Magnetic field and flavor effects on the gamma-ray burst neutrino flux

We reanalyze the prompt muon neutrino flux from gamma-ray bursts (GRBs) in terms of the particle physics involved, as in the example of the often-used reference Waxman-Bahcall GRB flux. We first reproduce this reference flux explicitly treating synchrotron energy losses of the secondary pions. Then we include additional neutrino production modes, the neutrinos from muon decays, the magnetic field effects on all secondary species, and flavor mixing with the current parameter uncertainties. We demonstrate that the combination of these effects modifies the shape of the original Waxman-Bahcall GRB flux significantly and changes the normalization by a factor of 3 to 4. As a consequence, the gamma-ray burst search strategy of neutrino telescopes may be based on the wrong flux shape, and the constraints derived for the GRB neutrino flux, such as the baryonic loading, may in fact be much stronger than anticipated.