Ghost and gluon propagators at finite temperatures within a rainbow truncation of Dyson–Schwinger equations

The finite-temperature behavior of ghost and gluon propagators is investigated within an approach based on the rainbow truncated Dyson–Schwinger equations in Landau gauge. In Euclidean space, within the Matsubara imaginary-time formalism, the gluon propagator is no longer an $O(4)$ symmetric function and possesses a discrete spectrum of the fourth momentum component. This leads to a different treatment of the transversal and longitudinal (with respect to the heat bath) parts of the propagator. Correspondingly, the gluon Dyson–Schwinger equation splits also into two parts. The resulting system of coupled equations is considered within the rainbow approximation and solved numerically. The solutions for the ghost and gluon propagators are obtained as functions of the temperature $T$, Matsubara frequency ${{\Omega }_{n}}$ and three-momentum squared ${{{\mathbf{k}}}^{2}}$. The effective parameters of the approach are taken from our previous fit of the corresponding Dyson–Schwinger solution to the lattice QCD data at zero temperature. It is found that, for zero Matsubara frequency, the dependence of the ghost and gluon dressing functions on ${{{\mathbf{k}}}^{2}}$ are not sensitive to the temperature $T$, while at ${{{\mathbf{k}}}^{2}} = 0$ their dependence on $T$ is quite strong. Dependence on the Matsubara frequency ${{\Omega }_{n}}$ is investigated as well.