Detection of ultra-high energy neutrinos will be useful for unraveling the dynamics of the most violent sources in the cosmos and for revealing the neutrino cross-section at extreme energy .
If there exists a Greisen-Zatsepin-Kuz ’ min ( GZK ) suppression of cosmic-ray events above E _ { GZK } \sim 5 \times 10 ^ { 19 } eV , as predicted by theory , then the only messengers of energies beyond E _ { GZK } are neutrinos .
Cosmic neutrino fluxes can initiate air-showers through interaction in the atmosphere , or in the Earth .
Neutrino trajectories will be downgoing to nearly horizontal in the former case , and “ Earth-skimming ” in the latter case .
Thus it is important to know the acceptances ( event rate/flux ) of proposed air-shower experiments for detecting both types of neutrino-initiated events .
We calculate these acceptances for fluorescence detectors , both space-based as with the EUSO and OWL proposals , and ground-based , as with Auger , HiRes and Telescope Array .
The neutrino cross-section \sigma ^ { CC } _ { \nu N } is unknown at energies above 5.2 \times 10 ^ { 13 } eV .
Although the popular QCD extrapolation of lower-energy physics offers the cross-section value of 0.54 \times 10 ^ { -31 } ( E _ { \nu } / 10 ^ { 20 } { eV } ) ^ { 0.36 } { cm } ^ { 2 } , new physics could raise or lower this value .
Therefore , we present the acceptances of horizontal ( HAS ) and upgoing ( UAS ) air showers as a function of \sigma ^ { CC } _ { \nu N } over the range 10 ^ { -34 } to 10 ^ { -30 } cm ^ { 2 } .
The dependences of acceptances on neutrino energy , shower-threshold energy , shower length , and shower column density are also studied .
We introduce a cloud layer , and study its effect on rates as viewed from space and from the ground .
For UAS , we present acceptances for events over land ( rock ) , and over the ocean ( water ) .
Acceptances over water are larger by about an order of magnitude , thus favoring space-based detectors .
We revisit the idea of Ref . ( ( 1 ) ) to infer \sigma ^ { CC } _ { \nu N } at E _ { \nu } \mathrel { \vbox { \hbox { $ > $ } \nointerlineskip \hbox { $ \sim$ } } } 10 ^ { 20 } from the ratio of HAS-to-UAS events , and obtain favorable results .
Included in our UAS calculations are realistic energy-losses for taus , and Earth-curvature effects .
Most of our calculation is analytic , allowing insight into the various subprocesses that collectively turn an incident neutrino into an observable shower .