Role of the Δ(1232) in pion-deuteron scattering at threshold within chiral effective field theory

We investigate the role of the delta isobar in the reaction πd→πd at threshold in chiral effective field theory. We discuss the corresponding power counting and argue that this calculation completes the evaluation of diagrams up to the order χ3/2, with χ the ratio of the pion to the nucleon mass. The net effect of all delta contributions at this order to the pion-deuteron scattering length is δaπdΔ=(2.4±0.4)×10−3mπ−1.