Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature

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 m₀²-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 T_c=131 MeV, and above T_c 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 m₀²(T) is almost flat in the temperature region from 0 to T_c, 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 m₀²(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.