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Probing the coupling of heavy dark matter to nucleons by detecting neutrino signature from the Earth's core

We argue that the detection of neutrino signature from the Earth's core can effectively probe the coupling of heavy dark matter ($m_χ>10^{4}$ GeV) to nucleons. We first note that direct searches for dark matter (DM) in such a mass range provide much less stringent constraint than the constraint provided by such searches for $m_χ\sim 100$ GeV. Furthermore the energies of neutrinos arising from DM annihilation inside the Sun cannot exceed a few TeVs at the Sun surface due to the attenuation effect. Therefore the sensitivity to the heavy DM coupling is lost. Finally, the detection of neutrino signature from galactic halo can only probe DM annihilation cross sections. We present neutrino event rates in IceCube and KM3NeT arising from the neutrino flux produced by annihilation of Earth-captured DM heavier than $10^{4}$ GeV. The IceCube and KM3NeT sensitivities to spin independent DM-proton scattering cross section $σ_{χp}$ in this mass range are presented for both isospin symmetric and isospin violating cases.