Poincar\'e Invariant Three-body Scattering

The Poincar\'e invariant Faddeev equation for three-body scattering is directly formulated in momentum space without employing a partial wave decomposition. The scattering amplitude is obtained as functions of vector momenta by solving the Faddeev equation in three dimensions through Pad\'e iteration. Based on a Malfliet-Tjon type potential, differential cross sections for elastic and break-up scattering (inclusive and exclusive) are calculated at selected energies up to the GeV scale. The reaction mechanisms at higher energies associated with different kinematic configurations such as quasi-free (QFS) and final state interaction (FSI) are investigated and compared to the corresponding non-relativistic cross sections. Especially, multiple rescattering contributions beyond the leading order of the two-body t matrix are analyzed as function of energy and kinematic configuration.