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

Ultra high energy neutrinos UHE $\nu_{\tau}$, $\bar\nu_{\tau}$ and $\bar{\nu}_e$ at PeV and higher energy may induce $\tau$ air-showers whose detectability is million to billion times amplified by their secondaries. We considered UHE $\nu_{\tau} N$ and UHE $\bar\nu_{e} e$ interactions beyond mountains as a source of such horizontal amplified $\tau$ air-showers. We also consider upward UHE $\nu_{\tau} N$ 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 $\tau$ - UHE $\nu_\tau$ origin. From these first data approximated UHE $\nu_\tau$ 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.