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

We investigate the quark-gluon mixed condensate 〈q¯σ⋅Gq〉≡m02〈q¯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, i.e. the second-order and crossover chiral phase transitions for the zero and finite current-quark masses, respectively. We also perform the two-loop renormalization-group (RG) evolution for the both condensates by increasing the renormalization scale μ=(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 −〈q¯σ⋅Gq〉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 m02 is almost flat below the chiral transition T (T0), and increases rapidly beyond it. From a simple linear parametrization, we obtain m02(T)/m02(0)≈(0.07,0.47)T/T0+(1,0.6) for (T≲T0,T≳T0) at μ=0.6GeV. The present results are compared with other theoretical ones including the lattice QCD simulations, and show qualitatively good agreement with them.