Relaxed fine-tuning in models with nonuniversal gaugino masses

Abstract

We study, in a bottom-up approach, the fine-tuning problem between soft supersymmetry (SUSY) breaking parameters and the $\ensuremath{\mu}$ term for the successful electroweak symmetry breaking in the minimal supersymmetric standard model. It is shown that certain ratios among nonuniversal gaugino masses at the grand unified theory (GUT) scale are necessary to reduce fine-tuning. In addition, when all the gaugino masses are regarded as independent ones in their origins, a small gluino mass ${M}_{3}\ensuremath{\lesssim}120\text{ }\text{ }\mathrm{GeV}$ and a nonvanishing $A$ term ${A}_{t}\ensuremath{\sim}O({M}_{3})$ associated with top squarks are also required at the GUT scale as well as the nonuniversality. On the other hand, when we consider some UV theory, which fixes ratios of soft SUSY breaking parameters as certain values aside from the overall magnitude, heavier spectra are allowed. It is favored that the gluino and $W$-ino masses are almost degenerate at the weak scale, while a wider region of $b$-ino mass is favorable.