SuperWIMP dark matter and 125 GeV Higgs boson in the minimal GMSB
  Recently, both the ATLAS and CMS experiments have observed an excess of
events that could be the first evidence for a 125 GeV Higgs boson. We
investigate an implication of the CP-even Higgs boson with mass around 125 GeV
in the context of the minimal gauge mediated supersymmetry breaking (mGMSB). In
mGMSB, gravitino is the lightest sparticle (LSP) and hence the dark matter
candidate. We consider the so-called superWIMP scenario where the dark matter
gravitino is non-thermally produced by the decay of the next-to-LSP (NLSP)
bino-like neutralino after its freeze-out. For a given $\tan \beta$ and the
number of the messengers ($N_m$) fixed, we find that the rest of the mGMSB
parameters, the SUSY breaking parameter and the messenger scale, are completely
fixed by the conditions of simultaneously realizing the observed dark matter
abundance and the 125 GeV Higgs boson mass, leading to the NLSP neutralino mass
around 1.5-2 TeV and the gravitino mass around 3-7 GeV, depending on the values
of $\tan \beta$ and $N_m$. The lifetime of the NLSP is found to be shorter than
1 sec, so that the success of the big bang nucleosynthesis remains intact. The
non-thermally produced gravitino behaves as the warm dark matter with the
free-streaming scale found to be $\lambda_{\rm FS} \simeq 0.1$ Mpc, whose value
is reasonable for observations of the power spectrum on both large and
sub-galactic scales in the Universe.
