Decaying Dark Matter in the Supersymmetric Standard Model with Freeze-in
  and Seesaw mechanims
  Inspired by the decaying dark matter (DM) which can explain cosmic ray
anomalies naturally, we consider the supersymmetric Standard Model with three
right-handed neutrinos (RHNs) and R-parity, and introduce a TeV-scale DM sector
with two fields \phi_{1,2} and a $Z_3$ discrete symmetry. The DM sector only
interacts with the RHNs via a very heavy field exchange and then we can explain
the cosmic ray anomalies. With the second right-handed neutrino N_2 dominant
seesaw mechanism at the low scale around 10^4 GeV, we show that \phi_{1,2} can
obtain the vacuum expectation values around the TeV scale, and then the
lightest state from \phi_{1,2} is the decay DM with lifetime around \sim
10^{26}s. In particular, the DM very long lifetime is related to the tiny
neutrino masses, and the dominant DM decay channels to \mu and \tau are related
to the approximate \mu-\tau symmetry. Furthermore, the correct DM relic density
can be obtained via the freeze-in mechanism, the small-scale problem for power
spectrum can be solved due to the decays of the R-parity odd meta-stable states
in the DM sector, and the baryon asymmetry can be generated via the soft
leptogensis.
