%A Si-Xue Qin and Craig D. Roberts %T Resolving the Betheā€“Salpeter Kernel %0 Journal Article %D 2021 %J Chin. Phys. Lett. %R 10.1088/0256-307X/38/7/071201 %P 071201%V 38 %N 7 %U {https://cpl.iphy.ac.cn/CN/abstract/article_105942.shtml} %8 2021-06-04 %X 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, $\varGamma$. Applicable even when the diagrammatic content of $\varGamma$ 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 $\varGamma$, 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.