Constraints on metastable superheavy dark matter coupled to sterile neutrinos with the Pierre Auger Observatory

Dark matter particles could be superheavy, provided their lifetime is much longer than the age of the universe. Using the sensitivity of the Pierre Auger Observatory to ultra-high energy neutrinos and photons, we constrain a specific extension of the Standard Model of particle physics that meets the lifetime requirement for a superheavy particle by coupling it to a sector of ultra-light sterile neutrinos. Our results show that, for a typical dark coupling constant of 0.1, the mixing angle $\theta_m$ between active and sterile neutrinos must satisfy, roughly, $\theta_m \lesssim 1.5\times 10^{-6}(M_X/10^9~\mathrm{GeV})^{-2}$ for a mass $M_X$ of the dark-matter particle between $10^8$ and $10^{11}~$GeV.