Antiparticle Contribution in the Cross Ladder Diagram for Bethe-Salpater Equation in the Light-Front

TL;DR

This paper develops a light-front integral equation for a two-boson bound state, incorporating crossed ladder diagrams and pair creation effects at order g^4, advancing the understanding of bound state dynamics.

Contribution

It introduces a truncated hierarchical approach to include crossed ladder diagrams and pair creation in the Bethe-Salpeter equation on the light front, at order g^4.

Findings

Derived a homogeneous integral equation for the bound state vertex.

Included pair creation processes in the crossed ladder diagram.

Enhanced the dynamical description of two-boson bound states.

Abstract

We construct the homogeneous integral equation for the vertex of the bound state in the light front with the kernel approximated to order g^4. We will truncate the hierarchical equations from Green functions to construct dynamical equations for the two boson bound state exchanging interacting intermediate bosons and including pair creation process contributing to the crossed ladder diagram.