Complete Relativistic Faddeev Calculations of Pion-Deuteron Scattering

Pion-deuteron elastic scattering in the region of the (3,3) resonance is calculated with two covariant reductions of the relativistic Faddeev equations. The two $S$-wave nucleon-nucleon channels and the six $S$- and $P$-wave pion-nucleon channels are included by means of separable $T$ matrices. Both of the space and the spin variables are treated relativistically, by use of the three-body helicity formalism of Wick. The results agree very well with the data at 142 and 182 MeV, but do not resolve the discrepancy at 256 MeV.