Constraints and tests of the OPERA superluminal neutrinos

The superluminal neutrinos detected by OPERA indicate Lorentz invariance violation (LIV) of the neutrino sector at the order of 10(-5). We study the implications of the result in this work. We find that such a large LIV implied by OPERA data will make the neutrino production process π → μ + ν(μ) kinematically forbidden for a neutrino energy greater than about 5 GeV. The OPERA detection of neutrinos at 40 GeV can constrain the LIV parameter to be smaller than 3×10(-7). Furthermore, the neutrino decay in the LIV framework will modify the neutrino spectrum greatly. The atmospheric neutrino spectrum measured by the IceCube Collaboration can constrain the LIV parameter to the level of 10(-12). The future detection of astrophysical neutrinos of galactic sources is expected to be able to give an even stronger constraint on the LIV parameter of neutrinos.