A consistent theory of decaying Dark Matter connecting IceCube to the Sesame Street

The high energy events observed at the IceCube Neutrino Observatory have triggered many investigations interpreting the highly energetic neutrinos detected as decay products of heavy unstable Dark Matter particles. However, while very detailed treatments of the IceCube phenomenology exist, only a few references focus on the (non-trivial) Dark Matter production part - and all of those rely on relatively complicated new models which are not always testable directly. We instead investigate two of the most minimal scenarios possible, where the operator responsible for the IceCube events is directly involved in Dark Matter production. We show that the simplest (four-dimensional) operator is not powerful enough to accommodate all constraints. A more non-minimal setting (at mass dimension six), however, can do both fitting all the data and also allowing for a comparatively small parameter space only, parts of which can be in reach of future observations. We conclude that minimalistic approaches can be enough to explain all data required, while complicated new physics seems not to be required by IceCube.