Supernova neutrinos: Earth matter effects and neutrino mass spectrum

We perform a detailed study of the Earth matter effects on supernova neutri nos. The dependences of these effects on the properties of the original neu trino fluxes, on the trajectory of the neutrinos inside the Earth and on th e oscillation parameters are described. We show that, for a large fraction (similar to 60%) of the possible arrival times of the signal, the neutrino flux crosses a substantial amount of the matter of the Earth at least for o ne of the existing detectors. For oscillation parameters from the LMA solut ion of the solar neutrino problem the Earth matter effect consists in an os cillatory modulation of the <(<upsilon>)over bar>(e) and/or upsilon (e) ene rgy spectra. The relative deviation with respect to the undistorted spectra can be as large as 20-30% for E greater than or similar to 20 MeV and 70-1 00% for E greater than or similar to 40 MeV. For parameters from the SMA an d LOW solutions the effect is localized at low energies (E less than or sim ilar to MeV) and is not larger than similar to 10%. The Earth matter effect s can be revealed (i) by the observation of oscillatory distortions of the energy spectra in a single experiment and (ii) by the comparison between th e spectra at different detectors. For a supernova at distance D = 10 Kpc, c omparing the results of SuperKamiokande (SK), SNO and LVD experiments one c an establish the effect at (2-3)sigma level, whereas larger statistical sig nificance ((4-5)sigma) is obtained if two experiments of SK-size or larger are available. Studies of the Earth matter effect will select or confirm th e solution of the solar neutrino problem, probe the mixing U-e3 and identif y the hierarchy of the neutrino mass spectrum. (C) 2001 Published by Elsevi er Science B.V.