Neutrino constraints on long-lived heavy dark sector particle decays

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 (chi) in the Earth's core. We consider a scenario of long-lived (tau chi similar to 1028 s), superheavy (m chi = 107-1010 GeV) dark matter that decays via chi -> nu tau nu over bar tau or chi -> nu mu nu over bar mu. 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 epsilon rho combined with the partial decay width B chi ->nu tau nu over bar tau Gamma chi in the range of (epsilon rho/10-10)B chi ->nu tau Gamma chi less than or similar to 1.5 x 10-29-1.5 x 10-28 s-1. For chi -> nu mu nu over bar mu, m chi = 108-1010 GeV, and E mu > 107 GeV, the range of constraints is (epsilon rho/10-10)B chi ->nu mu Gamma chi less than or similar to 3 x 10-29-7 x 10-28 s-1.