Neutrino superluminality without Cherenkov-like processes in Finslerian special relativity

TL;DR

This paper demonstrates that Finslerian special relativity can explain superluminal neutrinos without energy loss via Cherenkov-like processes, preserving causality and the principle of relativity.

Contribution

It introduces Finslerian special relativity as a framework that allows superluminal neutrinos without Cherenkov-like energy loss, maintaining energy-momentum conservation.

Findings

Cherenkov-like process is forbidden in Finslerian special relativity.

Energy-momentum conservation is preserved in this framework.

Superluminal neutrinos do not lose energy during propagation.

Abstract

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.