No Flavor Anisotropy in the High-Energy Neutrino Sky Upholds Lorentz Invariance

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.

💡 Research Summary

The paper investigates whether Lorentz‑invariance violation (LIV) could manifest as a flavor‑dependent directional asymmetry—so‑called “compass asymmetry”—in the flux of high‑energy astrophysical neutrinos observed by IceCube. Within the Standard‑Model Extension (SME) framework, LIV is encoded in effective operators of various mass dimensions (d = 2–8). CPT‑odd operators (a‑type) appear for odd d, while CPT‑even operators (c‑type) appear for even d. Each operator is a 3 × 3 complex matrix in flavor space and is expanded in spherical harmonics Yℓm( p̂ ) to capture its angular dependence. The ℓ = 0 terms are isotropic; ℓ > 0 terms are anisotropic and would produce a flavor‑dependent sky map if non‑zero.

The authors use the public 7.5‑year IceCube High‑Energy Starting Event (HESE) sample, which provides reconstructed direction, deposited energy, and a statistical estimate of the neutrino flavor (νe, νμ, ντ) for each event. Building on a Bayesian methodology developed in a previous IceCube analysis, they infer the “directional flavor composition” – the relative fractions of each flavor as a function of sky direction – and compare it to the predictions of the standard three‑flavor oscillation framework augmented by LIV.

The total Hamiltonian governing propagation is H = Hvac + HLIV, where Hvac contains the usual mass‑splitting term (∝ Δm²/E) and HLIV contains the SME coefficients. Because HLIV scales as E^{d‑3}, the effect grows rapidly with energy for d > 2, making PeV‑scale neutrinos especially sensitive. The authors treat the standard oscillation parameters (θ12, θ13, θ23, δCP, Δm²21, Δm²31) with Gaussian priors from global fits, and they model the astrophysical flux with a power‑law spectrum, a redshift distribution, and several possible source flavor ratios (e.g., 1:2:0, 0:1:0, etc.). They marginalize over these astrophysical uncertainties.

Two analysis strategies are explored. First, they constrain a single LIV coefficient at a time, fixing all others to zero, which yields straightforward one‑dimensional posterior limits. Second, they perform joint constraints on multiple coefficients (up to dozens) to assess possible degeneracies. In both cases, the likelihood is built from the Poisson probability of observing the measured flavor composition in each sky pixel, given the predicted composition for a set of LIV parameters.

The results show no statistically significant deviation from isotropy. Consequently, the authors set 95 % confidence upper limits on the real and imaginary parts of each SME coefficient. For dimensions d = 3–8, hundreds of anisotropic coefficients are constrained for the first time. For d = 2, only the nine anisotropic c‑type coefficients are bounded (the nine isotropic ones cannot be disentangled from standard oscillations). The new limits improve upon previous bounds from accelerator, atmospheric, and earlier IceCube studies by one to three orders of magnitude, thanks to the high energies and long baselines of the astrophysical neutrinos.

The paper concludes that high‑energy astrophysical neutrinos are a uniquely powerful probe of LIV, especially for direction‑dependent effects that have been largely unexplored. The methodology demonstrated here can be applied to larger data sets from IceCube‑Gen2, KM3NeT, or future radio‑based detectors, potentially tightening constraints further or revealing a genuine LIV signal.