Probing a Four Flavour vis-a-vis Three Flavour Neutrino Mixing for UHE Neutrino Signals at a 1 ${\mathrm{K}\mathrm{m}}^2$ Detector

We consider a four flavour scenario for the neutrinos where an extra sterile neutrino is introduced with the three families of active neutrinos and study the deviation from three flavour scenario in the ultra high energy (UHE) regime. We calculate the possible muon and shower yields at a 1 Km${}^2$ detector such as ICECUBE for these neutrinos from distant UHE sources namely Gamma Ray Bursts (GRBs) etc. Similar estimations for muon and shower yields are also obtained for three flavour case. Comparing the two results we find considerable differences of the yields for these two cases. This can be useful for probing the existence of a fourth sterile component using UHE neutrino flux.