Shifted focus point of the Higgs mass parameter from the minimal mixed mediation of supersymmetry breaking

We employ both the minimal gravity- and the minimal gauge mediations of supersymmetry breaking at the grand unified theory (GUT) scale in a single supergravity framework, assuming the gaugino masses are generated dominantly by the minimal gauge mediation effects. In such a "minimal mixed mediation model," a "focus point" of the soft Higgs mass parameter, m_{h_u}^2 emerges at 3-4 TeV energy scale, which is exactly the stop mass scale needed for explaining the 126 GeV Higgs boson mass without the "A-term" at the three loop level. As a result, m_{h_u}^2 can be quite insensitive to various trial stop masses at low energy, reducing the fine-tuning measures to be much smaller than 100 even for a 3-4 TeV low energy stop mass and -0.5 < A_t/m_0 < +0.1 at the GUT scale. The gluino mass is predicted to be about 1.7 TeV, which could readily be tested at LHC run2.