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

TL;DR

This study examines the temperature dependence of the quark-gluon mixed condensate in SU(2) light-flavor QCD, revealing its role as a chiral order parameter and its behavior across the chiral transition, with results consistent with lattice QCD.

Contribution

It introduces a temperature-dependent analysis of the mixed condensate using caloron solutions and RG evolution, providing new insights into chiral restoration patterns.

Findings

Mixed condensate is insensitive to RG evolution.

Quark condensate increases significantly with RG scale.

The ratio m^2_0(T)/m^2_0(0) increases sharply beyond T_0.

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.