Consistent Lorentz violation features from near-TeV IceCube neutrinos

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 $E_{\mathrm{LV}}=(6.4\pm 1.5)\times {10}^{17}\mathrm{GeV}$ and an intrinsic time difference $\mathrm{\Delta }{t}_{\mathrm{in}}=(-2.8\pm 0.7)\times {10}^2\mathrm{s}$, 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.

Figure 1

$\mathrm{\Delta }{t}_{\mathrm{obs}}/(1+z)$ versus the $K$ plot for near-TeV neutrino events. Points (black) are northern hemisphere track events from seven-year data [12, 14], up triangles (red) are southern hemisphere track events from the five-year search [14], and down triangles (blue) are shower events from the three-year search for all flavors [13]. The red colored region is the error band of the speed variation regularity from TeV and PeV GRB neutrinos [20, 27]. All of the northern hemisphere events detected during 2012–2015 fall within the error band.

Figure 2

Linear fitting for 18 northern hemisphere track events and high-energy events. (a) Points (black) are experimentally measured data of northern hemisphere track events, diamonds (red) are TeV event data, and squares (blue) are PeV event data. Error bars are estimated according to the Methods of Ref. [27]. The line (red) is the fitting result. There is a well linear correlation between $\mathrm{\Delta }{t}_{\mathrm{obs}}/(1+z)$ and $s·K$. (b) The zooming in plot focuses on near-TeV events. The red colored region shows the error range of fitting. Twelve of 18 northern hemisphere track events fall within the error band of the fitting.

Figure 3

Linear fitting for 12 northern hemisphere track events and high-energy events. The combined fitting indicates a Lorentz violation scale $E_{\mathrm{LV}}=(6.4\pm 1.5)\times {10}^{17}\mathrm{GeV}$ and an intrinsic time difference $\mathrm{\Delta }{t}_{\mathrm{in}}=(-2.8\pm 0.7)\times {10}^2\mathrm{s}$. (a) Points (black) are experimentally measured data of northern hemisphere track events, diamonds (red) are TeV event data, and squares (blue) are PeV event data. Error bars are estimated according to the Methods of Ref. [27]. The line (red) is the fitting result. There is also a well linear correlation between $\mathrm{\Delta }{t}_{\mathrm{obs}}/(1+z)$ and $s·K$. (b) The zooming in plot focuses on near-TeV events. The red colored region shows the error range of fitting.