Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature**Supported by National Natural Science Foundation of China (11365002), Guangxi Natural Science Foundation for Young Researchers (2013GXNSFBB053007, 2011GXNSFA018140), Guangxi Education Department (2013ZD049), Guangxi Grant for Excellent Researchers (2011-54), and Guangxi University of Science and Technology Foundation for PhDs (11Z16)

Li-Juan Zhou,Bo Zheng,Wei-Xing Ma,Hong-Wei Zhong

doi:10.1088/1674-1137/39/3/033101

Abstract

Based on the Dyson-Schwinger Equations (DSEs), the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated by solving the DSEs with rainbow truncation at zero- and finite- temperature, respectively. These condensates are important input parameters in QCD sum rule with zero and finite temperature, and in studying hadron physics, as well as predicting the quark mean squared momentum m20- also called quark virtuality in the QCD vacuum state. The present calculated results show that these physical quantities are almost independent of the temperature below the critical point temperature Tc = 131 MeV, and above Tc the chiral symmetry is restored. For comparison we calculate the temperature dependence of the “in-hadron condensate” for pion. At the same time, we also calculate the ratio of the quark gluon mixed vacuum condensate to the two-quark vacuum condensate by using these condensates, and the unknown quark mean squared momentum in the QCD vacuum state has been obtained. The results show that the ratio m20(T) is almost flat in the temperature region from 0 to Tc, although there are drastic changes of the quark vacuum condensate and the quark gluon mixed vacuum condensate at the region. Our predicted ratio comes out to be m20(T)=2.41 GeV2 at the Chiral limit, which is consistent with other theory model predictions, and strongly indicates the significance that the quark gluon mixed vacuum condensate has played in the virtuality calculations.

Highlights

With the development of heavy-ion collision experiments, more attentions have been turning to exploring the hot and dense QCD matter
The hot and dense matter can be studied via various approaches, such as: lattice QCD, QCD sum rules, Chiral perturbation theory as well as the Dyson-Schwinger equations (DSEs) and so on
Due to the asymptotic freedom feature of QCD, the QCD matter will take place a phase transition from hadronic phase, with quarks and gluons being bound states inside hadron, to the quark gluon plasma phase where the bound clusters of quarks and gluons have been deconfined at sufficient high temperature and /or density

Summary

Introduction

With the development of heavy-ion collision experiments, more attentions have been turning to exploring the hot and dense QCD matter. The hot and dense matter can be studied via various approaches, such as: lattice QCD, QCD sum rules, Chiral perturbation theory as well as the Dyson-Schwinger equations (DSEs) and so on. In QCD sum rules, various condensates are input parameters so that they play an important role to reproduce various hadronic properties phenomenologically in the operator product expansion calculations (OPE)[1, 2, 3]. We study the DSEs at finite temperature by use of the separable model interactions. The main interesting of this work lies on the consideration of nonzero temperature, which allow to study the QCD phase diagram along the axis of zero chemical potential, including deconfinement and the chiral symmetry restoration

Dyson-Schwinger Equations at zero temperature

Extension to Finite temperature

Calculations and results