Can a Single High-energy Neutrino from Gamma-ray Bursts be a Discovery?

Abstract

Current emission models of GeV-PeV neutrinos from gamma-ray bursts (GRBs) predict a neutrino flux with $\ll 1$ detected neutrinos per GRB with kilometer-scale neutrino observatories. The detection of this flux will require the stacking of data from a large number of GRBs, leading to an increased background rate, decreasing the significance of a single neutrino detection. We show that utilizing the temporal correlation between the expected gamma-ray and neutrino fluxes, one can significantly improve the neutrino signal-to-noise ratio. We describe how this temporal correlation can be used. Using realistic GRB and atmospheric neutrino fluxes and incorporating temporal, spectral and directional information, we estimate the probability of a single detected GRB-neutrino being a 5$\sigma$ discovery.