Clustering, GUT scale and neutrino masses in Ultrahigh energy cosmic   rays
  We determine the probability that an ultrahigh energy (above 5\cdot 10^{19} eV) proton created at a distance r with energy E arrives at earth above a threshold E_c. The clustering of ultrahigh energy cosmic rays suggests that they might be emitted by compact sources. We present a statistical analysis on the source density based on the multiplicities. The ultrahigh energy cosmic ray spectrum is consistent with the decay of GUT scale particles. By using a maximum likelihood analysis we determine the mass of these GUT scale particles. We consider the possibility that a large fraction of the ultrahigh energy cosmic rays are decay products of Z bosons which were produced in the scattering of ultrahigh energy cosmic neutrinos on cosmological relic neutrinos. Based on this scenario we determine the required mass of the heaviest relic neutrino as well as the necessary ultrahigh energy cosmic neutrino flux via a maximum likelihood analysis. 
Z. Fodor