Supernatural MSSM

Abstract

We point out that the electroweak fine-tuning problem in the supersymmetric standard models (SSMs) is mainly due to the high energy definition of the fine-tuning measure. We propose supernatural supersymmetry which has an order one high energy fine-tuning measure automatically. The key point is that all the mass parameters in the SSMs arise from a single supersymmetry breaking parameter. In this paper, we show that there is no supersymmetry electroweak fine-tuning problem explicitly in the minimal SSM (MSSM) with no-scale supergravity and Giudice-Masiero mechanism. We demonstrate that the $Z$-boson mass, the supersymmetric Higgs mixing parameter $\ensuremath{\mu}$ at the unification scale, and the sparticle spectrum can be given as functions of the universal gaugino mass ${M}_{1/2}$. Because the light stau is the lightest supersymmetric particle (LSP) in the no-scale MSSM, to preserve $R$ parity, we introduce a non-thermally generated axino as the LSP dark matter candidate. We estimate the lifetime of the light stau by calculating its two-body and three-body decays to the LSP axino for several values of axion decay constant ${f}_{a}$, and find that the light stau has a lifetime ${\ensuremath{\tau}}_{{\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}}$ in $[{10}^{\ensuremath{-}4},100]\text{ }\text{ }\mathrm{s}$ for an ${f}_{a}$ range $[{10}^{9},{10}^{12}]\text{ }\text{ }\mathrm{GeV}$. We show that our next to the LSP stau solutions are consistent with all the current experimental constraints, including the sparticle mass bounds, B-physics bounds, Higgs mass, cosmological bounds, and the bounds on long-lived charged particles at the LHC.