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 $\mathcal{L}$ much greater than Planck length ${\ell }_P=1.2\times 10^{-33}$cm, a spin-1/2 field in flat spacetime. The discrete structure of spacetime at ${\ell }_P$ yields corrections to the field propagation at scale $\mathcal{L}$. Next, Neutrino Bursts ($\bar{p}\approx 10^5$GeV) accompaning Gamma Ray Bursts that have travelled cosmological distances, $L\approx 10^{10}$l.y., are considered. The dominant correction is helicity independent and leads to a time delay w.r.t. the speed of light, $c$, of order $(\bar{p}{\ell }_P)L/c\approx 10^4$s. To next order in $\bar{p}{\ell }_P$ the correction has the form of the Gambini and Pullin effect for photons. Its contribution to time delay is comparable to that caused by the mass term. Finally, a dependence $L_{\mathrm{os}}^{-1}\propto {\bar{p}}^2{\ell }_P$ is found for a two-flavour neutrino oscillation length.

Comments: RevTeX, 5pp, no figures. Notation of a sum in Eq.(2) improved. Slight modifications in redaction. Final version to appear in Phys. Rev. Lett