Transverse momentum spectra of strange hadrons within extensive and nonextensive statistics

TL;DR

This study compares extensive and nonextensive statistical models in analyzing strange hadron transverse momentum spectra across different collision systems and energies, revealing how system size and energy influence statistical behavior and freezeout conditions.

Contribution

It introduces a generic (non)extensive statistical framework and compares its fit parameters with Tsallis and Boltzmann statistics, highlighting differences and system dependencies.

Findings

Large mass and strange quantum number particles freeze out earlier.

System approaches equilibrium with increasing energy and centrality.

Boltzmann statistics becomes suitable at high energies and large systems.

Abstract

Using generic (non)extensive statistics, in which the underlying system autonomously manifests its extensive and nonextensive statistical nature, we extract various fit parameters from the CMS experiment and compare these to the corresponding results obtained from Tsallis and Boltzmann statistics. The present study is designed to indicate the possible variations between the three types of statistical approaches and characterizes their dependence on collision energy, multiplicity, and size of the system of interest. We analyze the transverse momentum spectra $p_T$ of the strange hadrons \Kslxi produced in Pb+Pb collisions, at 2.76 TeV, in p+Pb collisions, at 5.02 TeV, and in $p+p$ collisions, at 7 TeV. From the comparison of the resulting fit parameters; temperature $T$, volume $V$, and nonextensvie parameter $d$, with calculations based on Tsallis and Boltzmann statistics, remarkable differences between the three types of statistics are determined besides a strong dependence on size and type of the colliding system. We conclude that the produced particles with large masses and large strange quantum numbers likely freeze out earlier than the ones with smaller masses and less strange quantum numbers. This conclusion seems not depending on the type of the particle or the collision but apparently manifesting transitions from chemical (larger temperature) to the kinetic freezeouts (lower temperature). For the first university (equivalent) class c=1, the decrease in the second one, $d$, with increasing energy and collision centrality highlights that the system departs from nonextensivity (non-equilibrium) and apparently approaches extensivity (equilibrium) indicating that the Boltzmann statistics becomes the proper statistical approach in describing that system. Last but not least, we present analytical expressions for the energy dependence of the various fit parameters.