Quantum Gravity Corrections to Neutrino Propagation

Massive spin-1/2 fields are studied in the framework of loop quantum gravity by considering a state approximating, at a length scale L much greater than Planck length ₏, a spin-1/2 field in flat spacetime. The discrete structure of spacetime at ₏ yields corrections to the field propagation at scale L. Neutrino bursts (p10^50ex{0ex}GeV) accompanying gamma ray bursts that have traveled cosmological distances L are considered. The dominant correction is helicity independent and leads to a time delay of order (p₏) L/c10^40ex{0ex}s. To next order in p₏, the correction has the form of the Gambini and Pullin effect for photons. A dependence L₎ₒ^-1p^2₏ is found for a two-flavor neutrino oscillation length.