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 rho-meson masses, that are changed little by including higher-order corrections. Repulsion generated by nonplanar diagrams in the vertex-consistent Bethe-Salpeter kernel for quark-quark scattering is sufficient to guarantee that diquark bound states do not exist.

16 pages, 12 figures, REVTEX4

References in corpus (19)

• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• The $\pi$, $K^{+}$, and $K^0$ electromagnetic form factors
• The Quark-Photon Vertex and the Pion Charge Radius
• Gluon propagators and quark confinement
• Nucleon mass and pion loops
• T-dependence of pseudoscalar and scalar correlations
• A Relativistic Quark Model for Mesons with an Instanton-Induced Interaction
• Describing a1 and b1 decays
• Diquarks: condensation without bound states
• Quark-Antiquark Bound States in the Relativistic Spectator Formalism
• Quark distrbutions in the nucleon based on a relativistic 3-body approach to the NJL model
• Dependence of the Chiral Symmetry Restoration Transition on the Quark Self-Energy Kernel
• K_{l3} transition form factors
• Quark-gluon vertex in a momentum subtraction scheme
• Continuum Strong QCD: Confinement and Dynamical Chiral Symmetry Breaking
• Instantaneous Bethe-Salpeter Equation: Analytic Approach for Nonvanishing Masses of the Bound-State Constituents
• Mesons as Bound States of Confined Quarks: Zero and Finite Temperature

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