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 ${\mathbf{Z}}_{10}$ models, for example, a superheavy $X$ particle has a lifetime of ${\tau }_X\simeq {10}^{11}-{10}^{26}\hspace{0.5em}\mathrm{yr}$ for a mass of $M_X\simeq {10}^{13}-{10}^{14}\hspace{0.5em}\mathrm{GeV}.$ This long lifetime is guaranteed by the absence of lower dimensional operators (of light particles) coupled to the $X.\mathrm{}$ We briefly discuss a possible explanation for the recently observed ultrahigh-energy cosmic ray events by the decay of this unstable $X$ particle.

• Received 19 May 1998

DOI:https://doi.org/10.1103/PhysRevD.58.103503