Lorentz invariance violation and Ice Cube neutrino events

The Ice Cube neutrino spectrum shows a flux which falls of as E-2 for sub PeV energies but there are no neutrino events observed above 3 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 cutoff in neutrino energy can be chosen to be between 2 and 6.3 PeV. We assume that neutrinos (antineutrinos) have a dispersion relation E-2 = p(2) - (xi(3)/M-P1) p(3), and find that both pi(+) and pi(-) decays are suppressed at neutrino energies of order of few PeV. We find that the mu(-) decay being a two-neutrino process is enhanced, whereas mu(+) decay is suppressed. The K+ -> pi(0)e(+)nu(e) is also suppressed with a cutoff neutrino energy of same order of magnitude, whereas K- -> pi(0)e(+)(nu) over bar (e), is enhanced. The n -> p(+)e(-)nu(e), decay is suppressed (while the n -> p(-)e(+)nu(e) is enhanced). This means that the (nu) over bar (e), expected from n decay arising from p + gamma -> Delta -> pi(+)n reaction will not be seen. This can explain the lack of Glashow resonance events at IceCube. 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.