We present a detailed analysis of the neutrino-induced muon signals coming from neutralino pair annihilations inside the Sun and the Earth with particular emphasis for light neutralinos. The theoretical model considered is an effective minimal supersymmetric extension of the standard model without gaugino-mass unification, which allows neutralinos of light masses (below 50 GeV). The muon events are divided into through-going and stopping muons, using the geometry of the Super-Kamiokande detector. In the evaluation of the signals, we take into account the relevant hadronic and astrophysics uncertainties and include neutrino oscillation and propagation properties in a consistent way. We derive the ranges of neutralino masses which could be explored at neutrino telescopes with a low muon-energy threshold (around 1 GeV) depending on the category of events and on the values of the various astrophysics and particle-physics parameters. A final analysis is focused on the upward muon fluxes which could be generated by those neutralino configurations which are able to explain the annual modulation data of the DAMA/LIBRA experiment. We show how combining these data with measurements at neutrino telescopes could help in pinning down the features of the dark matter particle and in restraining the ranges of the many quantities (of astrophysics and particle-physics origins) which enter in the evaluations and still suffer from large uncertainties.
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