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

TL;DR

The paper addresses whether proton-proton $p_T$ spectra can be understood via a two-component picture rather than hydrodynamics. It fits the soft part with a Boltzmann form $f(p_T)=A exp(-β p_T)$ and isolates the hard fragmentation component by subtracting this soft contribution, using a cut $p_0$ chosen so that $χ^2/ndf ≈ 1$. Across ALICE data at $√s=2.76$, 5.02, and 13$~$TeV, the soft and hard components show roughly constant means, while the total $⟨p_T⟩$ increases with multiplicity due to a larger hard-component weight. Pythia 8 Monash tune reproduces these trends, supporting the two-component interpretation as a robust alternative to hydrodynamic explanations in $pp$ 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 TeV, 5.02 TeV and 13 TeV at the LHC. The soft component is described by a Boltzmann fit, while the residual spectra are identified as hard QCD-like fragmentation. After separation, the subtracted spectra show no evolution in the shape or peak position with multiplicity, supporting a two-component interpretation. Mean transverse momenta for both contributions remain nearly constant, while Pythia 8 Monte Carlo simulations confirm these trends. Our results support the two-component description as a robust alternative to hydrodynamical interpretations.

Figures (4)

• Figure 1: The $\chi^2/\mathrm{ndf}$ values of the Boltzmann fits with respect to the cut parameter $p_0$ for ALICE pp collisions at $\sqrt{s} = 13$ TeV, shown for various multiplicity classes ALICE:2020nkc Vertical lines show the $p_0$ values for the highest and lowest multiplicities.
• Figure 2: Boltzmann-distribution fits shown on linear scale at $\sqrt{s} = 13$ TeV in pp collisions, for ALICE data in the (top) lowest and (bottom) highest multiplicity classes ALICE:2020nkc. Vertical lines indicate the obtained $p_0$ values for which $\chi^2/\mathrm{ndf} < 1.0$.
• Figure 3: Subtracted hadron spectra obtained by removing the fitted Boltzmann component from the ALICE data ALICE:2020nkc. The remaining spectra represent the fragmentation contribution in different multiplicity classes. Solid lines correspond to the original Boltzmann fits.
• Figure 4: The mean transverse momenta, $\langle p_{\rm T} \rangle$ obtained in the upper panel for the total spectra and in the lower panel the fragmentation and soft contributions from top to bottom, respectively, and as a function of charged particle multiplicity. Data points are taken from ALICE measurements at $\sqrt{s} = 2.76$ TeV, 5.02 TeV, and 13 TeV ALICE:2019dfiALICE:2015qqjALICE:2020nkc. The lines with uncertainty bands denote Pythia 8 predictions.