Superheavy dark matter with discrete gauge symmetries

We show that there are discrete gauge symmetries which naturally protect heavy X particles from decaying into ordinary light particles in the supersymmetric standard model. This makes the proposal that superheavy X particles constitute part of the dark matter in the present universe very attractive. It is more interesting that there is a class of discrete gauge symmetries which naturally accommodates a long-lived unstable X particle. We find that in some discrete Z(10) models, for example, a superheavy X particle has a lifetime of tau(X) similar or equal to 10(11) - 10(26) yr for a mass of M-X similar or equal to 10(13) - 10(14) GeV. This long lifetime is guaranteed by the absence of lower dimensional operators (of light particles) coupled to the X. We briefly discuss a possible explanation for the recently observed ultrahigh-energy cosmic ray events by the decay of this unstable X particle. [S0556-2821(98)08218-6].