  Motivated by the recent LHC hints of a Higgs boson around 125 GeV, we assume
a SM-like Higgs with the mass 123-127 GeV and study its implication in low
energy SUSY by comparing the MSSM and NMSSM. We consider various experimental
constraints at 2-sigma level (including the muon g-2 and the dark matter relic
density) and perform a comprehensive scan over the parameter space of each
model. Then in the parameter space which is allowed by current experimental
constraints and also predicts a SM-like Higgs in 123-127 GeV, we examine the
properties of the sensitive parameters (like the top squark mass and the
trilinear coupling A_t) and calculate the rates of the di-photon signal and the
VV^* (V=W,Z) signals at the LHC. Our typical findings are: (i) In the MSSM the
top squark and A_t must be large and thus incur some fine-tuning, which can be
much ameliorated in the NMSSM; (ii) In the MSSM a light stau is needed to
enhance the di-photon rate of the SM-like Higgs to exceed its SM prediction,
while in the NMSSM the di-photon rate can be readily enhanced in several ways;
(iii) In the MSSM the signal rates of pp -> h -> VV^* at the LHC are never
enhanced compared with their SM predictions, while in the NMSSM they may get
enhanced significantly; (iv) A large part of the parameter space so far
survived will be soon covered by the expected XENON100(2012) sensitivity
(especially for the NMSSM).
