Thermodynamic limit in high-multiplicity $pp$ collisions at $\sqrt{s}$ = 7 TeV

TL;DR

This paper investigates the particle composition in high-multiplicity proton-proton collisions at 7 TeV, demonstrating that at high multiplicities, the system approaches the thermodynamic limit, allowing for thermal model analysis to be valid.

Contribution

It shows that high-multiplicity $pp$ collisions can reach the thermodynamic limit, validating the use of thermal models in such small systems at high multiplicities.

Findings

At high multiplicity, different statistical ensembles converge to the same results.

Thermodynamic limit in $pp$ collisions is approached when $dN_{ch}/d a$ exceeds 20.

Final states with about 300 particles can reach thermodynamic equilibrium.

Abstract

An analysis is made of the particle composition in the final state of $pp$ collisions at 7 TeV as a function of the charged particle multiplicity ($dN_{ch}/d\eta$). The thermal model is used to determine the chemical freeze-out temperature as well as the radius and strangeness suppression factor $\gamma_s$. Three different ensembles are used in the analysis. The grand canonical ensemble, the canonical ensemble with exact strangeness conservation and the canonical ensemble with exact baryon number, strangeness and electric charge conservation. It is shown that for the highest multiplicity class the three ensembles lead to the same result. This allows us to conclude that this multiplicity class is close to the thermodynamic limit. It is estimated that the final state in $pp$ collisions could reach the thermodynamic limit when $dN_{ch}/d\eta$ is larger than twenty per unit of rapidity, corresponding to about 300 particles in the final state when integrated over the full rapidity interval.