Quantum Gravity Corrections to Neutrino Propagation

Abstract

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 ${\ell }_P$, a spin-1/2 field in flat spacetime. The discrete structure of spacetime at ${\ell }_P$ yields corrections to the field propagation at scale $L$. Neutrino bursts ( $\overline{p}\approx {10}^5\mathrm{GeV}$) 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 $\left(\overline{p}{\ell }_P\right)L/c\approx {10}^4\mathrm{s}$. To next order in $\overline{p}{\ell }_P$, the correction has the form of the Gambini and Pullin effect for photons. A dependence $L_{\mathrm{os}}^{-1\mathrm{}}\propto {\overline{p}}^2{\ell }_P$ is found for a two-flavor neutrino oscillation length.