It has been speculated that Lorentz-invariance violation (LIV) might be generated by quantum-gravity (QG) effects. As a consequence, particles may not travel at the universal speed of light. In particular, superluminal extragalactic neutrinos would rapidly lose energy via the bremssthralung of electron-positron pairs ($\nu \to \nu e^{+}{e}^{-}$), damping their initial energy into electromagnetic cascades, a figure constrained by Fermi-Large Area Telescope data. We show that the two cascade neutrino events with energies around 1 PeV recently detected by IceCube—if attributed to extragalactic diffuse events, as it appears likely—can place the strongest bound on LIV in the neutrino sector, namely, $\delta =(v^2-1)<\mathcal{O}({10}^{-18})$, corresponding to a QG scale $M_{\mathrm{QG}}\gtrsim {10}^5{M}_{\mathrm{Pl}}$ ($M_{\mathrm{QG}}\gtrsim {10}^{-4}{M}_{\mathrm{Pl}}$) for a linear (quadratic) LIV, at least for models inducing superluminal neutrino effects ($\delta >0$).

• Received 28 March 2013

DOI:https://doi.org/10.1103/PhysRevD.87.116009