On Mixing Supersymmetry and Family Symmetry Breakings

TL;DR

This paper proposes a toy model where Higgs fields are part of a non-Abelian family symmetry, with family partners acting as messengers for supersymmetry and family symmetry breaking, and explores a focusing mechanism to mitigate hierarchy issues.

Contribution

It introduces a novel mediation scheme involving non-Abelian family symmetry and demonstrates a focusing mechanism to address soft term hierarchies.

Findings

Existence of a focusing mechanism that reduces family-dependent hierarchies

Higgs fields transforming under non-Abelian family symmetry

Potential for unified mediation of supersymmetry and family symmetry breaking

Abstract

We present a toy model in which the Higgs sector fields transform as non-Abelian representations of a family symmetry group, and consider the possibility that the extra family partners of the Higgs particles act as messengers for both supersymmetry and family symmetry breakings. Although such mediation schemes generically produce family dependent soft supersymmetry breaking terms at the messenger scale, we demonstrate the existence of a focusing mechanism which may erase such hierarchies through renormalization group running.