Constraints on Lorentz-invariance violation in the neutrino sector from the ultrahigh-energy event KM3-230213A

Abstract: Lorentz invariance is a fundamental symmetry of spacetime and serves as the cornerstone of modern physics, supporting the constancy of the speed of light. A crucial implication of this principle is that no particle can propagate faster than this universal speed limit. In this study, we present a stringent neutrino-based test of Lorentz invariance, utilizing the highest-energy neutrino ever detected, known as event KM3-230213A. The detection of this neutrino, with measured energy of approximately 220 PeV, allows us to establish a lower bound on the scale of second-order Lorentz invariance violation, quantified as (\Lambda_2>5.0\times 10^{19}) GeV at 90 \% confidence level.