grand unified theory

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Beyond the Standard Model

Standard Model Evidence Hierarchy problem • Dark matter Cosmological constant problem Strong CP problem Neutrino oscillation Theories Technicolor Kaluza–Klein theory Grand Unified Theory Theory of everything String theory Supersymmetry MSSM • Superstring theory Supergravity Quantum gravity String theory Loop quantum gravity Causal dynamical triangulation Canonical general relativity Experiments Gran Sasso • INO • LHC SNO • Super-K • Tevatron

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Grand Unification, grand unified theory, or GUT refers to any of several very similar unified field theories or models in physics that predicts that at extremely high energies (above 10¹⁴ GeV), the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field.^[1]

Thus far, physicists have been able to merge electromagnetism and the weak nuclear force into the electroweak force, and work is being done to merge electroweak and quantum chromodynamics into a QCD-electroweak interaction sometimes called the electrostrong force. Beyond grand unification, there is also speculation that it may be possible to merge gravity with the other three gauge symmetries into a theory of everything.

Motivation

There is a general aesthetic assumption among high energy physicists that the more symmetrical a theory is, the more "beautiful" and "elegant" it is. Accordingly, the Standard Model gauge group, which is the direct product of three groups (modulo some finite group), is judged to be "ugly". Also, reasoning in analogy with the 19th-century unification of electricity with magnetism into electromagnetism, and especially the success of the electroweak theory, which utilizes the idea of spontaneous symmetry breaking to unify electromagnetism with the weak interaction, people wondered if it might be possible to unify all three groups in a similar manner. Physicists feel that three independent gauge coupling constants and a huge number of Yukawa coupling coefficients require far too many free parameters, and that these coupling constants ought to be explained by a theory with fewer free parameters. A gauge theory where the gauge group is a simple group only has one gauge coupling constant, and since the fermions are now grouped together in larger representations, there are fewer Yukawa coupling coefficients as well. In addition, the chiral fermion fields of the Standard Model unify into three generations of two irreducible representations () in SU(5), and three generations of an irreducible representation (16) in SO(10). This is a significant observation, as a generic combination of chiral fermions which are free of gauge anomalies will not be unified in a representation of some larger Lie group without adding additional matter fields. SO(10) also predicts a right-handed neutrino.

GUT specifically predicts relations among the fermion masses, such as between the electron and the down quark, the muon and the strange quark, and the tau lepton and the bottom quark for SU(5) and SO(10). Some of these mass relations hold approximately, but most don't. See Georgi-Jarlskog mass relation. If we look at the renormalization group running of the three-gauge couplings have been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU(5)/SO(10) GUTs, which are precisely the GUT groups which lead to a simple fermion unification. This is a significant result, as other Lie groups lead to different normalizations. However, if the supersymmetric extension MSSM is used instead of the Standard Model, the match becomes much more accurate. It is commonly believed that this matching is unlikely to be a coincidence. Also, most model builders simply assume supersymmetry (SUSY) because it solves the hierarchy problem—i.e., it stabilizes the electroweak Higgs mass against radiative corrections. And the Majorana mass of the right-handed neutrino SO(10) theories with its mass set to the gauge unification scale is examined, values for the left-handed neutrino masses (see neutrino oscillation) are produced via the seesaw mechanism. These values are 10–100 times smaller than the GUT scale, but still relatively close.

(For a more elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.)

Proposed theories

Several such theories have been proposed, but none is currently universally accepted. An even more ambitious theory that includes all fundamental forces, including gravitation, is termed a theory of everything. Some common mainstream GUT models are:

Not quite GUTs:

Note: These models refer to Lie algebras not to Lie groups. The Lie group could be [SU(4)×SU(2)×SU(2)]/Z₂, just to take a random example.

The most promising candidate is SO(10).^{[citation needed]} (Minimal) SO(10) does not contain any exotic fermions (i.e. additional fermions besides the Standard Model fermions and the right-handed neutrino), and it unifies each generation into a single irreducible representation. A number of other GUT models are based upon subgroups of SO(10). They are the minimal left-right model, SU(5), flipped SU(5) and the Pati-Salam model. The GUT group E₆ contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E₆ models comes from E₈ × E₈ heterotic string theory.

GUT models generically predict the existence of topological defects such as monopoles, cosmic strings, domain walls, and others. But none have been observed. Their absence is known as the monopole problem in cosmology. Most GUT models also predict proton decay, although not the Pati-Salam model, although current experiments still haven't detected proton decay. This experimental limit on the proton's lifetime pretty much rules out minimal SU(5).

Proton Decay. These graphics refer to the X bosons and Higgs bosons.

Dimension 6 proton decay mediated by the X boson in SU(5) GUT

Dimension 6 proton decay mediated by the X boson in flipped SU(5) GUT

Dimension 6 proton decay mediated by the triplet Higgs and the anti-triplet Higgs in SU(5) GUT

Some GUT theories like SU(5) and SO(10) suffer from what is called the doublet-triplet problem. These theories predict that for each electroweak Higgs doublet, there is a corresponding colored Higgs triplet field with a very small mass (many orders of magnitude smaller than the GUT scale here). In theory, unifying quarks with leptons, the Higgs doublet would also be unified with a Higgs triplet. Such triplets have not been observed. They would also cause extremely rapid proton decay (far below current experimental limits) and prevent the gauge coupling strengths from running together in the renormalization group.

Most GUT models require a threefold replication of the matter fields. As such, they do not explain why there are three generations of fermions. Most GUT models also fail to explain the little hierarchy between the fermion masses for different generations.

Ingredients

A GUT model basically consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a Yang-Mills action for that connection given by an invariant symmetric bilinear form over its Lie algebra (which is specified by a coupling constant for each factor), a Higgs sector consisting of a number of scalar fields taking on values within real/complex representations of the Lie group and chiral Weyl fermions taking on values within a complex rep of the Lie group. The Lie group contains the Standard Model group and the Higgs fields acquire VEVs leading to a spontaneous symmetry breaking to the Standard Model. The Weyl fermions represent matter.

Current status

As of 2009^[update], there is still no hard evidence that nature is described by a Grand Unified Theory. Moreover, since the Higgs particle has not yet been observed, the smaller electroweak unification is still pending.^[2] The discovery of neutrino oscillations indicates that the Standard Model is incomplete and has led to renewed interest toward certain GUT such as SO(10). One of the few possible experimental tests of certain GUT is proton decay and also fermion masses. There are a few more special tests for supersymmetric GUT.

The gauge coupling strengths of QCD, the weak interaction and hypercharge seem to meet at a common length scale called the GUT scale and equal approximately to 10¹⁶ GeV, which is slightly suggestive. This interesting numerical observation is called the gauge coupling unification, and it works particularly well if one assumes the existence of superpartners of the Standard Model particles. Still it is possible to achieve the same by postulating, for instance, that ordinary (non supersymmetric) SO(10) models break with an intermediate gauge scale, such as the one of Pati-Salam group.

The coining of the widely-used acronym GUT has been attributed to a paper published in 1978 by Texas A&M University theorist Dimitri Nanopoulos (previously at Harvard University).^{[citation needed]}

See also

• Grand unification energy
• Fundamental interaction
• Particle physics and representation theory
• Classical unified field theories
• X and Y bosons
• B-L quantum number

References

• An account of the origin of the term GUT
• Stephen Hawking, A Brief History of Time, includes a brief popular overview.