2002
DOI: 10.1103/physrevc.65.065203
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Bethe-Salpeter equation and a nonperturbative quark-gluon vertex

Abstract: A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic content is enumerable. We illustrate that fact using a vertex obtained via the complete resummation of dressed-gluon ladders. While this vertex is planar, the vertex-consistent kernel is nonplanar and that is true for any dressed vertex. In an exemplifying model the rainbow-ladder truncation of the gap and Bethe-Salpeter equations yields many results; e.g., pi- and… Show more

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Cited by 177 publications
(370 citation statements)
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References 47 publications
(63 reference statements)
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“…In these channels it can be seen algebraically that contributions beyond rainbow-ladder largely cancel between themselves owing to Eq. (24) [12,14,42,63]. The remaining columns in the table deserve special attention because they show clearly the path toward improvement.…”
Section: Meson Spectroscopymentioning
confidence: 99%
“…In these channels it can be seen algebraically that contributions beyond rainbow-ladder largely cancel between themselves owing to Eq. (24) [12,14,42,63]. The remaining columns in the table deserve special attention because they show clearly the path toward improvement.…”
Section: Meson Spectroscopymentioning
confidence: 99%
“…Exploratory lattice results are available in the quenched approximation [223], with unquenched updates under way. In the DSE framework the quark-gluon vertex has been tackled with three different strategies: (i) nonperturbative ansätze for selected tensor structures, constructed along continuations of resummed perturbation theory into the infrared and supplemented with information from the Slavnov-Taylor identities [189,222,[242][243][244][245][246][247]; (ii) explicit solutions of approximated Slavnov-Taylor identities [207]; and (iii) numerical solutions of truncations of the quark-gluon vertex DSE and FRGE [209,213,215,[248][249][250][251][252][253][254][255][256]. At least on a quantitative level the results from these approaches are not in very good agreement with each other.…”
Section: Munczek-nemirovsky Modelmentioning
confidence: 99%
“…Recent efforts have been made to perform calculations of meson masses beyond ladder-rainbow truncation [8,9,10]. These studies employ a quark-gluon vertex that is dressed by certain classes of diagrams constructed from 2-point gluon functions…”
Section: Introductionmentioning
confidence: 99%
“…In our previous work with the most general vertex dressing scheme to date [10], we extended the ladder-summed approximation of Refs. [8,9] (Fig. 1a) to self-consistently include the dressing of internal vertices (Figs.…”
Section: Introductionmentioning
confidence: 99%
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