Statistical Properties of Prompt Emission and X-Ray Afterglow Plateau Emission of Gamma-Ray Bursts with Jet Features

Gamma-ray bursts (GRBs) are widely recognized to exhibit jet-like emission structures, though previous studies often assumed isotropic emission due to observational constraints. This assumption limited our understanding of the intrinsic properties of GRBs. Here, we analyze 40 GRBs with observed X-ray plateaus and jet features, all with measured redshifts. By applying jet corrections to prompt and plateau-phase quantities, we probe their intrinsic behavior. We find that the jet-corrected prompt emission energy (Ejet) depends less strongly on the jet-corrected X-ray luminosity at the end of the plateau (LX,jet). An anti-correlation is also observed between the jet opening angle (θjet) and the rest frame peak energy (Ep,z): Ep,z∝θjet−0.44±0.13 for ISM and Ep,z∝θjet−0.78±0.13 for wind environments, indicating that more collimated jets yield higher peak energies. After jet correction, the LX-Ta,z correlation and the three-parameter LX-Ta,z-Eγ,iso, LX-Ta,z-Lp and LX-Ta,z-Ep,z relations are generally weakened. Among these, the first three remain relatively stable, suggesting they reflect intrinsic GRB physics, whereas the LX-Ta,z-Ep,z relation weakens significantly, implying it may be an artifact of the isotropic assumption. We also identify a new three-parameter correlation: θjet(ISM)∝Ejet(ISM)0.36±0.06Ep,z−0.62±0.09, θjet(Wind)∝Ejet(Wind)0.29±0.09Ep,z−0.61±0.09.