  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 ($10^{-6})$, 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.
