Interplay of Lorentz Invariance Violation and Earth's Matter Potential in High-Energy Neutrinos

TL;DR

This work investigates anisotropic LIV in neutrinos within the SME framework, highlighting how Earth's matter potential can qualitatively modify LIV-induced oscillations. By combining vacuum LIV phenomenology with a realistic Earth model, the authors show a crossover regime where $H_{ ext{SME}}$ becomes comparable to the matter potential $V$, leading to direction-dependent resonances and a neutrino–antineutrino asymmetry in propagation. They predict a novel LIV-driven $\tau$ regeneration mechanism that significantly boosts the $\nu_\tau$ flux at Earth-crossing paths, along with spectral redistribution to lower energies. The results emphasize that incorporating matter effects is crucial for LIV searches at large-scale neutrino telescopes and offer concrete signatures for IceCube-like and future detectors.

Abstract

Searches for Lorentz invariance violation (LIV) in the neutrino sector have traditionally focused on non-standard neutrino oscillations induced by LIV in vacuum. In this work, however, we study anisotropic LIV in matter. First, we review vacuum LIV phenomenology, explaining the energy and direction dependence of sidereal modulations for anisotropic coefficients in the Standard Model Extension. We then demonstrate that for high-energy neutrinos, the interplay between anisotropic LIV operators and the Earth's matter potential produces, distinct, observable signatures absent in the vacuum case. We identify a crossover regime where the energy-dependent LIV Hamiltonian becomes comparable to the matter potential, leading to strong interference effects. By analyzing the propagation of neutrinos through a realistic Earth model, we establish three key phenomenological consequences: (1) direction-dependent resonant enhancements of oscillation probabilities, (2) a macroscopic breakdown of neutrino-antineutrino symmetry for CPT-even operators, and (3) a significant increase of the $ν_τ$ flux due to LIV-driven injection of high-energy neutrinos into the $τ$ regeneration cycle. These results highlight that accounting for the interplay between LIV and matter is essential for future LIV searches at large-scale neutrino telescopes.

Figures (14)

• Figure 1: Muon neutrino survival probability with and without Lorentz-invariance violation. The Earth-crossing $\nu_\mu$ survival probability is plotted as a function of energy. Standard oscillations (black) scale as $1/E$, compared to SME-induced oscillations that scale as $E^0$ (orange) and $E^1$ (blue).
• Figure 2: Relationship between equatorial and local coordinates. The cosine of the zenith angle ($\cos\theta_z$), which determines the baseline $L$, is plotted against declination and right ascension. For detectors off the poles, this mapping depends on sidereal time.
• Figure 3: Time dependence of the neutrino baseline's for a detector located on/off the Earth's rotational axis. In the celestial equatorial coordinate system, the neutrino baseline is constant for IceCube, while it varies for all other large-scale Cherenkov neutrino telescopes.
• Figure 4: Time-dependence of standard neutrino oscillation probabilities in the celestial equatorial reference frame. We show the sidereal variation of the standard $\nu_\mu$-survival probabilities at the KM3NeT/ARCA detector location at a neutrino energy of $E=10$ GeV in the equatorial reference frame. We neglect matter effects, but show Earth's main layers for reference.
• Figure 5: Time-dependence of LIV-induced neutrino oscillation probabilities in the celestial equatorial reference frame. We show the sidereal variation of the vacuum $\nu_\mu$-survival probabilities at the KM3NeT/ARCA detector location for $c^{ty}_{33}=1\cdot 10^{-26}$ at a neutrino energy of $E=10$ TeV.