Revisiting the soft-hard separation in the transverse momentum spectra of $pp$ collisions

Abstract

We study the separation of soft and hard components in the transverse momentum spectra of charged particles as measured by ALICE in proton-proton collisions at $\sqrt{s}$ = 2.76, 5.02 and 13 TeV at the LHC. The soft component is described by a Boltzmann fit, while the residual spectra are identified as a hard QCD-like fragmentation contribution. After separation, the subtracted spectra show no significant evolution in shape or peak position with multiplicity, consistent with a two-component interpretation. Mean transverse momenta for both contributions remain nearly constant across multiplicity classes, while Pythia 8 Monte Carlo simulations confirm these trends. The robustness of the decomposition is demonstrated by a comparison between simulations with and without color reconnection, yielding consistent results. The terms `soft' and `hard' are used as operational labels within this framework and should not be interpreted as uniquely identified dynamical components. Our results are consistent with the two-component description as a viable and physically motivated alternative to hydrodynamical interpretations.