SU(8) Grand Unification from Composite Quarks and Leptons

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 the spontaneous $L$-$R$ symmetry violation caused by composite scalars reduces this initially vectorlike $SU(8)_{MF}$ theory down to the conventional $SU(5)$ GUT with an extra local family symmetry $SU(3)_{F}$ and three standard families of quarks and leptons. Though the tiny confinement scale for universal preons composing both quarks and leptons makes it impossible to directly confirm their composite nature, simultaneous emergence of several extra $SU(5)\times SU(3)_{F}$ multiplets of heavy composite fermions may help with a model verification. Generally, they may be located at scales from $O(100)$ $TeV$ up to the Planck mass scale depending on an interplay between the compositeness scale and scale of the family symmetry $SU(3)_{F}$. Some of them through a natural see-saw mechanism provide neutrino masses which, in contrast to conventional picture, appear to follow an inverted family hierarchy. Others mix with ordinary quark-lepton families in a way that there may arise a marked violation of unitarity in the CKM matrix for leptons.