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Under the minimal SUSY standard model (MSSM), the discrepancy in the muon g-2suggests the SUSY particles are of order 100 GeV, which is also supported bydiscussions on the little hierarchy problem. However, the LHC experiments havefound no scalar-quarks or gluinos in such mass range, and moreover, the Higgsboson mass of 126 GeV requires, within the MSSM framework, the scalar-top massof order 1-10 TeV. This current status forces us to abandon the simplestsupersymmetry-breaking frameworks of the CMSSM and the GMSB scenarios.  The V-MSSM is investigated in this dissertation, which is proposed as anextension of the MSSM with a (10 + 10bar) pair of the SU(5) decuplets. In theframework the Higgs mass is increased by effect from the extra matters, andthus the 126 GeV is achieved with the scalar-top having a lighter mass. Thisfact resurrects the CMSSM and the GMSB scenarios. This dissertation examinesthe GMSB scenario under the V-MSSM; it is called V-GMSB scenario.  It is shown that the V-GMSB has a potential to realize the 126 GeV mass ofthe Higgs boson with holding the explanation of the muon magnetic momentdiscrepancy, if the masses of the extra quarks are approximately less than 1.2TeV. Constraints on the V-GMSB from the LHC experiments are discussed then; itis concluded that the gluino mass must be approximately heavier than 1.1 TeV,and that the extra quarks be heavier than 300-650 GeV depending on the decaybranches of them.  LHC prospects are briefly discussed. As the extra quarks are expected to beapproximately less than 1.2 TeV, searches for the particles are of greatinterest at the 14 TeV LHC; constraints from the supersymmetry search,especially on the gluino mass, are expected to be much improved there.Therefore, it is expected that the fate of the V-GMSB is adjudicated at thecourt of the 14 TeV LHC.

Supersymmetry after the Higgs discovery and its LHC phenomenology