Finite T meson correlations and quark deconfinement

The finite temperature spatial (q) over barq correlation modes in the pi and rho channels are studied with the rainbow-ladder truncated quark Dyson-Schwinger equation and Bethe-Salpeter equation in the Matsubara formalism. To retain the finite range of the effective interaction while facilitating summation over fermion Matsubara modes necessary to ensure continuity at T = 0, a separable kernel is used. The model is fixed by T = 0 properties and it implements dynamical chiral symmetry breaking and quark confinement. Transition temperatures for deconfinement (T-d) and chiral restoration (T-c) are identified. Above and below these transitions we study M-pi(T), f(pi),(T) and the three-space transverse and longitudinal masses M-rho(T)(T) and M-rho(L)(T). We also study the intrinsic T-dependence of the electromagnetic coupling constant g(rho)(T) and the strong coupling constant g(rho pi pi)(T). For both this model and a related semi-analytic infrared dominant model, we analyze the high T behavior of the obtained masses in comparison to the M(T) --> 2 piT behavior found in lattice QCD simulations.