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 f1,2 is the decay DM with lifetime around similar to 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.