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.
