Editing Georgi–Glashow model (section)

==== 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.