The role of \nu_{\tau} ultrahigh energy astrophysics in Km^3 detectors

Abstract

We show that the expected ${\nu }_{\tau }$ signals, by their secondary tau tracks, in Km^3 detectors at highest cosmic ray energy window $1.7\cdot 10^{21}eV>E_{\tau }>1.6x10^{17}eV$, must overcome the corresponding ${\nu }_{\mu }$ (or muonic) ones. Indeed, the Lorentz-boosted tau range length grows (linearly) above muon range, for $E_{\tau }\text{RAISE}1.6x10^{8}GeV$ and reaches its maxima extension, $R_{{\tau }_{\max }}\simeq 191km$, at energy $E_{\tau }\simeq 3.8x10^{9}GeV$. At this peak the tau range is nearly 20 times the corresponding muon range (at the same energy) implying a similar ratio in ${\nu }_{\tau }$ over ${\nu }_{\mu }$ detectability. This dominance, however may lead (at present most abundant ${\nu }_{\tau }$ model fluxes) to just a rare spectacular event a year (if flavor mixing occurs). Lower energetic $\tau$ and ${\nu }_{\tau }$ signals $({\bar{\nu }}_{e}e\to {\bar{\nu }}_{\tau }\tau ,{\nu }_{\tau }N\to ...)$ at energy range ($10^5÷10^{7}GeV$) may be more easily observed in km^3 detectors at a rate of a few $({\bar{\nu }}_{e}e\to {\bar{\nu }}_{\tau }\tau )$ to tens event $({\nu }_{\tau }N\to \tau +$ anything) a year.

Comments: 14 pages LaTex, 1 postscript figure