Heavy-neutrino decays at neutrino telescopes

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It has been recently proposed that a sterile neutrino νₕ of mass mₕ=40--80 MeV, mixing |Uμₕ|²=10⁻³--10⁻², lifetime τₕ 10⁻⁹ s, and a dominant decay mode (νₕ → νμγ) could be the origin of the experimental anomalies observed at LSND, KARMEN and MiniBooNE. Such a particle would be abundant inside air showers, as it can be produced in kaon decays (K -> νₕ μ, Kₗ -> νₕ πμ). We use the Z-moment method to evaluate its atmospheric flux and the frequency of its decays inside neutrino telescopes. We show that the νₕ would imply around 10⁴ contained showers per year inside a 0.03 km³ telescope like ANTARES or the DeepCore in IceCube. These events would have a characteristic energy and zenith-angle distribution (Eν= 0.1--10 TeV and θ< 90ᵒ), which results from a balance between the reach of the heavy neutrino (that disfavors low energies) and a sizeable production rate and decay probability. The standard background from contained neutrino events (νₑ N → e X and neutral-current interactions of high inelasticity) is 100 times smaller. Therefore, although it may be challenging from an experimental point of view, a search at ANTARES and IceCube could confirm this heavy-neutrino possibility.