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

TL;DR

This work tests Lorentz invariance in the neutrino sector by searching for compass anisotropies in the directional flavor composition of high-energy astrophysical neutrinos with the IceCube HESE dataset spanning 7.5 years. It adopts the Standard Model Extension framework, incorporating LIV operators up to dimension $d=8$ and capturing anisotropic ($\ell>0$) effects across the sky, while marginalizing over neutrino production and spectral uncertainties. By predicting the sky-resolved flavor fractions $f_{\alpha,\oplus}$ as functions of energy, direction, and LIV coefficients, and comparing to IceCube in 12 sky pixels, the analysis yields 1071 upper limits on LIV parameters (with 816 improved or first-time constraints). The results indicate no evidence for flavor compass anisotropy, underscoring Lorentz invariance at high energies and establishing stringent, direction-dependent constraints that will sharpen with future detectors and larger data sets.

Abstract

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.

Figures (12)

• Figure 1: Effect of anisotropic Lorentz-invariance violation on the flavor composition of high-energy astrophysical neutrinos. Neutrinos are emitted by astrophysical sources located at different distances from Earth, of up to a few Gpc, distributed in redshift, $z$. They are emitted with different proportions of the different flavors, $\nu_e$, $\nu_\mu$, and $\nu_\tau$, as determined by the neutrino production mechanism. In this figure, as an example, they are emitted with a 1:2:0 ratio between $\nu_e$, $\nu_\mu$, and $\nu_\tau$; in producing our results, we explore all possibilities. En route to Earth, the neutrinos interact with a pervading Lorentz-invariance-violating field that, together with standard flavor-transition processes, modifies the proportions of the different neutrino flavors that reach Earth. If the field is anisotropic, this modification is different along different directions in the sky. We use the measurement of the "directional flavor composition", extracted from 7.5 years of IceCube HESE data, to constrain hundreds of possible forms of anisotropic Lorentz-invariance violation. See the main text for details.
• Figure 2: Energy dependence of the LIV effects on high-energy astrophysical neutrinos.Top: Tessellated sky map highlighting the two pixels for which we show results in this figure. Solid/dashed lines in the bottom two pannels correspond to the values inside the solid/dashed pixel, respectively. Center: Flavor-transition probability, Eq. (\ref{['equ:probability']}), averaged inside each of the two pixels, computed for a fixed illustrative value of the sole nonzero LIV parameter $(c_{\rm eff}^{(4)})_{22}^{\tau\tau}$. Bottom: High-energy neutrino flavor composition at Earth [before the energy averaging in Eq. (\ref{['equ:flavor_ratio']})], also averaged inside each of the two pixels, computed with the same LIV parameter. For this plot, we assume the flavor composition at the sources to be $\left( \frac{1}{3}, \frac{2}{3}, 0 \right)_{\rm S}$. Our limits on the LIV parameters come from the regimes where LIV and standard oscillations are comparable and where LIV dominates. (However, we use energy-averaged flavor ratios, Eq. (\ref{['equ:flavor_ratio']}), to place limits.) See Secs. \ref{['sec:nu_oscillations-prob']} and \ref{['sec:astro_nu-flavor']} for details.
• Figure 3: Directional flavor composition of high-energy astrophysical neutrinos at Earth, as predicted under Lorentz-invariance violation. In this plot, we compute the energy-averaged flavor composition at Earth, Eq. (\ref{['equ:flavor_ratio']}), by varying a single, illustrative LIV parameter, $(a^{(3)}_{\rm eff})_{10}^{e\mu}$, inside each pixel of our sky tessellation (Sec. \ref{['sec:stat_methods-inferring_flavor_composition']}). We show results obtained under our three benchmark choices of flavor composition at the sources (Sec. \ref{['sec:astro_nu-nuisance_fS']}). We also show the measured flavor composition in each pixel, extracted from the public 7.5-year IceCube HESE sample IceCube:2020wumIC75yrHESEPublicDataRelease in Ref. Telalovic:2023tcb. Our constraints on the LIV parameters come from contrasting our predictions for the flavor composition at Earth vs. the measurement from IceCube data. See Secs. \ref{['sec:astro_nu-flavor']}, Sec. \ref{['sec:stat_methods']}, and Sec. \ref{['sec:results']}, respectively, for details about the prediction of flavor composition at Earth, the measurement of the directional flavor composition from IceCube data, and the constraints we set on the LIV parameters.
• Figure 4: Impact of the neutrino flavor composition at the sources on the LIV effects. For this plot, we show results for an illustrative LIV parameter, $(a_{\rm eff}^{(3)})_{20}^{\mu\tau}$. The astrophysical neutrino sources responsible for the diffuse flux emit high-energy neutrinos with flavor composition $(f_{e, {\rm S}}, 1-f_{e, {\rm S}}, 0)$. For each choice of values of $f_{e, {\rm S}}$ and $(a_{\rm eff}^{(3)})_{20}^{\mu\tau}$, we compute the expected neutrino flavor composition at Earth, Eq. (\ref{['equ:flavor_ratio']}), and find where it is different from the standard-oscillation expectation by more than 50%, either in at least one pixel our sky tessellation---representing how we place constraints on LIV parameters---or averaged across the sky. We rely on spotting differences in the flavor composition in different directions of the sky to boost the sensitivity to anisotropic LIV effects. See Sec. \ref{['sec:astro_nu-nuisance_fS']} for details.
• Figure 5: Influence of the spectral index (left) and source redshift distribution (right) on the energy-averaged flavor composition at Earth under LIV. We compute the energy-averaged flavor composition at Earth, Eq. (\ref{['equ:flavor_ratio']}). Left, assuming a power-law neutrino energy spectrum with two different values of the spectral index, $\gamma = 3.67$ and 2.29, and varying the single nonzero isotropic LIV parameter, $(a_{\rm eff}^{(4)})_{00}^{e\mu}$. Because, in this case, LIV is isotropic, the flavor composition in this plot is the same everywhere in the sky. For comparison, from the public 7.5-year IceCube HESE sample, $\gamma = 2.89 \pm 0.23$IceCube:2020wum. Right, assuming that the number density of sources follows either the star-formation rate (SFR), which peaks at redshift $z = 1$, or is $\propto (1+z)^2$, which peaks at $z = z_{\rm max} = 4$, the maximum redshift in the computation of the diffuse neutrino flux, Eq. (\ref{['equ:diffuse_flux']}). We vary the value of the single nonzero isotropic LIV parameter, $(a_{\rm eff}^{(8)})_{00}^{e\mu}$.The uncertainties in the values of the spectral index and source redshift distribution have negligible effects on the flavor composition at Earth and, therefore, on the constraints we place on LIV parameters.