Non anomalous U(1)_H gauge model of flavor

TL;DR

This paper proposes a non anomalous $U(1)_H$ gauge symmetry model explaining fermion mass hierarchies, predicting specific relations among Yukawa couplings, the $$ term, and quark masses, with testable implications.

Contribution

It introduces a consistent non anomalous $U(1)_H$ gauge symmetry model that constrains fermion masses and predicts a zero up quark mass, offering testable low-energy predictions.

Findings

Lepton and down-type quark Yukawa unification limited to two generations.

The $$ term is below the SUSY breaking scale.

The model predicts a zero up quark mass, providing a testable signature.

Abstract

A non anomalous horizontal $U(1)_H$ gauge symmetry can be responsible for the fermion mass hierarchies of the minimal supersymmetric standard model. Imposing the consistency conditions for the absence of gauge anomalies yields the following results: i) unification of leptons and down-type quarks Yukawa couplings is allowed at most for two generations. ii) The $\mu$ term is necessarily somewhat below the supersymmetry breaking scale. iii) The determinant of the quark mass matrix vanishes, and there is no strong $CP$ problem. iv) The superpotential has accidental $B$ and $L$ symmetries. The prediction $m_{\rm up}=0$ allows for an unambiguous test of the model at low energy.