The origins of the extraterrestrial neutrinos observed in IceCube have yet to be determined. In this study we perform a one-point fluctuation analysis of the six-year high-energy starting event (HESE) shower data, with fixed non-Poissonian contributions from atmospheric, Galactic and some extragalactic components, as well as an isotropic (and weakly non-Poissonian) template. In addition to the star-forming galaxies and blazars, our analysis suggests the presence of an additional isotropic component, not associated with any known class of sources, with best-fit intensity of $(2.8\pm0.2)\times 10^{-18}\,(E/100~{\rm TeV})^{-2.7\pm 0.5}$ ${\mathrm{cm}^{-2}\, \mathrm{s}^{-1}\,\mathrm{sr}^{-1}\,\mathrm{GeV}^{-1}}$. For the first time, we also consider high-energy extrapolations of several phenomenological models for the diffuse Galactic emission (tuned to both local cosmic-ray data and diffuse gamma-ray emission in the GeV-TeV domain). We demonstrate the potential of our framework in discriminating between different scenarios, with possible implications on the physics of cosmic ray transport in the TeV-PeV range.
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