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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  qq̅  channel for the lowest boson Matsubara frequencies and find a competition of  qq̅  bound states and quasi-free two-quark states at  T  =  O  (100 MeV).

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