General Aspects of Tree Level Gauge Mediation

TL;DR

This paper explores the structure and phenomenological implications of tree level gauge mediation in supersymmetry, providing guidelines for model building and specific predictions for sfermion mass ratios in SO(10) models, testable at the LHC.

Contribution

It offers a general analysis of TGM, detailing sfermion and gaugino mass forms, and identifies specific sfermion mass ratios in SO(10) models based on minimal embeddings, with implications for collider tests.

Findings

Derived general formulas for sfermion and gaugino masses in TGM.

Identified two specific sfermion mass ratio patterns in SO(10) models.

Predicted testable mass ratios at the LHC based on group theory.

Abstract

Tree level gauge mediation (TGM) may be considered as the simplest way to communicate supersymmetry breaking: through the tree level renormalizable exchange of heavy gauge messengers. We study its general structure, in particular the general form of tree level sfermion masses and of one loop, but enhanced, gaugino masses. This allows us to set up general guidelines for model building and to identify the hypotheses underlying the phenomenological predictions. In the context of models based on the "minimal" gauge group SO(10), we show that only two "pure" embeddings of the MSSM fields are possible using $d< 120$ representations, each of them leading to specific predictions for the ratios of family universal sfermion masses at the GUT scale, $m^2_{\bar{5}} = 2 m^2_{10}$ or $m^2_{\bar{5}} = (3/4) m^2_{10}$ (in SU(5) notation). These ratios are determined by group factors and are peculiar enough to make this scheme testable at the LHC. We also discuss three possible approaches to the $\mu$-problem, one of them distinctive of TGM.