Bound state structure and electromagnetic form factor beyond the ladder approximation

TL;DR

This paper examines how including cross-ladder contributions affects the bound state structure and electromagnetic form factors in a two-boson Yukawa model, revealing that asymptotic behaviors remain consistent with counting rules.

Contribution

It introduces a detailed analysis of the impact of cross-ladder kernels on bound state properties beyond the ladder approximation using the Bethe-Salpeter equation.

Findings

Asymptotic form factors are unaffected by cross-ladder inclusion for fixed binding energy.

Electromagnetic form factors decrease according to counting rules.

Valence wave functions show minimal change with cross-ladder contributions.

Abstract

We investigate the response of the bound state structure of a two-boson system, within a Yukawa model with a scalar boson exchange, to the inclusion of the cross-ladder contribution to the ladder kernel of the Bethe-Salpeter equation. The equation is solved by means of the Nakanishi integral representation and light-front projection. The valence light-front wave function and the elastic electromagnetic form factor beyond the impulse approximation, with the inclusion of the two-body current, generated by the cross-ladder kernel, are computed. The valence wave function and electromagnetic form factor, considering both ladder and ladder plus cross-ladder kernels, are studied in detail. Their asymptotic forms are found to be quite independent of the inclusion of the cross-ladder kernel, for a given binding energy. The asymptotic decrease of form factor agrees with the counting rules. This analysis can be generalized to fermionic systems, with a wide application in the study of the meson structure.