Near-threshold amplitude of pion-deuteron scattering: One-loop contributions

The one-loop expression for the absorptive correction to the πd scattering length is discussed. Relevant Feynman diagrams are calculated both in the relativistic and in the nonrelativistic formalism. A simple expression is obtained for the one-loop correction that arises in the πd scattering length owing to the Fermi motion of the nucleons in the deuteron. This correction includes absorption effects. Fulfillment of the unitarity relation is verified explicitly.