Quark-gluon mixed condensate for the SU(2) light-flavor sector at finite temperature

Abstract

We investigate the quark-gluon mixed condensate <qbar sigma*G q> m^2_0 = <qbar q> for the SU(2) light-flavor sector at finite temperature (T). Relevant model parameters, such as the average (anti)instanton size, inter-(anti)instanton distance, and constituent-quark mass at zero virtuality, are modified as functions of T, employing the trivial-holonomy caloron solution. By doing that, we observe correct chiral restoration patterns depending on the current-quark mass m. We also perform the two-loop renormalization-group (RG) evolution for the both condensates by increasing the renormalization scale mu=(0.6~2.0) GeV. It turns out that the mixed condensate is insensitive to the RG evolution, whereas the quark condensate become larger considerably by the evolution. Numerically, we obtain -<qbar sigma*G q>^1/5 = (0.45 ~ 0.46) GeV at T=0 within the present theoretical framework, and the mixed condensate plays the role of the chiral order parameter for finite T. The ratio of the two condensates m^2_0 is almost flat below the chiral transition T (T_0), and increases rapidly beyond it. From a simple linear parametrization, we obtain m^2_0(T)/m^2_0(0) ~ (0.07, 0.47) T/T_0 + (1,0.6) for (T<T_0, T>T_0) at mu=0.6 GeV. The present results are compared with other theoretical ones including the lattice QCD simulations, and show qualitatively good agreement with them.