Limits on the Neutrino Velocity, Lorentz Invariance, and the Weak Equivalence Principle with TeV Neutrinos from Gamma-Ray Bursts

Understand

Five TeV neutrino events weakly correlated with five gamma-ray bursts (GRBs) were detected recently by IceCube.

• This work is an attempt to show that if the GRB identifications are verified, the observed time delays between the TeV neutrinos and gamma-ray photons from GRBs provide attractive candidates for testing fundamental physics with high accuracy.
• Based on the assumed associations between the TeV neutrinos and GRBs, we find that the limiting velocity of the neutrinos is equal to that of photons to an accuracy of $\sim1.9\times10^{-15}-2.5\times10^{-18}$, which is about $10^{4}-10^{7}$ times better than the constraint obtained with the neutrino possibly from a blazar flare.
• In addition, we set the most stringent limits up to date on the energy scale of quantum gravity for both the linear and quadratic violations of Lorentz invariance, namely $E_{\rm QG, 1}>6.3\times10^{18}-1.5\times10^{21}$ GeV and $E_{\rm QG, 2}>2.0\times10^{11}-4.2\times10^{12}$ GeV, which are essentially as good as or are an improvement of one order of magnitude over the results previously obtained by the GeV photons of GRB 090510 and the PeV neutrino from a blazar flare.