Astrophysical bounds on the high-energy evolution of neutrino mixing

While conventional oscillation experiments measure neutrino mixing parameters with high precision, these measurements are strictly confined to sub-TeV scales. At higher energies, renormalization-group effects can cause these parameters to evolve with the transferred momentum, $Q$. High-energy and ultra-high-energy astrophysical neutrinos, spanning TeV to EeV energies, probe high values of $Q$ unreachable by conventional experiments, offering an unprecedented test of high-energy mixing. We use the flavor composition of these neutrinos -- the relative proportions of $\nu_e$, $\nu_\mu$, and $\nu_\tau$ -- to constrain this evolution, both phenomenologically and within dimension-6 Standard Model Effective Field Theory. We account for astrophysical uncertainties -- an unavoidable requirement to obtain realistic results, even though this weakens the bounds. Although present IceCube measurements lack the sensitivity to detect this running, we forecast that upcoming multi-detector combinations will place unprecedented bounds on the high-energy evolution of neutrino mixing.