Search for sterile neutrinos by shower events at a future neutrino telescope

It is pointed out that searching for sterile neutrinos at high energy regions at a future IceCube-like facility has advantages compared with that of reactor or short baseline accelerator neutrino experiments, in which the size of the detector and energy resolution make it difficult to gain good sensitivity for a large mass-squared difference. In this study we show that it is possible to improve constraints on sterile neutrino mixing $\theta_{14}$ for 1 eV$^2~\lesssim \Delta m_{41}^2\lesssim$ 100 eV$^2$ by looking for a dip in the shower events at an IceCube-like neutrino telescope whose volume is at least 10 times as large as that of IceCube and duration is 10 years. We also give an analytic expression for the oscillation probabilities in two cases where the condition of one mass scale dominance is satisfied.