Measurement of Milli-Charged Particles with a moderately large cross section from the Earth's core at IceCube

It is assumed that heavy dark matter $\phi$ with O(TeV) mass captured by the Earth may decay to relativistic light milli-charged particles (MCPs). These MCPs could be measured by the IceCube neutrino telescope. The massless hidden photon model was taken for MCPs to interact with nuclei, so that the numbers and fluxes of expected MCPs may be evaluated at IceCube. Meanwhile, the numbers of expected neutrino background events were also evaluated at IceCube. Based on the assumption that no events are observed at IceCube in 10 years, the corresponding upper limits on MCP fluxes were calculated at 90\% C. L.. These results indicated that the MCPs from the Earth's core could be directly detected at O(1TeV) energies at IceCube when $2\times10^{-5}\lesssim\epsilon^2\lesssim4.5\times10^{-3}$. And a new region of 100 MeV < $m_{MCP}$ < 10 GeV and $4.47\times10^{-3}$ $\lesssim$ $\epsilon$ $\lesssim$ $9.41\times10^{-2}$ is ruled out in the $m_{MCP}$-$\epsilon$ plane with 10 years of IceCube data.