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In order to significantly reduce the fine-tuning associated with theelectroweak symmetry breaking in the minimal supersymmetric standard model(MSSM), we consider not only the minimal gravity mediation effects but also theminimal gauge mediation ones for a common supersymmetry breaking source at ahidden sector. In this "Minimal Mixed Mediation model," the minimal forms forthe Kahler potential and the gauge kinetic function are employed at tree level.The MSSM gaugino masses are radiatively generated through the gauge mediation.Since a "focus point" of the soft Higgs mass parameter, m_{h_u}^2 appearsaround 3-4 TeV energy scale in this case, m_{h_u}^2 is quite insensitive tostop masses. Instead, the naturalness of the small m_{h_u}^2 is more closelyassociated with the gluino mass rather than the stop mass unlike theconventional scenario. As a result, even a 3-4 TeV stop mass, which is known toexplain the 125 GeV Higgs mass at three-loop level, can still be compatiblewith the naturalness of the electroweak scale. On the other hand, therequirements of various fine-tuning measures much smaller than 100 and |\mu| <600 GeV constrain the gluino mass to be 1.6 TeV < M_3 < 2.2 TeV, which iswell-inside the discovery potential range of LHC RunII.

Naturalness-guided Gluino Mass Bound from the Minimal Mixed Mediation of SUSY Breaking