New closed expression of the interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states

TL;DR

This paper derives a new explicit closed-form expression for the interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states, based on QCD, facilitating both perturbative and nonperturbative studies.

Contribution

It presents a novel, explicit expression for the interaction kernel in the Bethe-Salpeter equation derived directly from QCD, applicable to different-flavor quark-antiquark pairs.

Findings

The kernel is expressed in terms of propagators and vertices, revealing its specific structure.

The expression is suitable for both perturbative and nonperturbative calculations.

It provides a practical tool for studying quark-antiquark bound states.

Abstract

The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived newly from QCD in the case where the quark and the antiquark are of different flavors. The technique of the derivation is the usage of the irreducible decomposition of the Green's functions involved in the Bethe-Salpeter equation satisfied by the quark-antiquark four-point Green's function. The interaction kernel derived is given a closed and explicit expression which shows a specific structure of the kernel since the kernel is represented in terms of the quark, antiquark and gluon propagators and some kinds of quark, antiquark and/or gluon three, four, five and six-point vertices. Therefore, the expression of the kernel is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.