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 l_P, a spin-1/2 field in flat spacetime. The discrete structure of spacetime at l_P yields corrections to the field propagation at scale L. Neutrino bursts ( p¯~10⁵ 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 \(p¯l_P\)L/c~10⁴ s. To next order in p¯l_P, the correction has the form of the Gambini and Pullin effect for photons. A dependence L^-1_os~p¯²l_P is found for a two-flavor neutrino oscillation length.