Resolving the Bethe–Salpeter Kernel

Abstract

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