Probing the stability of superheavy dark matter particles with high-energy neutrinos

Two of the most fundamental properties of the dark matter particle, the mass and the lifetime, are only weakly constrained by the astronomical and cosmological evidence of dark matter. We derive in this paper lower limits on the lifetime of dark matter particles with masses in the range 10 TeV-10^15 TeV from the non-observation of ultrahigh energy neutrinos in the AMANDA, IceCube, Auger and ANITA experiments. For dark matter particles which produce neutrinos in a two body or a three body decay, we find that the dark matter lifetime must be longer than O(10^26-10^28) s for masses between 10 TeV and the Grand Unification scale. Finally, we also calculate, for concrete particle physics scenarios, the limits on the strength of the interactions that induce the dark matter decay.