abdus Salam in 1974. Interest in preon models peaked in the 1980s but has slowed as the Standard Model of particle physics continues to describe the physics mostly successfully, and no direct experimental evidence for lepton and quark compositeness has been found.

In the hadronic sector, some effects are considered anomalies within the Standard Model. For example, the proton spin puzzle, the EMC effect, the distributions of electric charges inside the nucleons as found by Hofstadter in 1956, and the ad hoc CKM matrix elements.

When the term "preon" was coined, it was primarily to explain the two families of spin-½ fermions: leptons and quarks. More recent preon models also account for spin-1 bosons, and are still called "preons". Each of the preon models postulates a set of fewer fundamental particles than those of the Standard Model, together with the rules governing how those fundamental particles combine and interact. Based on these rules, the preon models try to explain the Standard Model, often predicting small discrepancies with this model and generating new particles and certain phenomena, which do not belong to the Standard Model.

Subatomic particle

In the physical sciences, subatomic particles are particles much smaller than atoms. The two types of subatomic particles are: elementary particles, which according to current theories are not made of other particles; and composite particles. Particle physics and nuclear physics study these particles and how they interact.

The idea of a particle underwent serious rethinking when experiments showed that light could behave like a stream of particles (called photons) as well as exhibiting wave-like properties. This led to the new concept of wave–particle duality to reflect that quantum-scale "particles" behave like both particles and waves (they are sometimes described as wavicles to reflect this). Another new concept, the uncertainty principle, states that some of their properties taken together, such as their simultaneous position and momentum, cannot be measured exactly. In more recent times, wave–particle duality has been shown to apply not only to photons but to increasingly massive particles as well.Interactions of particles in the framework of quantum field theory are understood as creation and annihilation of quanta of corresponding fundamental interactions. This blends particle physics with field theory.

Superpartner

In particle physics, a superpartner (also sparticle) is a class of hypothetical elementary particles. Supersymmetry is one of the synergistic theories in current high-energy physics that predicts the existence of these “shadow" particles.When considering extensions of the Standard Model, the s- prefix from sparticle is used to form names of superpartners of the Standard Model fermions (sfermions), e.g. the stop squark. The superpartners of Standard Model bosons have an -ino (bosinos) appended to their name, e.g. gluino, the set of all gauge superpartners are called the gauginos.

Supersymmetry

In particle physics, supersymmetry (SUSY) is a principle that proposes a relationship between two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin. A type of spacetime symmetry, supersymmetry is a possible candidate for undiscovered particle physics, and seen as an elegant solution to many current problems in particle physics if confirmed correct, which could resolve various areas where current theories are believed to be incomplete. A supersymmetrical extension to the Standard Model would resolve major hierarchy problems within gauge theory, by guaranteeing that quadratic divergences of all orders will cancel out in perturbation theory.

In supersymmetry, each particle from one group would have an associated particle in the other, which is known as its superpartner, the spin of which differs by a half-integer. These superpartners would be new and undiscovered particles. For example, there would be a particle called a "selectron" (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly "unbroken" supersymmetry, each pair of superpartners would share the same mass and internal quantum numbers besides spin. Since we expect to find these "superpartners" using present-day equipment, if supersymmetry exists then it consists of a spontaneously broken symmetry allowing superpartners to differ in mass. Spontaneously broken supersymmetry could solve many mysterious problems in particle physics including the hierarchy problem.

There is no evidence at this time to show whether or not supersymmetry is correct, or what other extensions to current models might be more accurate. In part this is because it is only since around 2010 that particle accelerators specifically designed to study physics beyond the Standard Model have become operational, and because it is not yet known where exactly to look nor the energies required for a successful search.

The main reasons for supersymmetry being supported by physicists is that the current theories are known to be incomplete and their limitations are well established, and supersymmetry would be an attractive solution to some of the major concerns. Direct confirmation would entail production of superpartners in collider experiments, such as the Large Hadron Collider (LHC). The first runs of the LHC found no previously-unknown particles other than the Higgs boson which was already suspected to exist as part of the Standard Model, and therefore no evidence for supersymmetry. Indirect methods include the search for a permanent electric dipole moment (EDM) in the known Standard Model particles, which can arise when the Standard Model particle interacts with the supersymmetric particles. The current best constraint on the electron electric dipole moment put it to be smaller than 10−28 e·cm, equivalent to a sensitivity to new physics at the TeV scale and matching that of the current best particle colliders. A permanent EDM in any fundamental particle points towards time-reversal violating physics, and therefore also CP-symmetry violation via the CPT theorem. Such EDM experiments are also much more scalable than conventional particle accelerators and offer a practical alternative to detecting physics beyond the standard model as accelerator experiments become increasingly costly and complicated to maintain.

These findings disappointed many physicists, who believed that supersymmetry (and other theories relying upon it) were by far the most promising theories for "new" physics, and had hoped for signs of unexpected results from these runs. Former enthusiastic supporter Mikhail Shifman went as far as urging the theoretical community to search for new ideas and accept that supersymmetry was a failed theory. However it has also been argued that this "naturalness" crisis was premature, because various calculations were too optimistic about the limits of masses which would allow a supersymmetry based solution.

Theory of everything

A theory of everything (TOE or ToE), final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe. Finding a TOE is one of the major unsolved problems in physics. Over the past few centuries, two theoretical frameworks have been developed that, as a whole, most closely resemble a TOE. These two theories upon which all modern physics rests are general relativity (GR) and quantum field theory (QFT). GR is a theoretical framework that only focuses on gravity for understanding the universe in regions of both large scale and high mass: stars, galaxies, clusters of galaxies, etc. On the other hand, QFT is a theoretical framework that only focuses on three non-gravitational forces for understanding the universe in regions of both small scale and low mass: sub-atomic particles, atoms, molecules, etc. QFT successfully implemented the Standard Model that describes the three non-gravitational forces: strong, weak, and electromagnetic force.Through years of research, physicists have experimentally confirmed with tremendous accuracy virtually every prediction made by these two theories when in their appropriate domains of applicability. In accordance with their findings, scientists also learned that GR and QFT, as they are currently formulated, are mutually incompatible – they cannot both be right. Since the usual domains of applicability of GR and QFT are so different, most situations require that only one of the two theories be used. As it turns out, this incompatibility between GR and QFT is only an issue in regions of extremely small scale - the Planck scale - , such as those that exist within a black hole or during the beginning stages of the universe (i.e., the moment immediately following the Big Bang). To resolve this incompatibility, a theoretical framework revealing a deeper underlying reality, unifying gravity with the other three interactions, must be discovered to harmoniously integrate the realms of GR and QFT into a seamless whole: the TOE is a single theory that, in principle, is capable of describing all phenomena in the universe.

In pursuit of this goal, quantum gravity has become one area of active research. One example is string theory, which evolved into a candidate for the TOE, but not without drawbacks (most notably, its lack of currently testable predictions) and controversy. String theory posits that at the beginning of the universe (up to 10−43 seconds after the Big Bang), the four fundamental forces were once a single fundamental force. According to string theory, every particle in the universe, at its most microscopic level (Planck length), consists of varying combinations of vibrating strings (or strands) with preferred patterns of vibration. String theory further claims that it is through these specific oscillatory patterns of strings that a particle of unique mass and force charge is created (that is to say, the electron is a type of string that vibrates one way, while the up quark is a type of string vibrating another way, and so forth).

Parameters of the Standard Model
Symbol Description Renormalization
scheme (point)
Value
me Electron mass 511 keV
mμ Muon mass 105.7 MeV
mτ Tau mass 1.78 GeV
mu Up quark mass μMS = 2 GeV 1.9 MeV
md Down quark mass μMS = 2 GeV 4.4 MeV
ms Strange quark mass μMS = 2 GeV 87 MeV
mc Charm quark mass μMS = mc 1.32 GeV
mb Bottom quark mass μMS = mb 4.24 GeV
mt Top quark mass On shell scheme 173.5 GeV
θ12 CKM 12-mixing angle 13.1°
θ23 CKM 23-mixing angle 2.4°
θ13 CKM 13-mixing angle 0.2°
δ CKM CP violation Phase 0.995
g1 or g' U(1) gauge coupling μMS = mZ 0.357
g2 or g SU(2) gauge coupling μMS = mZ 0.652
g3 or gs SU(3) gauge coupling μMS = mZ 1.221
θQCD QCD vacuum angle ~0
v Higgs vacuum expectation value 246 GeV
mH Higgs mass 125.09±0.24 GeV
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