Editing Georgi–Glashow model (section)

===Proton decay in SU(5)===
[[File:Proton decay GUT simple.svg|thumb|The most common source of [[proton decay]] in SU(5).  A left-handed and a right-handed [[up quark]] annihilate yielding an X<sup>+</sup> boson which decays to a [[positron]] and an anti-[[down quark]] of opposite handedness.]]

Unification of the Standard Model via an SU(5) group has significant phenomenological implications. Most notable of these is proton decay which is present in SU(5) with and without supersymmetry. This is allowed by the new vector bosons introduced from the [[adjoint representation]] of SU(5) which also contains the gauge bosons of the Standard Model forces. Since these new gauge bosons are in (3,2)<sub>−5/6</sub> [[bifundamental representation]]s, they violated baryon and lepton number. As a result, the new operators should cause protons to decay at a rate inversely proportional to their masses. This process is called dimension 6 proton decay and is an issue for the model, since the proton is experimentally determined to have a lifetime greater than the age of the universe. This means that an SU(5) model is severely constrained by this process.

As well as these new gauge bosons, in SU(5) models, the [[Higgs field]] is usually embedded in a '''5''' representation of the GUT group. The caveat of this is that since the Higgs field is an SU(2) doublet, the remaining part, an SU(3) triplet, must be some new field - usually called D or T. This new scalar would be able to generate proton decay as well and, assuming the most basic Higgs vacuum alignment, would be massless so allowing the process at very high rates.

While not an issue in the Georgi–Glashow model, a supersymmeterised SU(5) model would have additional proton decay operators due to the superpartners of the Standard Model fermions. The lack of detection of proton decay (in any form) brings into question the veracity of SU(5) GUTs of all types; however, while the models are highly constrained by this result, they are not in general ruled out.

==== Mechanism ====

In the lowest-order [[Feynman diagram]] corresponding to the simplest source of [[proton decay]] in SU(5), a left-handed and a right-handed [[up quark]] annihilate yielding an X<sup>+</sup> boson which decays to a right-handed (or left-handed) [[positron]] and a left-handed (or right-handed) anti-[[down quark]]:

:<math>\mathrm{u}_\mathsf{L} + \mathrm{u}_\mathsf{R} \to X^ + \to \mathrm{e}_\mathsf{R}^+ + \mathrm{\bar{d}}_\mathsf{L}\ ,</math>

:<math>\mathrm{u}_\mathsf{L} + \mathrm{u}_\mathsf{R} \to X^+\to \mathrm{e}_\mathsf{L}^+ + \mathrm{\bar{d}}_\mathsf{R} ~.</math>

This process conserves [[weak isospin]], [[weak hypercharge]], and [[color charge|color]]. GUTs equate anti-color with having two colors, <math>\ \bar{g} \equiv rb\ ,</math> and SU(5) defines left-handed normal leptons as "white" and right-handed antileptons as "black". The first vertex only involves fermions of the {{math|'''10'''}} representation, while the second only involves fermions in the {{math|'''5̅'''}} (or {{math|'''10'''}}), demonstrating the preservation of SU(5) symmetry.