  The superluminal behaviors of neutrinos were reported by the OPERA
collaboration recently. It was also noticed by Cohen and Glashow that, in
standard quantum field theory, the superluminal neutrinos would lose their
energy via the Cherenkov-like process rapidly. Finslerian special relativity
may provide a framework to cooperate with the OPERA neutrino superluminality
without Cherenkov-like process. We present clearly the symmetry, causal
structure and superluminality in Finsler spacetime. The principle of relativity
and the causal law are preserved. The energy and momentum are well defined and
conserved in Finslerian special relativity. The Cherenkov-like process is
proved to be forbidden kinematically and the superluminal neutrinos would not
lose energy in their distant propagations from CERN to the Gran Sasso
Laboratory. The energy dependence of neutrino superluminality is studied based
on the reported data of the OPERA collaboration as well as other groups.
