Fine Tuning in General Gauge Mediation

TL;DR

This paper investigates the fine-tuning issue in general gauge mediation models, analyzing how different messenger scales affect tuning and identifying parameter regions that reduce tuning, with implications for supersymmetric spectra and the $$ problem.

Contribution

It provides a detailed numerical analysis of fine-tuning across various messenger scales in gauge mediation, highlighting conditions that minimize tuning and the importance of specific mass ratios.

Findings

Parameter regions with ~10% tuning are identified for each messenger scale.

Lower messenger scales require narrower parameter regions and favor tachyonic stop initial conditions.

Spectra findings have implications for the $$ problem in supersymmetry.

Abstract

We study the fine-tuning problem in the context of general gauge mediation. Numerical analyses toward for relaxing fine-tuning are presented. We analyse the problem in typical three cases of the messenger scale, that is, GUT ($2\times10^{16}$ GeV), intermediate ($10^{10}$ GeV), and relatively low energy ($10^6$ GeV) scales. In each messenger scale, the parameter space reducing the degree of tuning as around 10% is found. Certain ratios among gluino mass, wino mass and soft scalar masses are favorable. It is shown that the favorable region becomes narrow as the messenger scale becomes lower, and tachyonic initial conditions of stop masses at the messenger scale are favored to relax the fine-tuning problem for the relatively low energy messenger scale. Our spectra would also be important from the viewpoint of the $\mu-B$ problem.