Mass Hierarchies with $m_{h}=125$ GeV from Natural SUSY

Our study starts with a sequence of puzzles that include $(a)$ at which level $μ$ problem involving electroweak symmetry breaking can be solved; $(b)$ in which paradigm masses of superpartners in the third family can be lighter than in the first two families; $(c)$ whether it is possible to accommodate 125 GeV Higgs boson simultaneously; and $(d)$ how natural such paradigm is. These issues are considered in the context of two-site SUSY models. Both the MSSM and NMSSM as low-energy effective theory below the scale of two-site gauge symmetry breaking are investigated. We find that the fine tuning can be indeed reduced in comparison with ordinary MSSM with $m_{h}=125$ GeV. In general, the fine tuning parameter $Δ$ is in the range of $20-400$.

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