Long lived superheavy dark matter with discrete gauge symmetries

The recently observed ultrahigh energy (UHE) cosmic rays beyond the Greisen-Zatsepin-Kuzmin bound can be explained by the decays of some superheavy X particles forming a part of dark matter in our universe. We consider various discrete gauge symmetries Z(N) to ensure the required long lifetime (tau(X)similar or equal to 10(10)-10(22) yr) of the X particle to explain the UHE cosmic rays in the minimal supersymmetric standard model (MSSM) with massive Majorana neutrinos. We show that there is no anomaly-free discrete gauge symmetry to make the lifetime of the X particle sufficiently long in the MSSM with the X particle. We find, however, possible solutions to this problem especially by enlarging the particle contents in the MSSM. We show a number of solutions introducing an extra pair of singlets Y and (Y) over bar which have fractional Z(N)(N = 2,3) charges. The present experimental constraints on the X particle are briefly discussed. [S0556-2821(99)02306-1].