Extracting the kinetic freeze-out properties of high energy pp collisions at the LHC with event shape classifiers

TL;DR

The paper addresses how to extract kinetic freeze-out properties in high-energy pp collisions and disentangle MPI-driven fluctuations from genuine collectivity. It applies the Tsallis Blast-Wave model with independent meson/baryon non-extensive parameters to identified hadron $p_T$ spectra in pp collisions at $\sqrt{s}=13$ TeV across event-shape classes: relative transverse activity $R_T$, unweighted transverse spherocity $S_O^{p_T=1}$, and flattenicity $\rho$. The results show that the non-extensive parameters decrease as events become more isotropic or MPI-dominated, while the average radial flow velocity increases with event activity; the kinetic freeze-out temperature remains broadly constant, and the effective temperature rises due to flow. Flattenicity provides a particularly clean handle to separate soft MPI-driven dynamics from jet fragmentation, and the study reveals a universal trend in the $T$ vs $q-1$ plane across pp and PbPb, highlighting a common freeze-out physics in high-density QCD matter.

Abstract

Event shape measurements are crucial for understanding the underlying event and multiple-parton interactions (MPIs) in high energy proton-proton (pp) collisions. In this paper, the Tsallis Blast-Wave model with independent non-extensive parameters for mesons and baryons, was applied to analyze transverse momentum spectra of charged pions, kaons, and protons in pp collision events at $\sqrt{s}=13$ TeV classified by event shape estimators relative transverse event activity, unweighted transverse spherocity, and flattenicity. Our analysis reveals consistent trends in the kinetic freeze-out temperature and non-extensive parameter across different collision systems and event shape classes. The use of diverse event-shape observables in pp collisions has significantly expanded the accessible freeze-out parameter space, allowing for a more comprehensive exploration of its boundaries. Among these event shape classifiers, flattenicity emerges as a unique observable for disentangling hard process contributions from additive MPI effects, allowing the isolation of collective motion effects encoded by the radial flow velocity. Through the analysis of the interplay between event-shape measurements and kinetic freeze-out properties, we gain deeper insights into the mechanisms responsible for flow-like signatures in pp collisions.

Figures (10)

• Figure 1: The TBW4 fits to hadron spectra in pp collisions at $\sqrt{s}=$ 13 TeV. Black, red, and blue correspond to $\pi$, $K$, and $p$ particles, respectively. The points represent the ALICE experimental data ALICE:2023yuk, and the lines represent the fit results. From top to bottom, the rows represent the $R_T$ intervals of 0-0.5, 0.5-1.5, 1.5-2.5, and 2.5-5. From left to right, the columns represent the forward, backward, and transverse regions. The uncertainties in the experimental data are the quadratic sum of statistical and systematic errors.
• Figure 2: The deviations of TBW4 fits to hadron spectra divided by data uncertainties in pp collisions at $\sqrt{s}=$ 13 TeV. Black, red, and blue correspond to $\pi$, $K$, and $p$ particles, respectively. From top to bottom, the rows represent the $R_T$ intervals of 0-0.5, 0.5-1.5, 1.5-2.5, and 2.5-5. From left to right, the columns represent the forward, backward, and transverse regions. The dashed lines represent where the difference between model and experiment data is three times the error of data.
• Figure 3: The TBW4 fits to hadron spectra in pp collisions at $\sqrt{s}=$ 13 TeV. Black, red, and blue correspond to $\pi$, $K$, and $p$ particles, respectively. The points represent the ALICE experimental data ALICE:2023bga, and the lines represent the fit results.From left to right, the columns represent sphericity intervals of 0-100%, 0-10%, and 90-100%. The top row shows the $p_T$ spectra, and the uncertainties in the experimental data are the quadratic sum of statistical and systematic errors. The Bottom show the deviations from the $p_T$ fit, and the dashed lines indicate where the difference between the model and experimental data is three times the data's uncertainty.
• Figure 4: The TBW4 fits to hadron spectra in pp collisions at $\sqrt{s}=$ 13 TeV. Black, red, and blue correspond to $\pi$, $K$, and $p$ particles, respectively. The points represent the ALICE experimental data ALICE:2024vaf, and the lines represent the fit results. From panel (a) to (h), the results of different flattenicity event classes for multiplicity-integrated events (V0M percentile $0–100\%$) are presented. The uncertainties in the experimental data are the quadratic sum of statistical and systematic errors.
• Figure 5: The deviations of TBW4 fits to hadron spectra divided by data uncertainties in pp collisions at $\sqrt{s}=$ 13 TeV. Black, red, and blue correspond to $\pi$, $K$, and $p$ particles, respectively. From From panel (a) to (h), the results of different flattenicity event classes for multiplicity-integrated events (V0M percentile $0–100\%$) are presented. The dashed lines represent where the difference between model and experiment data is three times the error of data.