Pseudo-scalar mesons at finite temperatures from a Dyson-Schwinger-Bethe-Salpeter approach

The truncated Dyson-Schwinger–Bethe-Salpeter equations are employed at non-zero temperature. The truncations refer to a rainbow-ladder approximation augmented with an interaction kernel which facilitates a special temperature dependence. At low temperatures, T → 0, we recover a quark propagator from the Dyson-Schwinger (gap) equation smoothly interpolating to the T = 0 results. Utilizing that quark propagator we evaluate the Bethe-Salpeter vertex function in the pseudo-scalar qq channel for the lowest boson Matsubara frequencies and find a competition of qq bound states and quasi-free two-quark states at T = O (100 MeV).