  The LHC data implies that the newly discovered Higgs boson h may be sterile
(highly SM-like). In supersymmetric SMs (SSMs), Higgs couplings are often
modified by Higgs mixing and stop loop corrections, so we study the Higgs
sterility in the Higgs and stop sectors in two SSMs: (I) The Minimal SSM
(MSSM). In the nearly decoupling region, the doublet-doublet mixing effect can
only enhance C_{hb\bar b} by 2m_Z^2/M_A^2. Sterility places M_A\gtrsim 900 GeV.
But it hardly constrains the stop sector due to the heaviness of Higgs boson
mass m_h; (II) The next to MSSM(NMSSM). In the presence of doublet-singlet
mixing, the mixing structure is complicated. We find a simple approximation to
understand Higgs sterility and its implications, says the amount of pushing-up
m_h\lesssim 5 GeV while the pulling-down scenario is favored. Stops can be
light here, so Higgs sterility significantly constrains them directly and
indirectly except for blind spots. We also study the LHC features of the whole
stop sector facing a sterile Higgs and find that, in virtue of decays between
stops and sbottom, characteristic signatures like same-sign leptons and multi
b-jets are promising probes.
