Possible cosmogenic neutrino constraints on Planck-scale Lorentz violation

Abstract

We study, within an effective field theory framework, O(E2MPl2) Planck-scale suppressed Lorentz invariance violation (LV) effects in the neutrino sector, whose size we parameterize by a dimensionless parameter ην. We find deviations from predictions of Lorentz invariant physics in the cosmogenic neutrino spectrum. For positive O(1) coefficients no neutrino will survive above 1019eV. The existence of this cutoff generates a bump in the neutrino spectrum at energies of 1017eV. Although at present no constraint can be cast, as current experiments do not have enough sensitivity to detect ultra-high-energy neutrinos, we show that experiments in construction or being planned have the potential to cast limits as strong as ην≲10−4 on the neutrino LV parameter, depending on how LV is distributed among neutrino mass states. Constraints on ην < 0 can in principle be obtained with this strategy, but they require a more detailed modeling of how LV affects the neutrino sector.