Relativistic Three-Body Scattering in a First Order Faddeev Formulation

TL;DR

This paper develops a relativistic approach to three-body scattering using first order Faddeev equations without partial wave decomposition, incorporating Poincaré invariance, and compares results to nonrelativistic models.

Contribution

It introduces a novel relativistic formulation of three-body scattering that operates directly in momentum space and maintains Poincaré invariance, advancing beyond traditional nonrelativistic methods.

Findings

Relativistic calculations differ from nonrelativistic results in scattering observables.

The approach successfully incorporates relativistic invariance in three-body scattering.

Predictions align with expected relativistic effects at high energies.

Abstract

Relativistic Faddeev equations for three-body scattering at arbitrary energies are solved in first order in the two-body transition operator in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincar{\'e} invariant quantum mechanics. Based on a Malfliet-Tjon type interaction, observables for elastic and breakup scattering are calculated and compared to the nonrelativistic ones.