On the rationality of the OPERA experiment as a signal of Lorentz violation

We show that the superluminal muon neutrinos in the recent OPERA experiment can exist theoretically. The refutation of the OPERA experiment from some theoretical arguments is not universally valid, but resulting from some implicit assumptions. Our argument can accommodate both the OPERA experiment for superluminal neutrinos and the ICARUS experiment of no evidence for the analogues Cherenkov radiation of muon neutrinos from CERN to the LNGS.