Resolving the Bethe-Salpeter kernel

Abstract

A novel method for constructing a Bethe-Salpeter kernel for the meson bound-state problem is described. It produces a closed-form kernel that is symmetry-consistent (discrete and continuous) with the gap equation defined by any admissible gluon-quark vertex. Applicable even when the diagrammatic content of that vertex is unknown, the scheme can foster new synergies between continuum and lattice approaches to strong interactions. The framework is illustrated by demonstrating that the presence of a dressed-quark anomalous magnetic moment in the gluon-quark vertex, an emergent feature of strong interactions, can remedy many defects of widely used meson bound-state kernels, including the level ordering of pseudoscalar and vector meson radial excitations.

9 pages, 3 figures. Accepted for publication as an "Express Letter" in Chinese Physics Letters

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• Dynamical diquarks in the ${\mathbf{\gamma }}^{(\ast )}\mathbf{p}\to \mathbf{N}(1535){\frac{1}{2}}^{-}$ transition
• Pion charge radius from pion+electron elastic scattering data
• Hadron and light nucleus radii from electron scattering
• Nucleon axial form factor at large momentum transfers
• Artificial Dynamical Effects in Quantum Field Theory
• Quark anomalous magnetic moment and its effects on the $\rho$ meson properties
• The electromagnetic form factors of heavy-light pseudo-scalar and vector mesons
• Distribution amplitudes of light diquarks
• Composition of low-lying $\mathbf{J}={\frac{3}{2}}^{\pm }\mathbf{\Delta }$-baryons
• Light-front Wave Functions of Vector Mesons in an Algebraic Model
• Pauli radius of the proton
• The Podolsky propagator in gap and bound-state equations
• Chiral symmetry restoration and properties of Goldstone bosons at finite temperature
• New insight on the quark condensate beyond chiral limit
• Radially excited pion: electromagnetic form factor and the box contribution to the muon's $g-2$
• A correspondence between the free and interacting field theories
• Distribution amplitudes of heavy-light pseudo-scalar and vector mesons from Dyson-Schwinger equations framework
• Partial wave analysis for the in-hadron condensate
• Revealing pion and kaon structure via generalised parton distributions
• $D^{\ast }D\pi$ and $B^{\ast }B\pi$ couplings from Dyson-Schwinger equations framework
• Semileptonic transitions: $B_{(s)}\to \pi (K)$; $D_s\to K$; $D\to \pi ,K$; and $K\to \pi$
• Pion GPDs: A path toward phenomenology
• Linking continuum and lattice quark mass functions via an effective charge