  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.
