Determination of the chemical potential in the Tsallis distribution at LHC energies

TL;DR

This paper analyzes the chemical potentials at kinetic freeze-out in LHC proton-proton collisions using the Tsallis distribution, revealing thermal equilibrium at kinetic freeze-out but not at chemical freeze-out.

Contribution

It introduces a method to determine chemical potentials at kinetic freeze-out in high-energy collisions within the Tsallis framework, improving analysis accuracy.

Findings

Temperature and volume are consistent across particle types at each energy.

Chemical potentials differ significantly among particles, indicating non-chemical equilibrium.

The Tsallis distribution effectively describes the thermodynamics of high-energy collision freeze-out.

Abstract

The transverse momentum distributions measured in $p-p$ collisions at the LHC determine the kinetic freeze-out stage of the collision. The parameters deduced from these distributions differ from those determined at chemical freeze-out. The present investigation focuses on the chemical potentials at kinetic freeze-out, these are not necessarily zero as they are at chemical freeze-out, the only constraint is that they should be equal for particles and antiparticles at LHC energies. The thermodynamic variables are determined in the framework of the Tsallis distribution. The chemical potentials in the Tsallis distribution analysis of $p-p$ collisions at four different LHC energies have correctly been taken into account. This leads to a much more satisfactory analysis of the various parameters and confirms the usefulness of the Tsallis distribution in high-energy collisions. In particular we find that the temperature $T$ and the volume $V$ at each beam energy are the same for all particle types considered (pions, kaons and protons). The chemical potentials for these particles are however very different. Hence we conclude that there is evidence for thermal equilibrium at kinetic freeze-out, albeit in the sense of the Tsallis distribution and there is no evidence for chemical equilibrium at the final stage of the collision.