Temperature dependence of Quark and Gluon condensate In The Dyson-Schwinger Equations At Finite Temperature

Abstract

Based on the Dyson-Schwinger Equations (DSEs) with zero- and finite temperature, the two quark condensate, the four quark condensate and quark gluon mixed condensate in non-perturbative QCD state are investigated by solving the DSEs respectively at zero and finite temperature. These condensates are important input parameters in QCD sum rule with zero and finite temperature and properties of hadronic study. The calculated results manifest that the three condensates are almost independent of the temperature below the critical point temperature $T_{c}$. The results also show that the chiral symmetry restoration is obtained above $T_{c}$. At the same time, we also calculate the ratio of the quark gluon mixed condensate to the two quark condensate which could be quark virtuality. The calculations show that the ratio $m^{2}_{0}(T)$ is almost flat in the region of temperature from $0$ to $T_{c}$, although there are drastic changes of the quark condensate and the quark gluon mixed condensate at this region of $T_{c}$.The predicted ratio comes out to be $m^{2}_{0}(T)= 2.41GeV^{2}$ for vacuum state at the Chiral limit, which suggests the significance that the quark gluon mixed condensate has played in OPE.