Horizontal Tau air showers from mountains in deep valley. Traces of UHECR neutrino tau

Abstract

Ultra High Energy (UHE) Tau neutrino may lead to a very peculiar imprint in future underground $Km^3$ detectors in water and ice as well as in air: rarest secondary tau tracks and decay which may exceed the muon ones. Indeed Bremsstrahlung at high energy lead to longer tracks for heavier leptons. Radiation lenght grows nearly with the square of the lepton mass. Indeed electrons are too light and their trace in matter (liquid or rock) is negligible (tens of centimeters); muons are much better observed, while tau are too short life time and too short range to be found. However, because relativistic time expansion, UHE tau traces in matter, above $10^{17} eV$, are relativistically boosted overcoming the corresponding muon tracks, already bounded by bremsstrahlung logarithmic regime. The tau crossing for Kms in water or ice may be confused with common muon tracks; their tau decay may be misunderstood as muonic catastrophic bremsstrahlung interactions. To economize UHE tau discovery, we suggest to look the tau decay in air into the deep valleys mountains, like Canyons or deep in excavation mines where horizontal air showers induce fluorescent or Cerenkov lights. The mountain valley width screens from horizontal secondary muons. The valley height increases the solid angle view. The horizontal air Kms-size gap offer a strong discriminator to filter UHE muons against tau. Tens event a year at PeV (W resonance peak) energies in $Km^3$ excavation gap should be observable . Hunting air shower in the night toward high mountains in Canyons or in a deep excavation may be the best and cheapest way to discover UHE neutrinos, either born by electron anti neutrino scattering on electrons at PeV energies, or by direct tau neutrino possibly relic of muonic flavour oscillation even at EeV energies.