Relativistic calculation for the reactions\bar p d → 5πp and\bar p d → 3πp at rest

We present a fully relativistic calculation for ¯pd → 5πp and ¯pd → 3πp that includes angular momentum and spin dynamics. We calculate the inclusive proton distributions from two diagrams: the leading “tree” diagram, and the diagram for pion rescattering. Pion-nucleon rescattering proceeds through the Δ, in the RaritaSchwinger formalism, thus preserving the correct angular dependence. We use realistic parameterizations of the deuteron, keeping both theS andD states. The loop integrations for the rescattering amplitude and the phase space integrations have been done numerically. We find that the combined effects of a correct treatment of the rescattered pion and relativity are small in comparison with a simple non-relativistic calculation.