Coherent Propagation of PeV Neutrinos and the Dip in the Neutrino Spectrum at IceCube

The energy spectrum of high-energy neutrinos reported by the IceCube collaboration shows a dip between 400 TeV and 1 PeV. One intriguing explanation is that high-energy neutrinos scatter with the cosmic neutrino background through a $\sim$ MeV mediator. Taking the density matrix approach, we develop a formalism to study the propagation of PeV neutrinos in the presence of the new neutrino interaction. If the interaction is flavored such as the gauged $L_\mu-L_\tau$ model we consider, the resonant collision may not suppress the PeV neutrino flux completely. The new force mediator may also contribute to the number of effectively massless degrees of freedom in the early universe and change the diffusion time of neutrinos from the supernova core. Astrophysical observations such as Big Bang Nucleosynthesis and supernova cooling provide an interesting test for the explanation.