Thermodynamic Limit in High-Multiplicity Proton-Proton Collisions at s=7 TeV

Natasha Sharma,Jean Cleymans,Boris Hippolyte

doi:10.1155/2019/5367349

Abstract

An analysis is made of the particle composition in the final state of proton-proton (pp) collisions at 7 TeV as a function of the charged particle multiplicity (dNch/dη). The thermal model is used to determine the chemical freeze-out temperature as well as the radius and strangeness suppression factor γs. 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 dNch/dη is larger than twenty per unit of rapidity, corresponding to about 300 particles in the final state when integrated over the full rapidity interval.

Highlights

In statistical mechanics the thermodynamic limit is the limit in which the total number of particles N and the volume V become large but the ratio N/V remains finite and results obtained in the microcanonical, canonical, and grand canonical ensembles become equivalent
In this paper we argue that this limit might be reached in high energy pp collisions if the total number of charged hadrons becomes larger than 20 per unit of rapidity in the mid-rapidity region, corresponding to roughly 300 particles in the final state when integrated over the full rapidity interval
In this paper we have investigated three different ensembles to analyze the variation of particle yields with the multiplicity of charged particles produced in proton-proton collisions at the center-of-mass energy of √s = 7 TeV

Summary

Introduction

In statistical mechanics the thermodynamic limit is the limit in which the total number of particles N and the volume V become large but the ratio N/V remains finite and results obtained in the microcanonical, canonical, and grand canonical ensembles become equivalent. In this paper we argue that this limit might be reached in high energy pp collisions if the total number of charged hadrons becomes larger than 20 per unit of rapidity in the mid-rapidity region, corresponding to roughly 300 particles in the final state when integrated over the full rapidity interval. In high energy collisions applications of the statistical model in the form of the hadron resonance gas model have been successful [5, 6] in describing the composition of the final state, e.g., the yields of pions, kaons, protons, and other hadrons In these descriptions use is made of the grand canonical ensemble and the canonical ensemble with exact strangeness conservation. A similar analysis was done in [14–16] for pp collisions at 200 GeV but without the dependence on charged multiplicity

Comparison of Different Statistical Ensembles

Discussion and Conclusions