Bethe-Salpeter Meson Masses Beyond Ladder Approximation.

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]