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 ( p̅ ≈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 (p̅ ℓ_P)L/c≈10⁴ s. To next order in p̅ ℓ_P, the correction has the form of the Gambini and Pullin effect for photons. A dependence L_os^-1∝p̅ ²ℓ_P is found for a two-flavor neutrino oscillation length.