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The high-energy (> 100MeV) emission observed by Fermi-LAT during the promptphase of some luminous gamma-ray bursts (GRBs) could arise from the cascadeinduced by interactions between accelerated protons and the radiation field ofGRBs. The photomeson process, which is usually suggested to operate in such ahadronic explanation, requires a rather high proton energy (> 10^17eV) for anefficient interaction. However, whether GRBs can accelerate protons to such ahigh energy is far from guaranteed, although they have been suggested as thecandidate source for ultrahigh-energy cosmic rays. In this work, we revisit thehadronic model for the prompt high-energy emission of GRBs with a smallermaximum proton energy than the usually adopted value estimated from the Bohmcondition. In this case, the Bethe-Heitler pair production process becomescomparably important or even dominates over the photomeson process. We showthat with a relatively low maximum proton energy with a Lorentz factor of 10^5in the comoving frame, the cascade emission can still reproduce various typesof high-energy spectrum of GRBs. For most GRBs without high-energy emissiondetected, the maximum proton energy could be even lower and relax theconstraints on the parameters of GRB jet resulting from the fact ofnon-detection of GRB neutrinos by IceCube.

Hadronic origin of prompt high-energy emission of gamma-ray bursts revisited: in the case of a limited maximum proton energy