Type: Article
Publication Date: 2019-06-21
Citations: 27
DOI: https://doi.org/10.1103/physrevd.99.123018
A recent proposal to associate 60 TeV to 2 PeV IceCube neutrino events with gamma-ray bursts (GRBs) indicates the Lorentz violation of cosmic neutrinos and leads further to the $CPT$ symmetry violation between neutrinos and antineutrinos. Here we find that another 12 northern hemisphere track events possibly correlated with GRBs from three-year IceCube data satisfy the same regularity at a lower energy scale around 1 TeV. The combined fitting indicates a Lorentz violation scale ${E}_{\mathrm{LV}}=(6.4\ifmmode\pm\else\textpm\fi{}1.5)\ifmmode\times\else\texttimes\fi{}{10}^{17}\text{ }\text{ }\mathrm{GeV}$ and an intrinsic time difference $\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{in}}=(\ensuremath{-}2.8\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{2}\text{ }\text{ }\mathrm{s}$, from which we find an earlier emission of neutrinos than photons at the GRB source. We also suggest analyzing neutrino events detected a few minutes before the GRB trigger time to test the $CPT$ violation of ultrahigh-energy neutrinos.