Kinetic Freeze-Out Properties from Transverse Momentum Spectra of Pions in High Energy Proton-Proton Collisions

Li-Li Li,Fu-Hu Liu

doi:10.3390/physics2020015

Abstract

Transverse momentum spectra of negative and positive pions produced at mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton collisions over a center-of-mass energy, s , range from a few GeV to above 10 TeV are analyzed by the blast-wave fit with Boltzmann (Tsallis) distribution. The blast-wave fit results are well fitting to the experimental data measured by several collaborations. In a particular superposition with Hagedorn function, both the excitation functions of kinetic freeze-out temperature ( T 0 ) of emission source and transverse flow velocity ( β T ) of produced particles obtained from a given selection in the blast-wave fit with Boltzmann distribution have a hill at s ≈ 10 GeV, a drop at dozens of GeV, and then an increase from dozens of GeV to above 10 TeV. However, both the excitation functions of T 0 and β T obtained in the blast-wave fit with Tsallis distribution do not show such a complex structure, but a very low hill. In another selection for the parameters or in the superposition with the usual step function, T 0 and β T increase generally quickly from a few GeV to about 10 GeV and then slightly at above 10 GeV, there is no such the complex structure, when also studying nucleus-nucleus collisions.

Highlights

Chemical and thermal or kinetic freeze-outs are two of important stages of system evolution in high energy collisions
The closed and open symbols presented in panels (a)–(e) represent the data of π − and π + measured by the NA61/SHINE [24], PHENIX [25], STAR [6], ALICE [26], and CMS [27,28] Collaborations, respectively, where in panel (a) only the spectra of π − are available, and panel (c) is for NSD events and other panels are for INEL events
The pp collisions are divided on the multiplicity classes in experiments on the Large Hadron Collider (LHC), we have used the minimum-bias INEL events [26,27,28] which can be regarded as the combination of the events in different multiplicity classes with different yields

Summary

Introduction

Chemical and thermal or kinetic freeze-outs are two of important stages of system evolution in high energy collisions. To describe different excitation degrees of interacting system at the two stages, one can use chemical and kinetic freeze-out temperatures respectively. At the stage of chemical freeze-out, the ratios of different types of particles are no longer changed, and the chemical freeze-out temperature can be obtained from the ratios of different particles in the framework of thermal model [1,2,3]. At the stage of kinetic freeze-out, the transverse momentum spectra of different particles are no longer changed, and the dissociation temperature [4] or kinetic freeze-out temperature can be obtained from the transverse momentum spectra according to the hydrodynamical model [4]. The random thermal motion and transverse flow reflect the excitation and expansion degrees of the interacting system (or emission source) respectively.

Objectives

Results

Conclusion