Comparison of Tsallis statistics with the Tsallis-factorized statistics in the ultrarelativistic $pp$ collisions

TL;DR

This paper compares the Tsallis and Tsallis-factorized statistics in describing transverse momentum distributions of hadrons in high-energy proton-proton collisions, highlighting their agreement at different energy regimes.

Contribution

It provides a detailed comparison between Tsallis and Tsallis-factorized statistics, clarifying their applicability and differences across energy ranges in high-energy collisions.

Findings

Tsallis-factorized statistics deviates from Tsallis statistics at low energies near unity entropic parameter.

At higher energies, Tsallis-factorized statistics closely matches Tsallis statistics.

The study clarifies the conditions under which each statistical approach is valid.

Abstract

The Tsallis statistics was applied to describe the experimental data on the transverse momentum distributions of hadrons. We considered the energy dependence of the parameters of the Tsallis-factorized statistics, which is now widely used for the description of the experimental transverse momentum distributions of hadrons, and the Tsallis statistics for the charged pions produced in $pp$ collisions at high energies. We found that the results of the Tsallis-factorized statistics deviate from the results of the Tsallis statistics only at low NA61/SHINE energies when the value of the entropic parameter is close to unity. At higher energies, when the value of the entropic parameter deviates essentially from unity, the Tsallis-factorized statistics satisfactorily recovers the results of the Tsallis statistics.