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/MνQG1)] or [1± (E/MνQG2)], 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 MνQG1 > 2.7(2.5)× 10 GeV for subluminal (superluminal) propagation, respectively, and MνQG2 > 4.6(4.1) × 10 GeV at the 95 % confidence level. A future galactic supernova at a distance of 10 kpc would have sensitivity to MνQG1 > 2(4) × 10 GeV for subluminal (superluminal) propagation, respectively, and MνQG2 > 2(4) × 10 GeV. With the current CNGS extraction spill length of 10.5 μs and with standard clock synchronization techniques, the sensitivity of the OPERA experiment would reach MνQG1 ∼ 7 × 10 GeV (MνQG2 ∼ 8× 10 GeV) after 5 years of nominal running. If the time structure of the SPS RF bunches within the extracted CNGS spills could be exploited, these figures would be significantly improved to MνQG1 ∼ 5× 10 GeV (MνQG2 ∼ 4× 10 GeV). These results can be improved further if similar time resolution can be achieved with neutrino events occurring in the rock upstream of the OPERA detector: we find potential sensitivities to MνQG1 ∼ 4× 10 GeV and MνQG2 ∼ 7× 10 GeV.