Editing Flipped SU(5) (section)

==The model==
The flipped {{math|SU(5)}} model states that the [[gauge group]] is:

:{{math|([[Special unitary group|SU(5)]] × [[Unitary group|U(1)]]<sub>''χ''</sub>)/'''Z'''<sub>5</sub>}}

Fermions form three families, each consisting of the [[Representations of Lie groups/algebras|representations]]

:{{math|{{overline|'''5'''}}<sub>−3</sub>}} for the lepton doublet, L, and the up quarks {{mvar|u<sup>c</sup>}};
:{{math|'''10'''<sub>1</sub>}} for the quark doublet, Q, the down quark, {{mvar|d<sup>c</sup>}} and the right-handed neutrino, {{math|N}};
:{{math|'''1'''<sub>5</sub>}} for the charged leptons, {{mvar|e<sup>c</sup>}}.

This assignment includes three right-handed neutrinos, which have never been observed, but are often postulated to explain the lightness of the observed neutrinos and [[neutrino oscillation]]s. There is also a {{math|[[Representations of Lie groups/algebras|'''10'''<sub>1</sub>]]}} and/or {{math|{{overline|'''10'''}}<sub>−1</sub>}} called the Higgs fields which acquire a [[VEV]], yielding the [[spontaneous symmetry breaking]]

:{{math|(SU(5) × U(1)<sub>''χ''</sub>)/'''Z'''<sub>5</sub> → (SU(3) × SU(2) × U(1)<sub>Y</sub>)/'''Z'''<sub>6</sub>}}

The {{math|SU(5)}} representations [[restricted representation|transform under this subgroup]] as the reducible representation as follows:

:<math>\bar{5}_{-3}\to (\bar{3},1)_{-\frac{2}{3}}\oplus (1,2)_{-\frac{1}{2}}</math> (u<sup>c</sup> and l)
:<math>10_{1}\to (3,2)_{\frac{1}{6}}\oplus (\bar{3},1)_{\frac{1}{3}}\oplus (1,1)_0</math> (q, d<sup>c</sup> and ν<sup>c</sup>)
:<math>1_{5}\to (1,1)_1</math> (e<sup>c</sup>)
:<math>24_0\to (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus (3,2)_{\frac{1}{6}}\oplus (\bar{3},2)_{-\frac{1}{6}}</math>.