Probes of Lorentz violation in neutrino propagation

It has been suggested that the interactions of energetic particles with the foamy structure of space-time thought to be generated by quantum-gravitational (QG) effects might violate Lorentz invariance, so that they do not propagate at a universal speed of light. We consider the limits that may be set on a linear or quadratic violation of Lorentz invariance in the propagation of energetic neutrinos, v/c=[1±(E/M_νQG1)] or [1±(E/M_νQG2)²], using data from supernova explosions and the OPERA long-baseline neutrino experiment. Using the SN1987a neutrino data from the Kamioka II, IMB, and Baksan experiments, we set the limits M_νQG1>2.7(2.5)×10¹⁰ GeV for subluminal (superluminal) propagation and M_νQG2>4.6(4.1)×10⁴ GeV at the 95% confidence level. A future galactic supernova at a distance of 10 kpc would have sensitivity to M_νQG1>2(4)×10¹¹ GeV for subluminal (superluminal) propagation and M_νQG2>2(4)×10⁵ GeV. With the current CERN neutrinos to Gran Sasso extraction spill length of 10.5 μs and with standard clock synchronization techniques, the sensitivity of the OPERA experiment would reach M_νQG1~7×10⁵ GeV (M_νQG2~8×10³ GeV) after 5 years of nominal running. If the time structure of the super proton synchrotron radio frequency bunches within the extracted CERN neutrinos to Gran Sasso spills could be exploited, these figures would be significantly improved to M_νQG1~5×10⁷ GeV (M_νQG2~4×10⁴ GeV). These results can be improved further if a similar time resolution can be achieved with neutrino events occurring in the rock upstream of the OPERA detector: we find potential sensitivities to M_νQG1~4×10⁸ GeV and M_νQG2~7×10⁵ GeV.