Abstract.
The effect of quark-gluon vertex dressing on the ground-state masses of the u/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.
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Watson, P., Cassing, W. & Tandy, P. Bethe-Salpeter Meson Masses Beyond Ladder Approximation. Few-Body-Systems 35, 129–153 (2004). https://doi.org/10.1007/s00601-004-0067-x
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DOI: https://doi.org/10.1007/s00601-004-0067-x