Ultra High Energy Cosmic Rays, Z-Shower and Neutrino Astronomy by Horizontal-Upward Tau Air-Showers.

Ultra High Cosmic Rays (UHECR) Astronomy may be correlated to a primary parental Neutrino Astronomy: indeed any far BL Lac Jet or GRB, sources of UHECR, located at cosmic edges, may send its signal, overcoming the severe GZK cut-off, by help of UHE ZeV energetic neutrino primary. These UHE neutrino scattering on relic light ones (spread on wide Hot Local Groups Halos) maybe fine-tuned : E_(nu) =(M_Z)^2/m_(nu) = 4 10^(22) eV *((0.1eV)/m_(nu)), to combine at once the observed light neutrino masses and the UHECR spectra, leading to a relativistic Z-Shower in Hot Dark Halos (e few tens Mpc wide) whose final nuclear component traces the UHECR event on Earth. Therefore UHECR (with no longer volme GZK constrains) may point to far BL Lac sources. This Z-Burst (Z-Shower) model calls for large neutrino fluxes. Even if Nature do not follow the present Z-model, UHECR while being cut-off by Big Bang Radiation, must produce a minimal UHE neutrino flux, the GZK neutrino secondaries. For both reasons such UHE Neutrino Astronomy must be tested on Earth. Lowest High Energy Astronomy is searched by AMANDA, ANTARES underground deterctors by muons tracks. We suggest a complementary higher energy Neutrino Tau Astronomy inducing Horizontal and Upward Tau AirShowers. Possible early evidence of such a New Neutrino UPTAUs (Upward Tau Showers at PeVs energies) Astronomy may be in BATSE records of Upward Terrestrial Gamma Flashes. Future signals must be found in detectors as EUSO, seeking Upward-Horizontal events: indeed even minimal, guaranteed, GZK neutrino fluxes may be better observed if EUSO threshold reaches 10^(19) eV by enlarging its telescope size.