Implications of a PeV neutrino spectral cut-off in gamma-ray burst models

The recent discovery of extragalactic PeV neutrinos opens a new window to the exploration of cosmic ray accelerators. The observed PeV neutrino flux is close to the Waxman-Bahcall upper bound implying that gamma-ray bursts (GRBs) may be the source of ultrahigh energy cosmic rays (UHECRs). Starting with the assumption of the GRB-UHECR connection, we show using both analytical estimates and numerical simulations that the observed neutrinos can originate at the jet as a result of photopion interactions with the following implications: the neutrino spectra are predicted to have a cut-off at energy less than or similar to 10 PeV; the dissipation responsible for the GRB emission and cosmic ray acceleration takes place at distances r(diss) similar or equal to 3 x 10(11)-3 x 10(13) cm from the central engine; the Thomson optical depth at the dissipation region is tau(T) similar to 1; the jet carries a substantial fraction of its energy in the form of Poynting flux at the dissipation region, and has a Lorentz factor Gamma similar or equal to 100-500. The non-detection of PeV neutrinos coincident with GRBs will indicate that GRBs are either poor cosmic accelerators or the dissipation takes place at small optical depths in the jet.