Lorentz invariance violation and icecube neutrino events

The IceCube neutrino spectrum shows a flux which falls of as E−2 for sub PeV energies but there are no neutrino events observed above 2 PeV. In particular the Glashow resonance expected at 6.3 PeV is not seen. We examine a Planck scale Lorentz violation as a mechanism for explaining the cutoff of observed neutrino energies around a few PeV. By choosing the one free parameter the cut-off in neutrino energy can be chosen to be between 2 and 6.3 PeV. We assume that neutrinos have a dispersion relation E2=p2−(ξ3/MPl) p3, and find that even when neutrinos are subluminal the pion decay is suppressed at neutrino energies of order of few PeV. We find that the muon decay being a two-neutrino process is enhanced. The K−→π0e−ν¯e is also suppressed with a cut-off neutrino energy of same order of magnitude. If no Glashow resonance events are seen in the future then the Lorentz violation can be a viable explanation for the IceCube observations at PeV energies.