In vacuo dispersion features for gamma-ray-burst neutrinos and photons

Over the past 15 years there has been considerable interest in the possibility of quantum-gravity-induced in vacuo dispersion, the possibility that spacetime itself might behave essentially like a dispersive medium for particle propagation. Two recent studies have exposed what might be in vacuo dispersion features for gamma-ray-burst (GRB) neutrinos of energy in the range of 100 TeV and for GRB photons with energy in the range of 10 GeV. We here show that these two features are roughly compatible with a description such that the same effects apply over four orders of magnitude in energy. We also show that it should not happen so frequently that such pronounced features arise accidentally, as a result of (still unknown) aspects of the mechanisms producing photons at GRBs or as a result of background neutrinos accidentally fitting the profile of a GRB neutrino affected by in vacuo dispersion.