The OPERA collaboration claims that muon neutrinos with a mean energy of 17.5 GeV travel 730 km from CERN to the Gran Sasso at a speed exceeding that of light by about 7.5 km/s or 25 ppm. However, we show that superluminal neutrinos may lose energy rapidly via the bremsstrahlung of electron-positron pairs (ν → ν + e- + e+). For the claimed superluminal velocity and at the stated mean energy, we find that most of the neutrinos would have suffered several pair emissions en route, causing the beam to be depleted of higher energy neutrinos. This presents a significant challenge to the superluminal interpretation of the OPERA data. Furthermore, we appeal to Super-Kamiokande and IceCube data to establish strong new limits on the superluminal propagation of high-energy neutrinos.
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