  The sweet spot supersymmetry (SUSY) solves the mu problem in the Minimal
Supersymmetric Standard Model (MSSM) with gauge mediated SUSY breaking (GMSB)
via the generalized Giudice-Masiero (GM) mechanism where only the mu-term and
soft Higgs masses are generated at the unification scale of the Grand Unified
Theory (GUT) due to the approximate PQ symmetry. Because all the other SUSY
breaking soft terms are generated via the GMSB below the GUT scale, there
exists SUSY electroweak (EW) fine-tuning problem to explain the 125 GeV Higgs
boson mass due to small trilinear soft term. Thus, to explain the Higgs boson
mass, we propose the GMSB with both the generalized GM mechanism and
Higgs-messenger interactions. The renormalization group equations are runnings
from the GUT scale down to EW scale. So the EW symmetry breaking can be
realized easier. We can keep the gauge coupling unification and solution to the
flavor problem in the GMSB, as well as solve the \mu/B_{\mu}-problem. Moreover,
there are only five free parameters in our model. So we can determine the
characteristic low energy spectra and explore its distinct phenomenology. The
low-scale fine-tuning measure can be as low as 20 with the light stop mass
below 1 TeV and gluino mass below 2 TeV. The gravitino dark matter can come
from a thermal production with the correct relic density and be consistent with
the thermal leptogenesis. Because gluino and stop can be relatively light in
our model, how to search for such GMSB at the upcoming run II of the LHC
experiment could be very interesting.
