Measurement of TeV dark particles due to decay of heavy dark matter in the earth core at IceCube

In an alternative dark matter scenario, it is assumed that there exist two species of dark matter: a heavy dark matter particle (HDM) with the mass of O(TeV) which is generated in early universe and a lighter dark matter particle (LDM) which is a relativistic product due to the decay of HDM. HDMs, captured by the earth, decay to high energy LDMs, and these particles can be measured by km${}^3$ neutrino telescopes, like the IceCube detector. In the present paper, a $Z^{\prime }$ portal dark matter model is taken for LDMs to interact with nuclei via a neutral current interaction mediated by a heavy gauge boson $Z^{\prime }$. With the different lifetimes of decay of HDMs and Z${}^{\prime }$ masses, the event rates of expected LDMs and neutrinos were evaluated at IceCube in the energy range between 1 TeV and 100 TeV. According to the IceCube data, the upper limit for LDM fluxes was estimated at 90% C.L. at IceCube. With $m_{Z^{\prime }}\lesssim 250GeV$ and ${\tau }_{\varphi }\lesssim 10^{20}$ s, finally, it is proved that LDMs could be directly measured in the energy range between O(1TeV) and O(10TeV) at IceCube.