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electroweak theory, a unified field theory that describes two of the fundamental forces in nature, electromagnetism (see electromagnetic radiation) and the weak interaction. The electroweak theory derived from efforts to produce a theory for the weak force analogous to quantum electrodynamics (QED), the quantum theory of the electromagnetic force. Although the weak force fails to meet a requirement for that theory—that it behave the same way at different points in space and time—because it acts only across distances smaller than an atomic nucleus, it was shown that the electromagnetic force, which can extend across interstellar distances, and the weak force are but different manifestations of a more fundamental force, the electroweak force. This made it possible to formulate a unified model that predicted the existence of mediating, or messenger, particles. The electroweak theory, for which Sheldon Glashow, Abdus Salam, and Steven Weinberg shared the 1979 Nobel Prize in Physics, was confirmed in 1983 by the discovery of the W and Z particles, two of a number of elementary particles it predicted.

See P. Renton, *Electroweak Interactions* (1990); J. Horejsi, *Introduction to Electroweak Unification* (1994); A. Salam, *Selected Papers of Abdus Salam* (1994); J. D. Walecka, *Theoretical Nuclear and Subnuclear Physics* (1995).

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

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 $10^\{14\}$ GeV), the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field.

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.

GUT theory 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 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.)

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:

- minimal left-right model — $SU(3)\_C\; times\; SU(2)\_L\; times\; SU(2)\_R\; times\; U(1)\_\{B-L\}$
- Georgi-Glashow model — $SU(5)$
- SO(10)
- Flipped SU(5) — $SU(5)\; times\; U(1)$
- Pati-Salam model — $SU(4)\; times\; SU(2)\; times\; SU(2)$
- flipped SO(10) — $SO(10)\; times\; U(1)$

- Trinification — $SU(3)\; times\; SU(3)\; times\; SU(3)$
- SU(6)
- E
_{6} - 331 model
- chiral color
- Heim Theory

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)]/Z_{2}, just to take a random example.

The most promising candidate is SO(10). (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. Notice that 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 E_{6} contains SO(10) but models based upon it are significantly more complicated. The primary reason for studying E_{6} models comes from E_{8} × E_{8} heterotic string theory.

GUT models generically predict the existence of topological defects such as monopoles, cosmic strings, domain walls, and others. None have been observed and their absence is known as the monopole problem in cosmology.

GUT models also generically predict proton decay, although current experiments still haven't detected proton decay. This experimental limit on the proton's lifetime pretty much rules out minimal SU(5).

Some GUT theories like SU(5) and SO(10) suffer from what is called the doublet-triplet problem in that these theories predict that for each electroweak Higgs doublet, there corresponds a colored Higgs triplet field with a very small mass (small, meaning many orders of magnitude smaller than the GUT scale here). After all, if you unify quarks with leptons, the Higgs doublet would also be unified with a Higgs triplet. These triplets have not been observed, and not only that, they would cause extremely rapid proton decay (way below current experimental limits) and completely mess up the running together of the gauge coupling strengths in the renormalization group.

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

As of 2005, 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. The discovery of neutrino oscillations indicate that the Standard Model is incomplete, and lead 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 $10^\{16\}$ 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.

- Grand unification energy
- Fundamental interaction
- Particle physics and representation theory
- Classical unified field theories
- UnifiedTheory.com

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

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Last updated on Wednesday October 08, 2008 at 13:53:42 PDT (GMT -0700)

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