Possible cosmogenic neutrino constraints on Planck-scale Lorentz violation

TL;DR

This paper investigates how Planck-scale Lorentz violation could affect ultra-high-energy cosmogenic neutrino spectra, predicting a cutoff and bump that future experiments might constrain or detect, thus testing fundamental physics.

Contribution

It introduces a framework to analyze Lorentz violation effects on neutrinos at Planck scale and predicts observable spectral features for future experimental tests.

Findings

Positive Lorentz violation leads to a neutrino cutoff above 10^{19} eV.

A spectral bump appears at around 10^{17} eV due to Lorentz violation.

Future experiments could constrain the Lorentz violation parameter to less than 10^{-4}.

Abstract

We study, within an effective field theory framework, $O(E^{2}/\Mpl^{2})$ Planck-scale suppressed Lorentz invariance violation (LV) effects in the neutrino sector, whose size we parameterize by a dimensionless parameter $\eta_{\nu}$. We find deviations from predictions of Lorentz invariant physics in the cosmogenic neutrino spectrum. For positive O(1) coefficients no neutrino will survive above $10^{19} \eV$. The existence of this cutoff generates a bump in the neutrino spectrum at energies of $10^{17} \eV$. 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 $\eta_{\nu} \lesssim 10^{-4}$ on the neutrino LV parameter, depending on how LV is distributed among neutrino mass states. Constraints on $\eta_{\nu} < 0$ can in principle be obtained with this strategy, but they require a more detailed modeling of how LV affects the neutrino sector.