Resolving The Bethe-Salpeter Kernel

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, Gamma. Applicable even when the diagrammatic content of Gamma 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 Gamma, 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.