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

Abstract We investigate the quark–gluon mixed condensate 〈 q ¯ σ ⋅ G q 〉 ≡ m 0 2 〈 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 ⋅ 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 0 2 is almost flat below the chiral transition T ( T 0 ), and increases rapidly beyond it. From a simple linear parametrization, we obtain m 0 2 ( T ) / m 0 2 ( 0 ) ≈ ( 0.07 , 0.47 ) T / T 0 + ( 1 , 0.6 ) for ( T ≲ T 0 , T ≳ T 0 ) at μ = 0.6 GeV . The present results are compared with other theoretical ones including the lattice QCD simulations, and show qualitatively good agreement with them.