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 P, a spin-1/2 field in flat spacetime. The discrete structure of spacetime at P yields corrections to the field propagation at scale L. Neutrino bursts ( p̄≈10⁵0ex0exGeV) 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 (p̄P)L/c≈10⁴0ex0exs. To next order in p̄P, the correction has the form of the Gambini and Pullin effect for photons. A dependence Lₒₛ^-1∝p̄²P is found for a two-flavor neutrino oscillation length.