Abstract
The Lorentz violation (LV) effect of ultra-relativistic particles can be tested by gamma-ray burst (GRB) neutrinos and photons. The IceCube Collaboration has observed plenty of ultra-high energy neutrinos, including four PeV scale neutrinos. Recent studies suggested a possible energy dependent speed variation of GRB neutrinos in a similar way to that of GRB photons. Here we find that all four PeV neutrinos with associated GRB candidates can satisfy a regularity found from TeV neutrinos about a linear form correlation between the observed time difference and the LV factor. Such regularity indicates a Lorentz violation scale ELV = (6.5 ± 0.4) × 1017 GeV, which is comparable with that determined by GRB photons. We also suggest that neutrinos and anti-neutrinos can be superluminal and subluminal respectively due to opposite signs of LV correction.
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