quickly. The angular distribution of the events suggests that most, if not all, of them are extragalactic in origin. Compared to the SN 1987A neutrinos, the IceCube neutrinos have a much longer baseline through the C$\nu$B, making them more sensitive to $\nu$SI; they have much higher energies, making them more powerful probes for massive mediators; and they have a diffuse (many-source) origin, thus averaging out the uncertainties for individual sources.

We take advantage of this new opportunity and explore the sensitivity of IceCube to $\nu$SI. With minimal assumptions about the interaction to reduce model dependence, we show that there are regions of parameter space where $\nu$SI could cause significant distortions to the neutrino spectrum. Because the flux is diffuse and the shape and normalization without interactions are not known, we must look for distortions to the spectrum that have characteristic shapes. This favors interactions with strong energy dependence, especially due to a resonance.

Our method generalizes earlier work, going beyond the pure attenuation considered in KT87 and Refs. [@Keranen:1997gz; @Hooper:2007jr] as well as the simplified treatment of regeneration considered in Refs. [@Goldberg:2005yw; @Baker:2006gm]. We improve upon these by using the propagation equation to describe the interaction of a neutrino beam 