PeV scale Supersymmetry breaking and the IceCube neutrino flux

The observation of very high energy neutrino events at IceCube has grasped a lot of attention in the fields of both astrophysics and particle physics. It has been speculated that these high energy neutrinos might originate either from purely conventional astrophysical sources or from the late decay of a super heavy (PeV scale) dark matter (DM) particle. In order for decaying DM to be a dominant source of the IceCube high-energy neutrinos, it would require an unusually suppressed value of the coupling of DM to neutrinos. We attempt to explain this small coupling in the context of an R-parity conserving minimal supergravity model which has right-handed neutrino superfields. With the main assumptions of super-partner masses at the PeV scale and also a reheating temperature not much larger than the PeV scale, we find in our model several natural order-of-magnitude "miracles", (i) the gravitino is produced via freeze-in as a DM candidate with the correct relic density (ii) the right-handed (RH) sneutrino makes up only a tiny fraction of the present day energy density of the universe, yet its decay lifetime to the gravitino and neutrinos is such that it naturally predicts the right order-of-magnitude for the IceCube neutrino flux. The long lifetime of the RH sneutrino is explained by the existence of a global R-symmetry which is only broken due to supersymmetry breaking effects. Our model also predicts a flux of 100 TeV gamma rays from the decaying RH sneutrino which are within the current observational constraints.