Family Unification with SO(10)

TL;DR

This paper explores a grand unification model based on the group SO(10)^3 imes S_3, which unifies all fermions into a single multiplet, suppresses flavor-changing effects, and naturally explains quark and lepton mass structures.

Contribution

It introduces a novel family unification framework with SO(10)^3 imes S_3 symmetry, achieving fermion unification and addressing flavor and mass hierarchy issues.

Findings

All known fermions are in a single irreducible multiplet.

The model suppresses SUSY flavor changing effects via degeneracy.

It naturally explains the doublet-triplet splitting and mass structures.

Abstract

Unification based on the group SO(10)^3 \times S_3 is studied. Each family has its own SO(10) group, and the S_3 permutes the three families and SO(10) factors. This is the maximal local symmetry for the known fermions. Family unification is achieved in the sense that all known fermions are in a single irreducible multiplet of the symmetry. The symmetry suppresses SUSY flavor changing effects by making all squarks and sleptons degenerate in the symmetry limit. Doublet-triplet splitting can arise simply, and non-trivial structure of the quark and lepton masses emerges from the gauge symmetry, including the "doubly lopsided" form.