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Two of the key unresolved issues facing Standard Model physics are (i) theappearance of a small but non-zero neutrino mass, and, (ii) the missing massproblem in the Universe. The focus of this paper is a previously proposed lowenergy effective theory that couples a dark scalar to Standard Model neutrinos.This provides a stable dark matter candidate as well as radiatively generatinga neutrino mass. Within this framework we will then construct an entirely newbound from the IceCube-170922A event which takes into account (i) the possibleneutrino mass hierarchies, (ii) the effect of cosmological redshift on e.g. thenumber density of cosmic neutrino background neutrinos, and, (iii) thenon-degeneracy of neutrino mass and flavour eigenstates. This builds on work byKelly and Machado (2018), where the authors placed new constraints onneutrinophilic and axion dark matter models. At low mediator masses, we find animprovement of an order of magnitude on current constraints from kaon decays.The constraint is complimentary (and slightly weaker) than current constraintsfrom Big Bang Nucleosynthesis and the Cosmic Microwave Background. We explorehow future higher energy events could improve this bound.

Linking Scalar Dark Matter and Neutrino Masses with IceCube 170922A