Super-Natural 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 super-natural 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 (GM) mechanism. We demonstrate that the $Z$-boson mass, the supersymmteric Higgs mixing parameter $\mu$ 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 2-body and 3-body decays to the LSP axino for several values of axion decay constant $f_a$, and find that the light stau has a lifetime $\tau_{\tilde \tau_1}$ in $[10^{-4},100]$ s for an $f_a$ range $[10^{9},10^{12}]$ 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 charge particles at the LHC.