Neutrinos from Gamma Ray Bursts
  The observed fluxes of cosmic rays and gamma rays are used to infer the maximum allowed high-energy neutrino flux allowed for Gamma Ray Bursts (GRBs), following Mannheim, Protheroe, and Rachen (2000). It is shown that if GRBs produce the ultrahigh-energy cosmic rays, they should contribute (a) at least 10% of the extragalactic gamma ray background between 3 MeV and 30 GeV, contrary to their observed energy flux which is only a minute fraction of this flux, and (b) a cumulative neutrino flux a factor of 20 below the AMANDA (Neutrino 2000) limit on isotropic neutrinos. This could have two implications, either GRBs do not produce the ultrahigh energy cosmic rays or that the GRBs are strongly beamed and emit most of their power at energies well above 100 GeV implausibly increasing the energy requirements, but consistent with the marginal detections of a few low-redshift GRBs by MILAGRITO, HEGRA-AIROBICC, and the Tibet-Array. All crucial measurements to test the models will be available in the next few years. These are measurements of (i) high-energy neutrinos with AMANDA-ICECUBE or an enlarged ANTARES/NESTOR ocean detector, (ii) GRB redshifts from HETE-2 follow-up studies, and (iii) GRB spectra above 10 GeV with low-threshold imaging air Cherenkov telescopes such as MAGIC and the space telescopes AGILE and GLAST. 
Karl Mannheim