We run all the couplings of the minimal supersymmetric (SUSY) extension of the standard model, taking account of the Yukawa sector. After identifying the scale at which the gauge couplings unify, we place bounds on the top-quark mass by requiring equality of the bottom-quark and r Yukawa couplings at that scale. For MSUSY = 1 TeV, M b =4.6 GeV, we find 139

The emission of particles from black holes created in the early Universe has detectable astrophysical consequences. The most stringent bound on their abundance has been obtained from the absence of a detectable diffuse flux of 100 MeV photons. Further scrutiny of these bounds is of interest as they, for instance, rule out primordial black holes as a dark matter candidate. We here point out that these bounds can, in principle, be improved by studying the diffuse cosmic neutrino flux. Measurements of near-vertical atmospheric neutrino fluxes in a region of low geomagnetic latitude can provide a competitive bound. The most favorable energy to detect a possible diffuse flux of primordial black hole origin is found to be a few MeV. We also show that measurements of the diffuse ν τ flux is the most promising to improve the existing bounds deduced from gamma-ray measurements. Neutrinos from individual black hole explosions can be detected in the GeV-TeV energy region. We find that the kilometer-scale detectors, recently proposed, are able to establish competitive bounds.

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It is proposed that the highest energy ∼ 10 20 eV cosmic ray primaries are protons which are decay products of a superheavy particle, G. The protons may be decay products either directly of a nearby (galactic) G or of a long-lived intermediate particle X which arises from decay of a distant (cosmological) G, then decays in or near our Galaxy. Such scenarios can occur in e.g. SU(15) grand unification and in some preon models.

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