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We propose a nonperturbative resummation scheme for the four-point connected quark-antiquark Green’s functionG4 that shows how the Bethe-Salpeter equation may be “unquenched” with respect to quark-antiquark loops. This mechanism allows to dynamically account for hadronic meson decays and multiquark structures whilst respecting the underlying symmetries. An initial approximation to the four-point Schwinger-Dyson equation - suitable for phenomenological application - is examined numerically in a couple of aspects. It is demonstrated that this approximation explicitly maintains the correct asymptotic limits and contains the physical resonance structures in the near timelike region in the quark-antiquark channel. [ABSTRACT FROM AUTHOR]

The effect of quark-gluon vertex dressing on the ground-state masses of theu/d-quark pseudoscalar, vector and axialvector mesons is considered with the Dyson-Schwinger equations. This extends the ladder-rainbow Bethe-Salpeter kernel to two-loops. To render the calculations feasible for this exploratory study, we employ a simple infrared dominant model for the gluon exchange that implements the vertex dressing. The resulting model, involving two distinct representations of the effective gluon exchange kernel, preserves both the axial-vector Ward-Takahashi identity and charge conjugation symmetry. Numerical results confirm that the pseudoscalar meson retains its Goldstone boson character. The vector meson mass, already at a very acceptable value at ladder level, receives only 30?MeV of attraction from this vertex dressing. For the axial-vector states, which are about 300?MeV too low in ladder approximation, the results are mixed: The 1+- state receives 290?MeV of repulsion, but the 1++ state is lowered further by 30?MeV. The exotic channels 0-- and 1-+ are found to have no states below 1.5?GeV in this model. [ABSTRACT FROM AUTHOR]