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OPERA has claimed the discovery of superluminal propagation of neutrinos. Weanalyze the consistency of this claim with previous tests of specialrelativity. We find that reconciling the OPERA measurement with informationfrom SN1987a and from neutrino oscillations requires stringent conditions. Thesuperluminal limit velocity of neutrinos must be nearly flavor independent,must decrease steeply in the low-energy domain, and its energy dependence mustdepart from a simple power law. We construct illustrative models that satisfythese conditions, by introducing Lorentz violation in a sector with lightsterile neutrinos. We point out that, quite generically, electroweak quantumcorrections transfer the information of superluminal neutrino properties intoLorentz violations in the electron and muon sector, in apparent conflict withexperimental data.

Interpreting OPERA results on superluminal neutrino