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

TL;DR

This paper derives an exact, explicit expression for the interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states, facilitating both perturbative and nonperturbative QCD studies.

Contribution

It provides a novel, closed-form expression for the Bethe-Salpeter kernel based on Green's functions derived from QCD, improving computational approaches.

Findings

Exact expression for the B-S kernel involving few Green's functions

Suitable for perturbative calculations

Applicable to nonperturbative QCD investigations

Abstract

The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived from the Bethe-Salpeter equations satisfied by the quark-antiquark four-point Green's function. The latter equations are established based on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green's function and some other kinds of Green's functions which follow directly from the QCD generating functional. The B-S kernel derived is given an exact and explicit expression which contains only a few types of Green's functions. This expression is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.