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 $\textit{ν}$ , $\textit{ν}$ , and $\textit{ν}$ 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 ( ).

Denmark

Bernanda Telalovic

Mauricio Bustamante

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

To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an $\textit{N}$-independent reduction of SU($\textit{N}$) tensor products. To this end, we label each irreducible representation by a pair of Young diagrams, with parts acting on quarks and antiquarks. By combining this with a column-wise multiplication of Young diagrams, we generalize the Littlewood-Richardson rule for the product of two Young diagrams to the product of two Young diagram pairs, achieving a general-$\textit{N}$ decomposition.

Germany

Stefan Keppeler

Sweden

Malin Sjodahl

Austria

An $\textit{N}$-independent tensor decomposition for SU($\textit{N}$)