  The OPERA collaboration has claimed the discovery of supeluminal neutrino
propagation. However the superluminal interpretation of the OPERA result was
refuted by Cohen and Glashow because it was shown that such superluminal
neutrinos would lose energy rapidly via the bremsstrahlung of electron-positron
pairs (arXiv:1109.6562). We note that the superluminal interpretation is still
possible if there exists a new (dark) neutrino which can propagate with a
superluminal velocity and which couples with usual neutrinos only via the mass
mixing leading to neutrino oscillations. It is supposed that the physical laws
are invariant under rotations and translations in a preferred reference frame.
Two possible pictures to parameterize departures from Lorentz invariance are
discussed: a "conventional" tachyonic dark neutrino and the modification of the
Lagrangian by adding perturbations with the maximum attainable speed of the
dark neutrino which is larger than the speed of light in vacuum. We analyze
also the MINOS and SN1987a data and show that they are consistent with the
conjecture that there exists the superluminal dark neutrino.
