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

Abstract

We investigate the quark-gluon mixed condensate qσ · Gq ≡ m 2 0 qq 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 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 − qσ ·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 m 2 0 is almost flat below the chiral transition T (T0), 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 /T0 + (1, 0.6) for (T T0, T T0) 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.