2025ApJ...980..188Z

Gamma-ray bursts (GRBs) are widely suggested as potential sources of ultrahigh-energy cosmic rays. The kinetic energy of the jets dissipates, leading to the production of an enormous amount of gamma-ray photons and possibly also the acceleration of protons. The accelerated protons will interact with the radiation of the GRB via the photomeson and Bethe-Heitler processes, which can initiate electromagnetic cascades. This process can give rise to broadband radiation up to the GeV-TeV gamma-ray regime. The expected gamma-ray flux from cascades depends on the properties of the GRB jet, such as the dissipation radius R_diss, the bulk Lorentz factor Γ, and the baryon loading factor η_p. Therefore, observations of Fermi-LAT can impose constraints on these important parameters. In this study, we select 12 GRBs of high keV-MeV fluence and constrain the baryon loading factor, under different combinations of the bulk Lorentz factor and the dissipation radius based on Fermi-LAT's measurements. Our findings indicate a strong constraint of η_p < 10 for most selected GRBs over a large parameter space except for large dissipation radii (≳10¹⁵ cm) and high bulk Lorentz factors (≳600). The constraint is comparable to, and in some GRBs even stronger than, that from high-energy neutrinos for stacked GRBs. Our results suggest that for a typical bulk Lorentz factor of several hundred, the dissipation radii of GRBs need to be large to avoid overshooting the GeV gamma-ray flux during the prompt emission phase of GRBs, which can be used to constrain GRBs.