Directly search for Ultra-High Energy WIMPs at IceCube

I study the possibility of directly detecting Ultra-high energy (UHE from now on) WIMPs by the IceCube experiment, via the WIMPs interaction with the nuclei in the ice. I evaluate galactic and extragalactic UHE WIMP and astrophysical and atmospheric neutrino event rates at energy range of 10 TeV - 10 PeV. I assume UHE WIMPs $\chi$ are only from the decay of superheavy dark matter $\phi$, that is $\phi\to\chi\bar{\chi}$. If the lifetime of superheavy dark matter $\tau_{\phi}$ is taken to be $5\times10^{21}$s, WIMPs can be detected at energies above O(40-100)TeV in this detection. Since UHE WIMP fluxes are actually depended on $\tau_{\phi}$, if superheavy dark matter can decay to standard model particles (that is $\tau_{\phi}$ is constrained to be larger than O($10^{26}$-$10^{29}$)s), UHE WIMPs could not be detected by IceCube.