SUSY resonances from UHE neutralinos in neutrino telescopes and in the sky

In the Top-down scenarios, the decay of super-heavy particles(m~10^{12-16}GeV), situated in dark-matter halos not very far from our Galaxy,can explain the ultra-high-energy (UHE) cosmic-ray spectrum beyond theGriesen-Zatasepin-Kuzmin cut-off. In the MSSM, a major component of the UHEcosmic-ray flux at PeV-EeV energies could be given by the lightest neutralino\chi, that is the lightest stable supersymmetric particle. Then, the signal ofUHE \chi's on earth might emerge over the interactions of a comparable neutrinocomponent. We compute the event rates for the resonant production of "right"selectrons and "right" squarks in mSUGRA, when UHE neutralinos of energy largerthan 10^5 GeV scatter off electrons and quarks in an earth-based detector likeIceCube. When the resonant channel dominates in the total \chi-e,\chi-qscattering cross section, the only model parameters affecting the correspondingvisible signal rates turn out to be the physical masses of the resonantright-scalar and of the lightest neutralino. We compare the expected number ofsupersymmetric events with the rates corresponding to the expected Glashow Wresonance and to the continuum UHE \nu-N scattering for realistic power-lawspectra. We find that the event rate in the leptonic selectron channel isparticularly promising, and can reach a few tens for a one-year exposure inIceCube. Finally, we note that UHE neutralinos at much higher energies (up tohundreds ZeV) may produce sneutrino resonances by scattering off relicneutrinos in the Local Group hot dark halo. The consequent \tilde{\nu}-burstinto hadronic final states could mimic Z-burst events, although with quitesmaller conversion efficiency.Comment: 23 pages, 4 figures; one reference adde