Critical point and Bose-Einstein condensation in pion matter

V A Kuznietsov,O S Stashko,M I Gorenstein,O V Savchuk

doi:10.1103/physrevc.104.055202

Abstract

The Bose-Einstein condensation and the liquid-gas first order phase transition are studied in the interacting pion matter. Two phenomenological models are used: the mean-field model and the hybrid model. Free model parameters are fixed by fitting the lattice QCD data on the pion Bose condensate density at zero temperature. In spite of some minor differences the two model demonstrate an identical qualitative and very close quantitative behavior for the thermodynamic functions and electric charge fluctuations. A peculiar property of the considered models is an intersection of the Bose-Einstein condensation line and the line of the first order phase transition at the critical end point.

Highlights

The Bose statistics [1] and Bose-Einstein condensation (BEC) phenomenon [2] were predicted almost hundred years ago
The BEC can happen in condensed matter, nuclear physics, astrophysics, and cosmology
In most of these situations, particle interactions should be taken into account. If both the attractive and repulsive interactions between particles are taken into account, the system reveals the first-order liquid-gas phase transition (FOPT) and the critical endpoint (CP)

Summary

INTRODUCTION

The Bose statistics [1] and Bose-Einstein condensation (BEC) phenomenon [2] were predicted almost hundred years ago. The Bose condensate (BC) of pions was observed at low temperature, T < m, and large electric (isospin) chemical potential, m < μ < 2m, where m is the pion mass (in what follows we use an approximate value m = 140 MeV, neglecting a small difference between the masses of neutral and charged pions) In this specific region of the (μ, T ) phase diagram the QCD matter is expected in a form of the interacting pions. A description of the repulsive and attractive interaction in statistical systems of hadrons is often performed in terms of the following phenomenological approaches: Mean-field approximation, effective-mass model, excluded volume approximation, etc.

IDEAL PION GAS

Mean-field model

INTERACTING PION GAS

Hybrid model

Fluctuations of higher orders

SUMMARY