Effect of event classification on the Tsallis-thermometer

TL;DR

This study investigates how event classification in ALICE pp collisions at $\sqrt{s}=13$ TeV shapes the Tsallis-thermometer parameters $T$ and $q$ by fitting identified-hadron spectra with the Tsallis-Pareto distribution. It finds that multiplicity and flattenicity preserve the expected $T$-scaling with particle density and show weak $q$ sensitivity, while transverse spherocity drives larger $q$ in jetty events, signaling geometry-driven non-extensivity. A data-driven parametrization reveals a proportional relation $\kappa = T/\langle p_T\rangle \approx 4.26 \pm 0.18$, enabling a simple estimate of the effective temperature from the mean transverse momentum and validating the $T$–$\langle p_T\rangle$ link across event classes. Overall, the Tsallis-thermometer proves effective at disentangling multiplicity and event-shape effects, linking soft and hard processes in small systems and suggesting applications to light-ion collisions near the QGP onset.

Abstract

We analyze identified hadron spectra in pp collisions at $\sqrt{s} = 13$ TeV measured by ALICE within a non-extensive statistical framework. Spectra classified by multiplicity, flattenicity, and spherocity were fitted with the Tsallis-Pareto distribution, and the parameters were studied on the Tsallis-thermometer. Multiplicity and flattenicity classes follow a previously observed scaling, while the non-extensivity parameter shows a distinct sensitivity to the spherocity. A data-driven parametrization confirms a proportionality between the Tsallis temperature and mean transverse momentum, offering a simple estimate of the effective temperature. These results highlight the ability of the Tsallis-thermometer to capture both multiplicity and event-shape effects, linking soft and hard processes in small systems.

Figures (5)

• Figure 1: Two-dimensional probability distributions of $N_\mathrm{ch}$--$(1-\rho)$ (left) and $N_\mathrm{ch}$--$S^{p_{\rm T}=1}_\mathrm{0}$ (right) from PYTHIA 8 simulations at $\sqrt{s}$=13 TeV.
• Figure 2: The Tsallis-thermometer for $\pi^\pm$, K$^\pm$, p and $\bar{\rm p}$ for ALICE pp collisions at $\sqrt{s}\xspace=13$ TeV depending on V0M, flattenicity and spherocity ALICE:2020nkcALICE:2024vafALICE:2023bga (opaque markers). The points are compared to data taken in Au--Au, pp, p--Pb and Pb--Pb collisions at lower center-of-mass energies Biro:2020kve (semi-transparent markers).
• Figure 3: Tsallis temperature (top) and non-extensivity (bottom) parameters as a function of ${\rm d}N_{\rm ch}/{\rm d}\eta$ based on V0M, flattenicity and spherocity-dependent data ALICE:2020nkcALICE:2024vafALICE:2023bga.
• Figure 4: Top: coefficient $\kappa$ for the various datasets (points) and the average with uncertainty (band). The boxes represent the fit results of the individual hadron species with uncertainties. Bottom: Tsallis temperature parameters as a function of ${\rm d}N_{\rm ch}/{\rm d}\eta$ based on V0M, flattenicity and spherocity-dependent data ALICE:2020nkcALICE:2024vafALICE:2023bga, compared to $\left<p_\mathrm{T}\xspace\right>\xspace/\kappa$ extracted with the data-driven method (solid line) and from PYTHIA 8 simulations (dotted line).
• Figure 5: The Tsallis-thermometer for $\pi^\pm$, K$^\pm$, p and $\bar{\rm p}$ for ALICE pp collisions at $\sqrt{s}\xspace=13$ TeV depending on V0M, flattenicity and spherocity ALICE:2020nkcALICE:2024vafALICE:2023bga (opaque markers), compared to Tsallis fit and a $\left<p_\mathrm{T}\xspace\right>$ fit calculations based on PYTHIA 8 (solid and dotted lines, respectively).