Discovering Ultra High Energy Neutrinos by Horizontal and Upward tau Air-Showers: First evidences in Terrestrial Gamma Flashes

Ultra high energy (UHE) neutrinos and anti-neutrino tau and anti-neutrino electron at PeVs and higher energy may induce tau air-showers whose detectability is million to billion times amplified by their secondaries. We considered UHE neutrino tau and UHE anti-neutrino electron interactions beyond mountains as a source of such horizontal amplified tau air-showers. We also consider upward UHE neutrino-N interaction on Earth crust at horizont and their UHE tau air-showers beaming toward high mountains gamma detectors.We show their detectability. We notice that such rare upward tau air-shower may hit even nearby satellite and flash them by short diluted gamma-burst at the edge of Gamma Ray Observatory detection threshold. We identify these events with recent (1994) discovered (BATSE) Terrestrial Gamma Flashes and we claim their probable UHE tau and UHE neutrino tau origin. From these data approximated UHE neutrino flux and $\Delta m_{\nu_\mu \nu_\tau}$ lower bound are derived. Known $X-\gamma-\mathrm{TeV}$ active galactic and extragalactic sources have been identified in most TGF arrival directions. Partial TGF Galactic signature is also manifest.