Focus Point Gauge Mediation with Incomplete Adjoint Messengers and Gauge Coupling Unification

TL;DR

This paper investigates focus point gauge mediation with adjoint messengers, achieving reduced fine-tuning and successful gauge coupling unification at a higher scale, explaining the Higgs mass with moderate fine-tuning.

Contribution

It introduces a focus point gauge mediation scenario with incomplete adjoint messengers, maintaining gauge coupling unification at an elevated scale and controlling fine-tuning.

Findings

Achieves Higgs mass with fine-tuning Δ=60-150.

Maintains gauge coupling unification at a scale above the GUT scale.

Proton decay constraints are satisfied due to heavy colored Higgs multiplets.

Abstract

As the mass limits on supersymmetric particles are gradually pushed to higher values due to their continuing non-observation at the CERN LHC, looking for focus point regions in the supersymmetric parameter space, which shows considerably reduced fine-tuning, is increasingly more important than ever. We explore this in the context of gauge mediated supersymmetry breaking with messengers transforming in the adjoint representation of the gauge group, namely, octet of color SU(3) and triplet of weak SU(2). A distinctive feature of this scenario is that the focus point is achieved by fixing a single combination of parameters in the messenger sector, which is invariant under the renormalization group evolution. Because of this invariance, the focus point behavior is well under control once the relevant parameters are fixed by a more fundamental theory. The observed Higgs boson mass is explained with a relatively mild fine-tuning $\Delta=$ 60-150. Interestingly, even in the presence of incomplete messenger multiplets of the SU(5) GUT group, the gauge couplings still unify perfectly, but at a scale which is one or two orders of magnitude above the conventional GUT scale. Because of this larger unification scale, the colored Higgs multiplets become too heavy to trigger proton decay at a rate larger than the experimentally allowed limit.