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{{Beyond the Standard Model|expanded=Theories}}


A '''Grand Unified Theory''' ('''GUT''') is a model in [[particle physics]] in which at high energy, the three [[gauge theory|gauge interactions]] of the [[Standard Model]] which define the [[electromagnetism|electromagnetic]], [[Weak interaction|weak]], and [[strong interaction|strong]] [[fundamental interaction|interactions]], are merged into one single interaction characterized by one larger [[gauge theory|gauge symmetry]] and thus one unified [[coupling constant]]. During the [[grand unification epoch]], the gauge force separated from the [[gravity|gravitational force]].  
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Models that do not unify all interactions using one [[simple group|simple Lie group]] as the gauge symmetry, but do so using [[semisimple group]]s, can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well.
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Unifying [[gravity]] with the other three interactions would provide a [[theory of everything]] (TOE), rather than a GUT. Nevertheless, GUTs are often seen as an intermediate step towards a TOE.
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Because their masses are predicted to be just a few orders of magnitude below the [[Planck scale]], at the [[GUT scale]], well beyond the reach of foreseen particle colliders experiments, novel particles predicted by GUT models cannot be observed directly.  Instead, effects of grand unification might be detected through indirect observations such as [[proton decay]], electric dipole moments of elementary particles, or the properties of [[neutrino]]s.<ref>
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{{cite book
|last=Ross |first=G.
|year=1984
|title=Grand Unified Theories
|pages=
|publisher=[[Westview Press]]
|isbn=978-0-8053-6968-7
}}</ref> Some grand unified theories predict the existence of [[magnetic monopoles]].


{{As of|2012}}, all 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. 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.
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{{unsolved|physics|Are the three forces of the Standard Model unified at high energies? By which symmetry is this unification governed? Can Grand Unification explain the number of Fermion generations and their masses?}}
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Historically, the first true GUT which was based on the [[simple group|simple Lie group]] [[SU(5)|'''SU'''(5)]], was proposed by [[Howard Georgi]] and [[Sheldon Glashow]] in 1974.<ref>
 
{{cite journal
  <li></li>
|last=Georgi |first=H.
 
|last2=Glashow |first2=S.L.
  <li>
|year=1974
 
|title=Unity of All Elementary Particle Forces
  <li>?mod=viewthread&tid=2988428</li>
|journal=[[Physical Review Letters]]
 
|volume=32 |pages=438–441
  <li>
|doi=10.1103/PhysRevLett.32.438
 
|bibcode=1974PhRvL..32..438G
  </ul>
}}</ref> The [[Georgi–Glashow model]] was preceded by the [[Semisimple Lie algebra]] [[Pati–Salam model]] by [[Abdus Salam]] and [[Jogesh Pati]],<ref>
{{cite journal
|last=Pati |first=J.
|last2=Salam |first2=A.
|year=1974
|title=Lepton Number as the Fourth Color
|journal=[[Physical Review D]]
|volume=10 |pages=275–289
  |doi=10.1103/PhysRevD.10.275
|bibcode = 1974PhRvD..10..275P }}</ref> who pioneered the idea to unify gauge interactions.


The acronym GUT was first coined in 1978 by CERN researchers [[John Ellis (physicist)|John Ellis]], Andrzej Buras, [[Mary K. Gaillard]], and [[Dimitri Nanopoulos]], however in the final version of their paper<ref>{{cite journal
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|last1=Buras |first1=A.J.
|last2=Ellis |first2=J.
|last3=Gaillard |first3=M.K.
|last4=Nanopoulos |first4=D.V.
|year=1978
|title=Aspects of the grand unification of strong, weak and electromagnetic interactions
|journal=[[Nuclear Physics B]]
|volume=135 |issue=1 |pages=66–92
|doi=10.1016/0550-3213(78)90214-6
|url=http://cdsweb.cern.ch/record/132734/files/197712054.pdf
|accessdate=2011-03-21
|bibcode = 1978NuPhB.135...66B }}</ref> they opted for the less anatomical ''GUM'' (Grand Unification Mass). Nanopoulos later that year was the first to use<ref>
{{cite journal
|last=Nanopoulos |first=D.V.
|year=1979
|title=Protons Are Not Forever
|url=http://www-spires.fnal.gov/spires/find/hep/www?rawcmd=r+HUTP-78-A062
|journal=[[Orbis Scientiae]]
|volume=1 |pages=91
|id=Harvard Preprint HUTP-78/A062
}}</ref> the acronym in a paper.<ref>
{{cite journal
|last=Ellis |first=J.
|title=Physics gets physical
|journal=[[Nature (journal)|Nature]]
|volume=415 |page=957 |year=2002
|doi=10.1038/415957b
|issue=6875
|bibcode=2002Natur.415..957E
}}</ref>


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The fact that the [[electric charge]]s of [[electron]]s and [[proton]]s seem to cancel each other exactly to extreme precision is essential for the existence of the macroscopic world as we know it, but this important property of elementary particles is not explained in the Standard Model of particle physics. While the description of [[strong interaction|strong]] and [[weak interaction|weak]] interactions within the Standard Model is based on [[gauge theory|gauge symmetries]] governed by the [[simple Lie group|simple symmetry groups]] [[SU(3)|'''SU'''(3)]] and [[SU(2)|'''SU'''(2)]] which allow only discrete charges, the remaining component, the [[weak hypercharge]] interaction is described by an [[Abelian Group|abelian symmetry]] [[U(1)|'''U'''(1)]] which in principle allows for arbitrary charge assignments.<ref group=note>There are however certain constraints on the choice of particle charges from theoretical consistency, in particular [[gauge anomaly|anomaly cancellation]].</ref> The observed [[charge quantization]], namely the fact that all known [[elementary particle]]s carry electric charges which appear to be exact multiples of {{frac|1|3}} of the [[elementary charge|"elementary" charge]], has led to the idea that [[hypercharge]] interactions and possibly the strong and weak interactions might be embedded in one Grand Unified interaction described by a single, larger simple symmetry group containing the Standard Model. This would automatically predict the quantized nature and values of all elementary particle charges. Since this also results in a prediction for the relative strengths of the [[fundamental interaction]]s which we observe, in particular the [[weak mixing angle]], Grand Unification ideally reduces the number of independent input parameters, but is also constrained by observations.
 
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Grand Unification is reminiscent of the unification of electric and magnetic forces by [[Maxwell equations|Maxwell's theory of electromagnetism]] in the 19th century, but its physical implications and mathematical structure are qualitatively different.
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[[File:SU(5) representation of fermions.png|thumb|Schematic representation of fermions and bosons in '''SU'''(5) GUT showing '''5'''+'''10''' split in the multiplets. Neutral bosons (photon, Z-boson, and neutral gluons) are not shown but occupy the diagonal entries of the matrix in complex superpositions]]
 
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:''For an elementary introduction to how [[Lie algebra]]s are related to particle physics, see the article [[Particle physics and representation theory]].''
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{{main|SU(5) (physics)}}
 
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[[File:Georgi-Glashow charges.svg|200px|right|thumb|The pattern of [[weak isospin]]s, [[weak hypercharge]]s, and strong charges for particles in the [[Georgi-Glashow model|SU(5) model]], rotated by the predicted [[weak mixing angle]], showing electric charge roughly along the vertical. In addition to [[Standard Model]] particles, the theory includes twelve colored X bosons, responsible for [[proton decay]].]]
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'''SU'''(5) is the simplest GUT. The smallest [[simple Lie group]] which contains the [[standard model]], and upon which the first Grand Unified Theory was based, is
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<math> SU(5) \supset SU(3)\times SU(2)\times U(1)</math>.
  <li>[http://www.0917qiche.com/bbs/forum.php?mod=viewthread&tid=254001 http://www.0917qiche.com/bbs/forum.php?mod=viewthread&tid=254001]</li>
 
 
Such group symmetries allow the reinterpretation of several known particles as different states of a single particle field. However, it is not obvious that the simplest possible choices for the extended "Grand Unified" symmetry should yield the correct inventory of elementary particles. The fact that all currently known (2009) matter particles fit nicely into three copies of the smallest [[group representation]]s of '''SU'''(5) and immediately carry the correct observed charges, is one of the first and most important reasons why people believe that a Grand Unified Theory might actually be realized in nature.
  <li>[http://poodlehack.com/activity/p/310774/ http://poodlehack.com/activity/p/310774/]</li>
 
 
The two smallest [[group representation#Reducibility|irreducible representations]] of '''SU'''(5) are '''5''' and '''10'''. In the standard assignment, the '''5'''  contains the [[Charge Conjugation|charge conjugates]] of the right-handed [[Quark|down-type quark]] [[Quantum chromodynamics|color]] [[Triplet state|triplet]] and a left-handed [[lepton]] [[isospin]] [[Doublet state|doublet]], while the '''10''' contains the six [[Quark|up-type quark]] components, the left-handed [[Quark|down-type quark]] [[Quantum chromodynamics|color]] triplet, and the right-handed [[electron]]. This scheme has to be replicated for each of the three known [[Generation (particle physics)|generations of matter]]. It is notable that the theory is [[Gauge anomaly|anomaly free]] with this matter content.
  <li>[http://bbs.cdscjd.com/forum.php?mod=viewthread&tid=4509573 http://bbs.cdscjd.com/forum.php?mod=viewthread&tid=4509573]</li>
 
 
The hypothetical [[neutrino#Handedness|right-handed neutrinos]] are not contained in any of these representations, which can explain their relative heaviness (see [[seesaw mechanism]]).
  <li>[http://www.youxisky.com/bbs/forum.php?mod=viewthread&tid=764117 http://www.youxisky.com/bbs/forum.php?mod=viewthread&tid=764117]</li>
 
 
===SO(10)===
</ul>
{{main|SO(10) (physics)}}
 
[[File:E6GUT.svg|200px|right|thumb|The pattern of [[weak isospin]], W, weaker isospin, W', strong g3 and g8, and baryon minus lepton, B, charges for particles in the [[SO(10)]] Grand Unified Theory, rotated to show the embedding in [[E6 (mathematics)|E<sub>6</sub>]].]]
 
The next simple Lie group which contains the standard model is
 
<math>SO(10)\supset SU(5)\supset SU(3)\times SU(2)\times U(1)</math>.
 
Here, the unification of matter is even more complete, since the [[group representation|irreducible]] [[spinor]] [[group representation|representation]] '''16''' contains both the <math>\mathbf{\overline{5}}</math> and '''10''' of '''SU'''(5) and a right-handed neutrino, and thus the complete particle content of one generation of the extended [[standard model]] with [[Neutrino|neutrino masses]]. This is already the largest [[Simple Lie group|simple group]] which achieves the unification of matter in a scheme involving only the already known matter particles (apart from the [[Higgs mechanism|Higgs sector]]).
 
Since different standard model fermions are grouped together in larger representations, GUTs specifically predict 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]]).
 
The boson matrix for '''SO'''(10) is found by taking the 15x15 matrix from the '''10'''+'''5''' representation of '''SU'''(5) and adding an extra row and column for the right handed neutrino. The bosons are found by adding a partner to each of the 20 charged bosons (2 right-handed W bosons, 6 massive charged gluons and 12 X/Y type bosons) and adding an extra heavy neutral Z-boson to make 5 neutral bosons in total. The boson matrix will have a boson or its new partner in each row and column. These pairs combine to create the familiar 16D Dirac [[spinor]] matrices of '''SO'''(10).
 
===SU(8)===
Assuming 4 generations of fermions instead of 3 makes a total of '''64''' types of particles. These can be put into '''64 = 8 + 56''' representations of SU(8). This can be divided into '''SU(5)xSU(3)<sub>F</sub>xU(1)''' which is the '''SU(5)''' theory together with some heavy bosons which act on the generation number.  
 
===O(16)===
Again assuming 4 generations of fermions, the '''128''' particles and anti-particles can be put into a single spinor representation of '''O(16)'''.
 
===Symplectic Groups and Quaternion Representations===
Symplectic gauge groups could also be considered. For example '''Sp(8)''' has a representation in terms of 4x4 quaternion unitary matrices which has a '''16''' dimensional real representation and so might be considered as a candidate for a gauge group. '''Sp(8)''' has 32 charged bosons and 4 neutral bosons. It's subgroups include '''SU(4)''' so can at least contain the gluons and photon of '''SU(3)xU(1)'''. Although it's probably not possible to have weak bosons acting on chiral fermions in this representation. A quaternion representation of the fermions might be:
 
:<math>\begin{bmatrix}
e+i\overline{e}+jv+k\overline{v} \\
u_r+i\overline{u_r}+jd_r+k\overline{d_r} \\
u_g+i\overline{u_g}+jd_g+k\overline{d_g} \\
u_b+i\overline{u_b}+jd_b+k\overline{d_b} \\
\end{bmatrix}_L
</math>
 
A further complication with [[quaternion]] representations of fermions is that there are two types of multiplication: left multiplication and right multiplication which must be taken into account. It turns out that including left and right-handed 4x4 quaternion matrices is equivalent to including a single right-multiplication by a unit quaternion which adds an extra SU(2) and so has an extra neutral boson and two more charged bosons. Thus the group of left and right handed 4x4 quaternion matrcies is Sp(8)xSU(2) which does include the standard model bosons:
 
:<math> SU(4,H)_L\times H_R = Sp(8)\times SU(2) \supset SU(4)\times SU(2) \supset SU(3)\times SU(2)\times U(1) </math>
 
If <math>\psi</math> is a quaternion valued spinor, <math>A^{ab}_\mu</math> is quaternion hermitian 4x4 matrix coming from Sp(8) and <math>B_\mu</math> is a pure imaginary quaternion (both of which are 4-vector bosons) then the interaction term is:
 
::<math>\overline{\psi^{a}} \gamma_\mu\left( A^{ab}_\mu\psi^b + \psi^a B_\mu \right) </math>
 
===E8 and Octonion Representations===
It can be noted that a generation of 16 fermions can be put into the form of an [[Octonion]] with each element of the octonion being an 8-vector. If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional (grassman-) [[Jordan algebra]], which has the symmetry group of one of the exceptional Lie groups ('''F'''<sub>4</sub>, '''E'''<sub>6</sub>, '''E'''<sub>7</sub> or '''E'''<sub>8</sub>) depending on the details.
 
:<math>
\psi=\begin{bmatrix}
a & e & \mu \\
\overline{e} & b & \tau \\
\overline{\mu} & \overline{\tau} & c
\end{bmatrix}
</math>
 
:<math>
[\psi_A,\psi_B] \subset J_3(O)
</math>
Because they are fermions the anti-commutators of the Jordan algebra become commutators. It is known that '''E'''<sub>6</sub> has subgroup '''O'''(10) and so is big enough to include the Standard Model. An '''E'''<sub>8</sub> gauge group, for example, would have 8 neutral bosons, 120 charged bosons and 120 charged anti-bosons. To account for the 248 fermions in the lowest multiplet of '''E'''<sub>8</sub>, these would either have to include anti-particles (and so have [[Baryogenesis]]), have new undiscovered particles, or have gravity-like ([[Spin connection]]) bosons affecting elements of the particles spin direction. Each of these poses theoretical problems.
 
===Beyond Lie Groups===
Other structures have been suggested including Lie 3-algebras and [[Lie superalgebra]]s. Neither of these fit with [[Yang–Mills theory]]. In particular Lie superalgebras would introduce bosons with the wrong statistics. [[Supersymmetry]] however does fit with Yang-Mills. For example N=4 Super Yang Mills Theory requires an SU(N) gauge group.
 
==Unification of forces and the role of supersymmetry==
The unification of forces is possible due to the energy scale dependence of force [[coupling constant|coupling parameters]] in [[quantum field theory]] called [[renormalization group|renormalization group running]], which allows parameters with vastly different values at usual energies to converge to a single value at a much higher energy scale.<ref>
 
{{cite book
|last=Ross |first=G.
|year=1984
|title=Grand Unified Theories
|pages=
|publisher=[[Westview Press]]
|isbn=978-0-8053-6968-7
}}</ref>
 
The [[renormalization group]] running of the three gauge couplings in the [[Standard Model]] has 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) or 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 [[supersymmetry|supersymmetric]] extension [[Minimal Supersymmetric Standard Model|MSSM]] is used instead of the Standard Model, the match becomes much more accurate. In this case, the coupling constants of the strong and electroweak interactions meet at the [[grand unification energy]], also known as the GUT scale:
 
<math>\Lambda_{\text{GUT}} \approx 10^{16}\,\text{GeV}</math>.
 
It is commonly believed that this matching is unlikely to be a coincidence, and is often quoted as one of the main motivations to further investigate [[supersymmetry|supersymmetric theories]] despite the fact that no supersymmetric partner particles have been experimentally observed (March 2011). Also, most model builders simply assume [[supersymmetry]] because it solves the [[hierarchy problem]]—i.e., it stabilizes the electroweak [[MSSM Higgs Mass|Higgs mass]] against [[Renormalization|radiative correction]]s.{{Citation needed|date=September 2011}}
 
==Neutrino masses==
Since [[Majorana fermion|Majorana]] masses of the right-handed neutrino are forbidden by '''SO'''(10) symmetry, '''SO'''(10) GUTs predict the Majorana masses of right-handed neutrinos to be close to the [[GUT scale]] where the symmetry is [[Spontaneous symmetry breaking|spontaneously broken]] in those models. In [[Supersymmetry|supersymmetric]] GUTs, this scale tends to be larger than would be desirable to obtain realistic masses of the light, mostly left-handed neutrinos (see [[neutrino oscillation]]) via the [[seesaw mechanism]]. neutrinos have been suspected in the late sixties by Paul Baril who takes time from running PFB (his electronic security company.
 
==Proposed theories==
 
Several such theories have been proposed, but none is currently universally accepted. An even more ambitious theory that includes ''all'' [[Fundamental interaction|fundamental forces]], including [[gravitation]], is termed a [[theory of everything]]. Some common [[mainstream]] GUT models are:
{{col-begin}}
{{col-break}}
* minimal [[left-right model]]&nbsp;— '''SU'''(3)<sub>C</sub> × '''SU'''(2)<sub>L</sub> × '''SU'''(2)<sub>R</sub> × '''U'''(1)<sub>B-L</sub>
* [[Georgi–Glashow model]]&nbsp;— '''SU'''(5)
* [[SO(10) (physics)|'''SO'''(10)]]
* [[Flipped SU(5)|Flipped '''SU'''(5)]]&nbsp;— '''SU'''(5) × '''U'''(1)
* [[Pati-Salam model]]&nbsp;— '''SU'''(4) × '''SU'''(2) × '''SU'''(2)
* [[flipped SO(10)|Flipped '''SO'''(10)]]&nbsp;— '''SO'''(10) × '''U'''(1)
{{col-break}}
* [[Trinification]]&nbsp;— '''SU'''(3) × '''SU'''(3) × '''SU'''(3)
* [[SU(6) (physics)|'''SU'''(6)]]
* [[E6 (mathematics)|'''E'''<sub>6</sub>]]
* [[331 model]]
* [[chiral color]]
 
{{col-end}}
Not quite GUTs:
{{col-begin}}
{{col-break}}
* [[Technicolor (physics)|Technicolor models]]
* [[Little Higgs]]
* [[Preon]]s
* [[String theory]]
{{col-break}}
* [[M-theory]]
* [[Loop quantum gravity]]
* [[Causal dynamical triangulation| Causal dynamical triangulation theory]]
{{col-end}}
''Note'': These models refer to [[Lie algebra]]s not to [[Lie group]]s. The Lie group could be ['''SU'''(4)×'''SU'''(2)×'''SU'''(2)]/'''Z'''<sub>2</sub>, just to take a random example.
 
The most promising candidate is [[SO(10)|'''SO'''(10)]].{{Citation needed|date=November 2007}} (Minimal) '''SO'''(10) does not contain any [[exotic fermion]]s (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)|'''SU'''(5)]], [[flipped SU(5)]] and the [[Pati-Salam model]]. The GUT group '''E'''<sub>6</sub> contains '''SO'''(10), but models based upon it are significantly more complicated. The primary reason for studying '''E'''<sub>6</sub> models comes from '''E'''<sub>8</sub> × '''E'''<sub>8</sub> [[heterotic string theory]].
 
GUT models generically predict the existence of [[topological defect]]s such as [[magnetic monopoles|monopoles]], [[cosmic strings]], [[Domain wall (string theory)|domain wall]]s, and others. But none have been observed. Their absence is known as the [[monopole problem]] in [[physical cosmology|cosmology]]. Most GUT models also predict [[proton decay]], although not the [[Pati-Salam model]]; current experiments still haven't detected proton decay. This experimental limit on the proton's lifetime pretty much rules out minimal '''SU'''(5).
 
<gallery caption="Proton Decay. These graphics refer to the [[X and Y bosons|X bosons]] and [[Higgs boson]]s." widths="250px" heights="300px" perrow="3">
 
Image:Proton_decay2.svg|Dimension 6 proton decay mediated by the ''X'' boson <math>(3,2)_{-\frac{5}{6}}</math> in '''SU'''(5) GUT
 
Image:proton decay3.svg|Dimension 6 proton decay mediated by the ''X'' boson <math>(3,2)_{\frac{1}{6}}</math> in flipped '''SU'''(5) GUT
 
Image:proton decay4.svg|Dimension 6 proton decay mediated by the triplet Higgs <math>T (3,1)_{-\frac{1}{3}}</math> and the anti-triplet Higgs <math>\bar{T} (\bar{3},1)_{\frac{1}{3}}</math> in '''SU'''(5) GUT
 
</gallery>
 
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 [[color charge|colored]] Higgs triplet field with a very small mass (many orders of magnitude smaller than the GUT scale here). In theory, unifying [[quark]]s with [[lepton]]s, 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 (mathematics)|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 Lie groups|representations]] of the Lie group and chiral [[Weyl fermion]]s taking on values within a complex rep of the Lie group. The Lie group contains the [[Standard Model group]] and the Higgs fields acquire [[VEV]]s leading to a [[spontaneous symmetry breaking]] to the [[Standard Model]]. The Weyl fermions represent matter.
 
==Current status==
 
{{As of|2012}}, there is still no hard evidence that nature is described by a Grand Unified Theory. Moreover, since we have no idea which [[Higgs particle]] has been observed, the smaller electroweak unification is still pending.<ref>
{{cite book
|last=Hawking |first=S.W. |year=1996 |title=A Brief History of Time: The Updated and Expanded Edition.'' |edition=2nd |publisher=[[Bantam Books]] |isbn=0-553-38016-8 |page=XXX}}</ref> The discovery of [[neutrino oscillation]]s 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 [[Quantum chromodynamics|QCD]], the [[weak interaction]] and [[hypercharge]] seem to meet at a common length scale called the [[Grand unification energy|GUT scale]] and equal approximately to 10<sup>16</sup> 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 [[superpartner]]s 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
 
==See also==
 
*[[Paradigm shift]]
*[[Classical unified field theories]]
*[[X and Y bosons]]
*[[B − L]] quantum number
 
==Notes==
{{reflist|group=note}}
 
==References==
{{reflist}}
 
===Further reading===
* [[Stephen Hawking]], [[A Brief History of Time]], includes a brief popular overview.
*DR. Chaim Tejman http://www.grandunifiedtheory.org.il/
 
==External links==
*[http://math.ucr.edu/~huerta/oral.pdf The Algebra of Grand Unified Theories]
*[http://www.scholarpedia.org/article/Grand_unification Scholarpedia: Grand Unification]
 
[[Category:Particle physics]]
[[Category:Physical cosmology]]
[[Category:Physics beyond the Standard Model]]

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