Do high-energy neutrinos travel faster than photons in a discrete space-time?

The recent OPERA measurement of high-energy neutrino velocity, once independently verified, implies new physics in the neutrino sector. We revisit the theoretical inconsistency of the fundamental high-energy cutoff attributing to quantum gravity with the parity-violating gauge symmetry of local quantum field theory describing neutrinos. This inconsistency suggests high-dimension operators of neutrino interactions. Based on these studies, we try to view the OPERA result, high-energy neutrino oscillations and indicate to observe the restoration of parity conservation by measuring the asymmetry of high-energy neutrinos colliding with left- and right-handed polarized electrons.