On the energy of neutrinos from gamma ray bursts

Ultra high energy protons accelerated at the shocks causing gamma ray bursts photoproduce pions, and then neutrinos in situ. I consider here the sources of losses in this process, namely adiabatic and synchrotron losses by both pions and muons. When the shocks under consideration are external, i.e., those between the ejecta and the surrounding interstellar medium, I show that neutrinos produced by pion decay are unaffected by losses; those produced by muon decay, in the strongly beamed emission required by afterglow observations of GRB 971214, are limited in energy, but still exceed 10 eV . In particular, this means that ultra high energy neutrinos will be produced through afterglows. Subject headings: gamma rays: bursts – acceleration of particles – elementary particles – shock waves – relativity – cosmology: miscellaneous