No flavor anisotropy in the high-energy neutrino sky upholds Lorentz invariance

A bstract Discovering Lorentz-invariance violation (LIV) would upend the foundations of modern physics. Because LIV effects grow with energy, high-energy astrophysical neutrinos provide the most sensitive tests of Lorentz invariance in the neutrino sector. We examine an understudied yet phenomenologically rich LIV signature: compass asymmetries, where neutrinos of different flavors propagate preferentially along different directions. Using the directional flavor composition of high-energy astrophysical neutrinos, i.e., the abundances of ν e , ν μ , and ν τ across the sky, we find no evidence of LIV-induced flavor anisotropy in 7.5 years of IceCube High-Energy Starting Events. Thus, we place upper limits on the values of hundreds of LIV parameters with operator dimensions 2–8, tightening existing limits by orders of magnitude and bounding hundreds of parameters for the first time ( https://github.com/BernieTelalovic/LIV_constraints_from_HESE_flavour_isotropy ).