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Neutrino superluminality without Cherenkov-like processes in Finslerian special relativity
Recently, Cohen and Glashow [A.G. Cohen, S.L. Glashow, Phys. Rev. Lett. {\bf
107}, 181803 (2011)] pointed out that the superluminal neutrinos reported by
the OPERA would lose their energy rapidly via the Cherenkov-like process. The
Cherenkov-like process for the superluminal particles would be forbidden if the
principle of special relativity holds in any frame instead violated with a
preferred frame. We have proposed that the Finslerian special relativity could
account for the data of the neutrino superluminality (arXiv:1110.6673[hep-ph]).
The Finslerian special relativity preserves the principle of special relativity
and involves a preferred direction while consists with the causality. In this
paper, we prove that the energy-momentum conservation is preserved and the
energy-momentum is well defined in Finslerian special relativity. The
Cherenkov-like process is forbidden in the Finslerian special relativity. Thus,
the superluminal neutrinos would not lose energy in their distant propagation.Comment: 9 pages, no figure. Version for publication in PL
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