Pseudo-scalar qqbar bound states at finite temperatures within a Dyson-Schwinger-Bethe-Salpeter approach


Pseudo-scalar qqbar bound states at finite temperatures within a Dyson-Schwinger-Bethe-Salpeter approach

Dorkin, S. M.; Kaptari, L. P.; Kämpfer, B.

The combined 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 which delivers, e.g. mass functions B, quark renormalization wave function A, and two-quark condensate $\la q \bar q \ra$ smoothly interpolating to the T=0 results, despite the broken O(4) symmetry in the heat bath and discrete Matsubara frequencies. Besides the Matsubara frequency difference entering the interaction kernel, often a Debye screening mass term is introduced when extending the T=0 kernel to non-zero temperatures. At larger temperatures, however, we are forced to drop this Debye mass in the infra-red part of the longitudinal interaction kernel to keep the melting of the two-quark condensate in a range consistent with lattice QCD results. Utilizing that quark propagator for the first few hundred fermion Matsubara frequencies 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). This indication of pseudo-scalar meson dissociation below the anticipated QCD deconfinement temperature calls for an improvement of the approach, which is based on an interaction adjusted to the meson spectrum at T=0.

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Publ.-Id: 27767