We discuss the fine-tuning issue within the MSSM framework. Following the idea that the fine-tuning can measure effects of some missing mechanism, we impose non-universal gaugino masses at the GUT scale, and explore the low scale implications. We realize that the fine-tuning parametrized with EW can be as low as zero. We consider the stop mass with a special importance and focus on the mass scales as mt ≤ 700 GeV, which are excluded by the current experiments when the stop decays into a neutralino along with a top quark or a chargino along with a bottom quark. We find that the stop mass can be as low as about 250 GeV with EW ∼ 50. We find that the solutions in this region can be exluded only up to 60% when stop decays into a neutralino-top quark, and 50% when it decays into a chargino-b quark. Setting 65% CL to be potential exclusion and 95% to be pure exclusion limit such solutions will be tested in near future experiments, which are conducted with higher luminosity. In addition to stop, the region with low fine-tuning and light stops predicts masses for the other supersymmetric particles such as mb 700 GeV, mτ 1 TeV, mχ± 1 120 GeV. The details for the mass scales and decay rates are also provided by tables of benchmark points.

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We study the anomalous magnetic moment of the muon in supersymmetric E 6 models and generic Uð1Þ 0 models to probe the model reactions and to find constraints on the large parameter space of these models. For future searches, by imposing the existing bounds coming from collider searches and theoretical considerations upon the Uð1Þ 0 model parameters, we examine the lightest Higgs boson mass m h and the mass of the additional Z boson m Z 2 in such singlet extensions of the MSSM. We observed that not only supersymmetric E 6 models but also generic Uð1Þ 0 models are sensitive to the imposition of the considered bounds. Indeed, without the muon anomaly constraints E 6 models and generic Uð1Þ 0 models can predict m h as large as $150 GeV and $180 GeV, respectively. However, in addition to the mentioned constraints when a 1 range for the anomalous magnetic moment of the muon is considered, we observe that generic Uð1Þ 0 models do not favor the mass of the lightest Higgs boson to be larger than 140 GeV; it should be smaller than 135 GeV in E 6 models.