We explore the model building and phenomenology of flavored gauge-mediation models of supersymmetry breaking in which the electroweak Higgs doublets and the $SU(2)$ messenger doublets are connected by a discrete non-Abelian symmetry. The embedding of the Higgs and messenger fields into representations of this non-Abelian Higgs-messenger symmetry results in specific relations between the Standard Model Yukawa couplings and the messenger-matter Yukawa interactions. Taking the concrete example of an ${\mathcal{S}}_3$ Higgs-messenger symmetry, we demonstrate that, while the minimal implementation of this scenario suffers from a severe $\mu /B_{\mu }$ problem that is well known from ordinary gauge mediation, expanding the Higgs-messenger field content allows for the possibility that $\mu$ and $B_{\mu }$ can be separately tuned, allowing for the possibility of phenomenologically viable models of the soft supersymmetry-breaking terms. We construct toy examples of this type that are consistent with the observed 125 GeV Higgs boson mass.

• Received 26 January 2018

DOI:https://doi.org/10.1103/PhysRevD.97.095028

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society