Ultra-High-Energy Tau Neutrinos as Probes of Lorentz Invariance

Abstract Neutrino telescopes have detected astrophysical neutrinos with energies up to 𝒪(100) PeV. Several current and proposed experiments aim to observe neutrinos at even higher energies, with the goal of detecting cosmogenic neutrinos. This increase in neutrino energy makes tests of Lorentz invariance violation (LIV) particularly appealing, since the effects of higher-dimension LIV operators on neutrino propagation grow rapidly with energy. In this work, we investigate the potential of the upcoming experiments GRAND and POEMMA to probe LIV in the neutrino sector through the detection of ultra-high-energy tau neutrinos. We generate the cosmogenic neutrino flux using SimProp and interface it with a calculation of neutrino flavor transition probabilities in the presence of LIV effects. Deviations from standard flavor transition probabilities manifest as changes in the expected tau neutrino event rates at GRAND and POEMMA. We first consider the case with a single nonzero LIV operator of various dimensions, and find that the projected sensitivities exceed existing limits from lower-energy probes by orders of magnitude. We then explore scenarios with multiple nonzero LIV parameters and show that their interplay can significantly modify the sensitivities compared to the single-parameter case. Overall, we find that upcoming observations of ultra-high-energy tau neutrinos will place some of the most stringent constraints on LIV.