How many of the observed neutrino events can be described by cosmic ray interactions in the Milky Way?

Cosmic rays diffuse through the interstellar medium and interact with matter and radiations as long as they are trapped in the Galactic magnetic field. The IceCube experiment has detected some TeV-PeV neutrino events whose origin is yet unknown. We study if all or a fraction of these events can be described by the interactions of cosmic rays with matter. We consider the average target density needed to explain them for different halo sizes and shapes, the effect of the chemical composition of the cosmic rays, the impact of the directional information of the neutrino events, and the constraints from gamma-ray bounds and their direction. We do not require knowledge of the cosmic ray escape time or injection for our approach. We find that, given all constraints, at most 0.1 of the observed neutrino events in IceCube can be described by cosmic ray interactions with matter. In addition, we demonstrate that the currently established chemical composition of the cosmic rays contradicts a peak of the neutrino spectrum at PeV energies.