Probing superheavy dark matter through lunar radio observations of ultrahigh-energy neutrinos and the impacts of neutrino cascades

Ultrahigh-energy neutrinos (UHE$\nu$s) can be used as a valuable probe of superheavy dark matter above $\sim 10^9$ GeV, the latter being difficult to probe with collider and direct detection experiments due to the feebly interacting nature. Searching for radio emissions originating from the interaction of UHE$\nu$s with the lunar regolith enables us to explore energies beyond $10^{12}$ GeV, which astrophysical accelerators cannot achieve. Taking into account the interaction of UHE$\nu$s with the cosmic neutrino background and resulting standard neutrino cascades to calculate the neutrino flux on Earth, for the first time, we investigate sensitivities of such lunar radio observations to very heavy dark matter. We also examine the impacts of cosmogenic neutrinos that have the astrophysical origin. We show that the proposed ultra-long wavelength lunar radio telescope, as well as the existing low-frequency array, can provide the most stringent constraints on decaying or annihilating superheavy dark matter with masses at $\gtrsim 10^{12}$ GeV. The limits are complementary to or even stronger than those from other UHE$\nu$ detectors, such as the IceCube-Gen2 radio array and GRAND.