Transverse momentum fluctuation under the Tsallis distribution at high energies

TL;DR

This study investigates how the Tsallis distribution influences transverse momentum fluctuations in high energy collisions, revealing dependence on distribution form, entropic parameter, and expectation value definitions.

Contribution

It introduces a comparison of fluctuation behavior under Boltzmann-Gibbs and Tsallis statistics in high energy physics, highlighting the impact of the entropic parameter and distribution form.

Findings

Fluctuation depends on the distribution form and weakly on expectation value definition.

Fluctuation increases with the Tsallis entropic parameter.

Variation of fluctuation is larger under Boltzmann-Gibbs expectation than Tsallis expectation across $ta$.

Abstract

We studied the effects of the Tsallis distribution on the transverse momentum fluctuation in high energy collisions. The parton-hadron duality and the Bose-Einstein type correlation between partons were assumed. The fluctuation was calculated in the boost-invariant picture for the expectation value used in the Boltzmann-Gibbs statistics and for the expectation value used in the Tsallis nonextensive statistics. It was shown that the fluctuation is a function of $\eta$ which is the ratio of the inverse temperature to the correlation length. We found the following points: (1) the fluctuation depends on the form of the distribution and depends weakly on the definition of the expectation value used in the statistics,(2) the fluctuation increases as the entropic parameter value of the Tsallis distribution increases, and (3) the variation of the fluctuation as a function of the entropic parameter for the expectation value used in the Boltzmann-Gibbs statistics is larger than that for the expectation value used in the Tsallis nonextensive statistics in the wide range of $\eta$.