Manifestation of three-body forces in three-body Bethe-Salpeter and light-front equations

TL;DR

This paper compares three-body bound state equations in Bethe-Salpeter and light-front frameworks, revealing significant differences that are mitigated by including three-body forces, especially at small exchange masses.

Contribution

It demonstrates the importance of three-body forces in reconciling differences between Bethe-Salpeter and light-front approaches for three-particle systems.

Findings

Light-front underbinds compared to Bethe-Salpeter in ladder truncation.

Including three-body forces reduces the binding energy discrepancy.

At small exchange masses, both approaches yield similar results.

Abstract

Bethe-Salpeter and light-front bound state equations for three scalar particles interacting by scalar exchange-bosons are solved in ladder truncation. In contrast to two-body systems, the three-body binding energies obtained in these two approaches differ significantly from each other: the ladder kernel in light-front dynamics underbinds by approximately a factor of two compared to the ladder Bethe-Salpeter equation. By taking into account three-body forces in the light-front approach, generated by two exchange-bosons in flight, we find that most of this difference disappears; for small exchange masses, the obtained binding energies coincide with each other.