As suggested by some extensions of the Standard Model of particle physics, dark matter may be a super-weakly interacting lightest stable particle, while the next-to-lightest particle (NLP) is charged and meta-stable. One could test such a possibility with neutrino telescopes, by detecting the charged NLPs produced in high-energy neutrino collisions with Earth matter. We study the production of charged NLPs by both atmospheric and astrophysical neutrinos; only the latter, which is largely uncertain and has not been detected yet, was the focus of previous studies. We compute the resulting fluxes of the charged NLPs, compare those of different origins, and analyze the dependence on the underlying particle physics setup. We point out that even if the astrophysical neutrino flux is very small, atmospheric neutrinos, especially those from the prompt decay of charmed mesons, may provide a detectable flux of NLP pairs at neutrino telescopes such as IceCube. We also comment on the flux of charged NLPs expected from proton-nucleon collisions, and show that, for theoretically motivated and phenomenologically viable models, it is typically sub-dominant and below detectable rates.
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