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

Many quantum gravity theories predict deviations from Lorentz invariance, a foundational principle of modern physics, at energy scales exceeding the Planck scale. The presence of Lorentz invariance violation (LIV) would modify the dispersion relations of particles in vacuum and render certain decay channels kinematically permissible. In this study, we derive stringent constraints on the energy scale of LIV in the neutrino sector by investigating the impact of neutrino decay channels on the neutrino spectrum in the presence of LIV. Utilizing the spectra derived from the joint fit of KM3NeT, IceCube, and Auger data as a benchmark, we demonstrate that to be compatible with the highest-energy neutrino event ever detected, known as event KM3-230213A, the second-order LIV energy scale must satisfy <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Λ</a:mi><a:mn>2</a:mn></a:msub><a:mo>&gt;</a:mo><a:mn>5.0</a:mn><a:mo>×</a:mo><a:msup><a:mn>10</a:mn><a:mn>19</a:mn></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>GeV</a:mi></a:math> at 90% confidence level. Furthermore, our analyses indicate that the current data do not impose a stringent constraint on the energy scale associated with the first-order LIV.