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Supersymmetry with a Heavy Lightest Supersymmetric Particle

To escape the current LHC supersymmetry (SUSY) search constraints while preserve the naturalness condition, we propose the heavy Lightest Supersymmetric Particle (LSP) SUSY. According to the different dependence on the LSP mass, we systematically classify the discriminating variables into three categories. We find the strong dependence of all current SUSY searches on variables in the first category render the weak sensitivity for the heavy LSP SUSY. Especially, all the current LHC SUSY search constraints can be evaded if the LSP mass is around 600 GeV or higher. In the Minimal Supersymmetric Standard Model (MSSM), we find that the heavy LSP SUSY does not induce more fine-tuning than Higgs boson mass. Moreover, the muon anomalous magnetic moment can be satisfied within 3-$σ$ level. We systematically study the viable parameter space for heavy LSP SUSY, and present four benchmark points which realize our proposal concretely. An improved collider search for those benchmark points, which mainly relies on the variable in the second category, is discussed in detail.