Ultra-high energy cosmic neutrinos from gamma-ray bursts

Based on the recent association of IceCube TeV and PeV neutrino events with gamma -ray bursts (GRBs) by considering the Lorentz violation of neutrinos, we provide a new estimate on the GRB neutrino flux with a more significant result compared to the previous constraint by the IceCube Collaboration. Among these 24 neutrino "shower " events above 60 TeV, 12 events are associated with GRBs. Such a result is compatible with the prediction from GRB fireball models. Analysis of track events provides a consistent result with the shower events to associate high energy cosmic neutrinos with GRBs under the same Lorentz violation features of neutrinos. We also make a background estimation and reveal GRBs as a significant source for the ultra -high energy IceCube neutrino events. Our work supports the Lorentz violation and CPT -violation of neutrinos, indicating new physics beyond relativity.