Neutrino constraints on long-lived heavy dark sector particle decays in the Earth

Recent theoretical work has explored dark matter accumulation in the Earth and its drift toward the center of the Earth that, for the current age of the Earth, does not necessarily result in a concentration of dark matter (χ) in the Earth's core. We consider a scenario of long-lived (τχ∼1028 s), superheavy (mχ=107-1010 GeV) dark matter that decays via χ→ντν¯τ or χ→νμν¯μ. We show that an IceCube-like detector over 10 years can constrain a dark matter density that mirrors the Earth's density or has a uniform density with density fraction ϵρ combined with the partial decay width Bχ→ντν¯τΓχ in the range of (ϵρ/10-10)Bχ→ντΓχ1.5×10-29-1.5×10-28 s-1. For χ→νμν¯μ, mχ=108-1010 GeV, and Eμ>107 GeV, the range of constraints is (ϵρ/10-10)Bχ→νμΓχ3×10-29-7×10-28 s-1.