Fermi Limit on the Neutrino Flux from Gamma-ray Bursts

If gamma-ray bursts (GRBs) produce high energy cosmic rays, neutrinos are expected to be generated in GRBs due to photo-pion productions. However we stress that the same process also generates electromagnetic (EM) emission induced by the production of secondary electrons and photons, and that the EM emission is expected to be correlated to the neutrino flux. Using the Fermi/LAT observational results on gamma-ray flux from GRBs, the GRB neutrino emission is limited to be below ~20 GeV/m^2 per GRB event on average, which is independent of the unknown GRB proton luminosity. This neutrino limit suggests that the full IceCube needs stacking more than 130 GRBs in order to detect one GRB muon neutrino.