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Bethe-Salpeter Meson Masses Beyond Ladder Approximation
High Energy Physics - Phenomenology · Submitted 30 Jun 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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 2-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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.96 | 0.82 | 0.06 | asserted 0.88 |
| s1 | This extends the ladder-rainbow Bethe-Salpeter kernel to 2-loops. | contribution 0.89 | 0.87 | 0.05 | asserted 0.99 |
| s2 | 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. | method 0.92 | 0.87 | 0.03 | asserted 0.99 |
| s3 | 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. | method 0.79 | 0.89 | 0.08 | asserted 1.00 |
| s4 | Numerical results confirm that the pseudoscalar meson retains its Goldstone boson character. | result 0.81 | 0.92 | 0.19 | asserted 1.00 |
| s5 | The vector meson mass, already at a very acceptable value at ladder level, receives only 30 MeV of attraction from this vertex dressing. | result 1.00 | 0.91 | 0.13 | asserted 1.00 |
| s6 | 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. | result 1.00 | 0.95 | 0.21 | asserted 1.00 |
| s7 | The exotic channels $0^{--}$ and $1^{-+}$ are found to have no states below 1.5 GeV in this model. | result 1.00 | 0.96 | 0.11 | asserted 1.00 |
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Original 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 2-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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References
How the literature uses it
13 arXiv papers cite this in 24 sentences
Papers citing it · 16 sentences without a confident label
Compares with it 1 paper
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The result of our Abelian correction can be directly compared with the study of [ref] .
Bethe-Salpeter studies of mesons beyond rainbow-ladder · Results · 1.00
Cites it as background 3 papers
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While there have been several studies attempting to improve upon this simplest of all truncations, in the form of including unquenching effects due to quarks, e.g. [ref] , we here take a different viewpoint.
Pion-cloud effects in the BSE description of mesons · Introduction · 0.86
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Beyond this approximation, models with dressed vertex contributions [ref] and unquenching effects [ref] have been considered, and more sophisticated numerical methods to solve both the homogeneous and the inhomogeneous equation have been recently developed [ref] .
Higher order heavy quark Green's functions in Coulomb gauge · Introduction · 0.80
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Beyond this approximation, models with dressed vertex contributions [ref] and unquenching effects [ref] have been considered, and more sophisticated numerical methods to solve both the homogeneous and the inhomogeneous equation have been recently developed [ref] .
Quark sector of Coulomb gauge Quantum Chromodynamics · Faddeev equation for baryons · 0.86
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