High-energy neutrinos are expected to originate from different stages in a gamma-ray burst (GRB) event. In this work we revisit the dissipative photospheric scenario, in which the GRB prompt emission is produced around the photospheric radius. Meanwhile, possible dissipation mechanisms (e.g., internal shocks or magnetic reconnection) could accelerate cosmic-rays (CRs) to ultra-high energies and then produce neutrinos via hadronuclear and photohadronic processes, which are referred to as prompt neutrinos. In this paper, we obtain the prompt neutrino spectrum of a single GRB within a self-consistent analytical framework, in which the jet-cocoon structure and possible collimation effects are included. We investigate a possible neutrino signal from the cocoon, which has been ignored in the previous studies. We show that if a GRB event happens at a distance of the order of Mpc, there is a great chance to observe the neutrino emission from the cocoon by IceCube, which is even more promising than jet neutrinos since the opening angle of the cocoon is much larger. We also figure out the diffuse neutrino flux of GRB cocoons and find that it could be comparable with that of the jets. Our results are consistent with the latest result reported by the IceCube collaboration that no significant correlation between neutrino events and observed GRBs is seen in the new data (Aartsen et al. 2017).
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