Title: The Eightfold Way for composite quarks and leptons: SU(8) GUT
(Submitted on 20 Nov 2017 (v1), revised 17 Jul 2018 (this version, v5), latest version 31 Aug 2018 (v6))
Abstract: We consider the $L$-$R$ symmetric composite model for quarks and leptons where constituent preons possessing some local $SU(N)_{MF}$ metaflavor symmetry are bound by the chiral $SO(n)_{L}\times SO(n)_{R}$ gauge metacolor forces. The strengthening of the 't Hooft's anomaly matching condition, when the massless fermion composites are required to complete a single representation of the $SU(N)_{MF}$ rather than some set of its representations, allows to fix the number of basic metaflavors $N$. Particularly, just eight left-handed and eight right-handed preons and their composites preserving the global chiral symmetry $SU(8)_{L}\times SU(8)_{R}$ are turned out to underlie the physical world at small distances that uniquely identifies the local metaflavor symmetry $SU(8)_{MF}$ as its effective unified symmetry. We next show that an appropriate $L$-$R$ symmetry violation reduces this seemingly vectorlike $SU(8)_{MF}$ theory with similar left-handed and right-handed fermion multiplets down to the conventional $SU(5)$ GUT with an extra local family symmetry $SU(3)_{F}$ and three standard generations of quarks and leptons. Though the tiny radius of compositeness for universal preons composing both quarks and leptons makes it impossible to immediately confirm their composite nature, a few special $% SU(5)\times SU(3)_{F}$ multiplets of extra composite fermions located at the scales from $O(1)$ $TeV$ up to the Planck mass scale predicted by the theory may appear of actual experimental interest. Some of them can be directly observed, the others populate the $SU(5)$ GUT desert. Due to their mixing with ordinary quark-lepton families there may arise a marked violation of unitarity in the mass matrices for leptons and down quarks depending on the interplay between the compositeness scale and scale of the family symmetry $% SU(3)_{F}$.