Partial Derivation of Transformation Properties of Quarks and Leptons

Abstract

Under the assumptions that $SU(3)_c\times U(1)_Y \times G^{\prime}$ with $G^{\prime}$ simple is a local symmetry group at high energies, that color is parity-conserving, and the Y-charges are irreducible, we show that anomaly constraints imply the minimal set of fermions is fifteen in number. Given this minimal set, we further show that $G^{\prime}$ must be $SU(2)$ and the unbroken gauge symmetry is {\it either} color {\it or} the product of color with electric charge.