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Recently, Cohen and Glashow [A.G. Cohen, S.L. Glashow, Phys. Rev. Lett. {\bf107}, 181803 (2011)] pointed out that the superluminal neutrinos reported bythe OPERA would lose their energy rapidly via the Cherenkov-like process. TheCherenkov-like process for the superluminal particles would be forbidden if theprinciple of special relativity holds in any frame instead violated with apreferred frame. We have proposed that the Finslerian special relativity couldaccount for the data of the neutrino superluminality (arXiv:1110.6673[hep-ph]).The Finslerian special relativity preserves the principle of special relativityand involves a preferred direction while consists with the causality. In thispaper, we prove that the energy-momentum conservation is preserved and theenergy-momentum is well defined in Finslerian special relativity. TheCherenkov-like process is forbidden in the Finslerian special relativity. Thus,the superluminal neutrinos would not lose energy in their distant propagation.

Neutrino superluminality without Cherenkov-like processes in Finslerian special relativity