Phenomenology of NMSSM in TeV scale mirage mediation

Abstract

We study the next-to-minimal supersymmetric standard model (NMSSM) with the TeV scale mirage mediation, which is known as a solution for the little hierarchy problem in supersymmetry. Our previous study showed that 125 GeV Higgs boson is realized with O(10) % fine-tuning for 1.5 TeV gluino (1 TeV stop) mass. The $\mu$ term could be as large as 500 GeV without sacrificing the fine-tuning thanks to a cancellation mechanism. The singlet-doublet mixing is suppressed by $\tan\beta$. In this paper, we further extend this analysis. We argue that approximate scale symmetries play a role behind the suppression of the singlet-doublet mixing. They reduce the mixing matrix to a simple form that is useful to understand the results of the numerical analysis. We perform a comprehensive analysis of the fine-tuning including the singlet sector by introducing a simple formula for the fine-tuning measure. This shows that the singlet mass of the least fine-tuning is favored by the LEP anomaly for moderate $\tan\beta$. We also discuss prospects for the precision measurements of the Higgs couplings at LHC and ILC and direct/indirect dark matter searches in the model.