Evolution of the underlying event and non-extensive thermodynamics in pp collisions from RHIC to LHC energies

Abstract

We investigate the geometrical and thermodynamical aspects of particle production in pp collisions over a broad center-of-mass energy, ranging from $\sqrt{s}=62.4$ GeV to 13 TeV using PYTHIA8. We study the azimuthal dependence of charged-particle production relative to the leading particle. This includes the study of the Tsallis--Pareto parameters extracted from the charged-particle transverse-momentum spectra in fixed $Δϕ$ intervals relative to the leading charged particle. The simultaneous analysis of charged-particle multiplicity and event topology demonstrates that the underlying event (UE) dominated region can be extended beyond the conventional transverse side region across RHIC and LHC energies. To further disentangle effects from soft and hard particle production mechanisms, the study is performed in different transverse spherocity and charged-particle flattenicity classes. We demonstrate that the UE region extends beyond the conventional transverse region, validating an enlarged angular interval of $40^\circ\lesssim|Δϕ|\lesssim140^\circ$ from RHIC to LHC energies. Event-shape selections reveal that jetty events consistently exhibit larger $q$ and lower $T_{\rm s}$ than isotropic events. The $Δϕ$ profiles of charged-particle multiplicity and transverse spherocity remain universal in shape across collision energies despite the strong increase in overall event activity, whereas the Tsallis parameters retain a residual, leading-particle-driven energy dependence in the near- and away-side regions.