Non-universal, Non-anomalous U(1)' in a Model with Anomaly Mediated SUSY Breaking

TL;DR

This paper presents a supersymmetric model with a non-anomalous U(1)' gauge symmetry that resolves the tachyonic slepton problem and naturally explains fermion mass hierarchies without requiring anomalous symmetries.

Contribution

It introduces a non-anomalous U(1)' symmetry in a SUSY model that cancels anomalies without extra exotics and addresses multiple issues in anomaly mediated SUSY breaking.

Findings

Solves tachyonic slepton mass problem with FI D-terms.

Provides a natural explanation for fermion mass hierarchy.

Offers a counterexample to the necessity of anomalous U(1)' for realistic fermion mixing.

Abstract

We construct a Minimum Supersymmetry Standard Model expanded by a non-anomalous family (NAF) U(1)'_{NAF} gauge symmetry. All gauge anomalies are cancelled with no additional exotics other than the three right-handed neutrinos. The FI D-terms associated with the U(1)'_{NAF} symmetry lead to additional positive contributions to slepton squared masses. In a RG invariant way, this thus solves the tachyonic slepton mass problem in Anomaly Mediated Supersymmetry Breaking. In addition, the U(1)'_{NAF} symmetry naturally gives rise to the fermion mass hierarchy and mixing angles, and determines the mass spectrum of the sparticles. Our model also provides a counter example to the previous claim that the only U(1)' that can give rise to realistic fermion mass hierarchy and mixing pattern must be anomalous.