The Relativistic Three-Body Bound State in Three-Dimensions

TL;DR

This paper develops a 3D relativistic framework for studying three-body bound states, crucial for high-energy scattering calculations where traditional methods are ineffective.

Contribution

It formulates relativistic Faddeev equations in momentum space, incorporating Poincaré invariance, and provides the first relativistic 3B wave function in this context.

Findings

Relativistic effects significantly influence binding energies.

First formulation of relativistic 3B wave function in 3D.

Framework suitable for high-energy scattering calculations.

Abstract

Studying of the relativistic three-body bound state in a three-dimensional (3D) approach is a necessary first step in a process to eventually perform scattering calculations at GeV energies, where partial-wave expansions are not useful. To this aim we recently studied relativistic effects in the binding energy and for the first time, obtained the relativistic 3B wave function \cite{Hadizadeh_PRC90}. The relativistic Faddeev integral equations for the bound state are formulated in terms of momentum vectors, and relativistic invariance is incorporated within the framework of Poincar\'e invariant quantum mechanics.