Study of trijet production in proton-proton collisions at different energies

The 3-jet events produced from proton-proton collisions at center of mass energies [Formula: see text]13, 13.6, 14, 20, and 27 TeV were considered. These energies match those of the Large Hadron Collider, both present and maybe future energies, we require one jet to exist in the central pseudorapidity region [Formula: see text] and two jets in a forward (same hemisphere) region [Formula: see text]. We compare the predictions of PYTHIA, HERWIG++, and SHERPA, among other Monte Carlo Event Generators. We examine the distributions of the jets' transverse momentum, jet multiplicity, azimuthal angle, and pseudorapidity. We also examine the distribution of azimuthal angle differences between the center jet and the forward dijet system. We compared PYTHIA8 predictions with CMS data at [Formula: see text]TeV for dijet azimuthal angle differences ([Formula: see text]). The cross section rises with [Formula: see text] and peaks near π, reflecting momentum conservation in hard scattering. The relevant Rivet analysis code was used to obtain the results. Three event generators are examined in the study, and the results show both similarities and variations in their predictions. All three generators agree at low jet multiplicities. There are differences at greater multiplicities when the collision energies rise: HERWIG's predictions rise while PYTHIA8's fall in comparison to SHERPA. Other investigations show similar patterns, with generators agreeing in some regions (like central η distributions) but diverging in others (like high/low η or high [Formula: see text]). These differences are likely due to the underlying theoretical models used by each generator. The results obtained emphasize the significance of generator-specific tuning for precision QCD research and new physics investigations at existing and future colliders.