Editing Grand Unified Theory (section)

=== SU(5) ===
{{main|Georgi–Glashow model}}

[[File:Georgi-Glashow charges.svg|200px|right|thumb|The pattern of [[weak isospin]]s, weak hypercharges, 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.]]

{{math|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
: <math> \rm SU(5) \supset SU(3)\times SU(2)\times U(1) .</math>

Such group symmetries allow the reinterpretation of several known particles, including the photon, W and Z bosons, and gluon, 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 matter particles fit perfectly into three copies of the smallest [[group representation]]s of {{math|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.

The two smallest [[group representation#Reducibility|irreducible representations]] of {{math|SU(5)}} are {{math|'''5'''}} (the defining representation) and {{math|'''10'''}}. (These bold numbers indicate the dimension of the representation.) In the standard assignment, the {{math|'''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 {{math|'''10'''}} contains the six [[Quark|up-type quark]] components, the left-handed 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.

The hypothetical [[neutrino#Chirality|right-handed neutrinos]] are a singlet of {{math|SU(5)}}, which means its mass is not forbidden by any symmetry; it doesn't need a spontaneous electroweak symmetry breaking which explains why its mass would be heavy{{clarify|date=March 2016}} (see [[seesaw mechanism]]).