Three-body forces in Bethe-Salpeter and light-front equations

TL;DR

This paper compares three-body binding energies in relativistic Bethe-Salpeter and light-front equations for scalar particles, revealing significant differences that are mitigated by including three-body forces in the light-front approach.

Contribution

It introduces the effect of three-body forces generated by two exchange particles in flight to reconcile differences between the two relativistic frameworks.

Findings

Three-body binding energies differ significantly between the two approaches.

Including three-body forces in light-front dynamics reduces the discrepancy.

For small exchange masses, both approaches yield similar binding energies.

Abstract

In relativistic frameworks, given by the Bethe-Salpeter and light-front bound state equations, the binding energies of system of three scalar particles interacting by scalar exchange particles are calculated. 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 particles in flight, we find that most of this difference disappears; for small exchange masses, the obtained binding energies coincide with each other.