A recent work [Y. Huang and B.-Q. Ma, Commun. Phys. 1, 62 (2018)] associated all four PeV neutrinos observed by IceCube to gamma-ray bursts, and revealed a regularity which indicates a Lorentz-violation scale $E_{\mathrm{LV}}=(6.5\pm 0.4)\times {10}^{17}\mathrm{GeV}$ with opposite sign factors $s=\pm 1$ between neutrinos and antineutrinos. The association of “time delay” and “time advance” events with neutrinos and antineutrinos (or vice versa) is only a hypothesis since the IceCube detector cannot tell the chirality of the neutrinos, and further experimental tests are needed to verify this hypothesis. We derive the values of the $CPT$-odd Lorentz violating parameters in the standard-model extension (SME) framework, and perform a threshold analysis on the electron-positron pair emission of the superluminal neutrinos (or antineutrinos). We find that different neutrino/antineutrino propagation properties, suggested by Y. Huang and B.-Q. Ma, can be described in the SME framework with both Lorentz invariance and $CPT$ symmetry violation, but with a threshold energy constraint. A viable way on testing the $CPT$ symmetry violation between neutrinos and antineutrinos is suggested.

• Received 16 October 2018

DOI:https://doi.org/10.1103/PhysRevD.99.043013

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society