Fermion masses and mixing angles from gauge symmetries

TL;DR

This work argues that the observed fermion mass hierarchies and mixing angles can emerge from the simplest gauge extension of the MSSM: a horizontal U(1) flavor symmetry supplemented by a family-independent piece, with anomaly cancellation achieved via the Green-Schwarz mechanism in a string-theoretic context. Imposing left–right symmetry and symmetric mass matrices yields texture zeros in the quark and lepton sectors, constraining the pattern of Yukawa couplings such that the leading entries come from renormalizable terms and the rest from higher-dimension operators suppressed by the breaking scale. The resulting relations among mass ratios and CKM elements arise from the U(1) charges and the hierarchy parameters epsilon and bar{epsilon}, with key predictions including m_d m_b / m_s^2 ~ m_u m_t / m_c^2 at the unification scale and sin^2(theta_W) = 3/8. The framework links Yukawa textures to a string-inspired symmetry structure, suggesting a path to identifying a concrete 4D string compactification that reproduces the observed fermion spectrum and mixings.

Abstract

The structure of the quark and lepton masses and mixing angles provides one of the few windows we have on the underlying physics generating the \sm. In an attempt to identify the underlying symmetry group we look for the simplest gauge extension of the SUSY standard model capable of generating the observed structure. We show that the texture structure and hierarchical form found in the (symmetric) quark and lepton mass matrices follows if one extends the gauge group of the standard model to include an horizontal $U(1)$ gauge factor, constrained by the need for anomaly cancellation. This $U(1)$ symmetry is spontaneously broken slightly below the unification/string scale leaving as its only remnant the observed structure of masses and mixings. Anomaly cancellation is possible only in the context of superstring theories via the Green Schwarz mechanism with $sin^2(θ_W)=3/8$.