Uncertainties in theoretical predictions for γd → π⁰d observables near threshold due to the use of different elementary amplitudes

We discuss possible uncertainties in theoretical predictions for γd → π⁰d observables near threshold due to the use of different elementary γN → πN amplitudes using an approach which is based on time-ordered perturbation theory. Results are presented for unpolarized cross sections and all possible spin asymmetries of differential and total cross sections. Our results indicate that the estimations of the uncertainty on the γd → π⁰d observables show important sensitivity to the modeling of the elementary γN → πN operator. A comparison to presently available experimental data is given. The results presented here are of particular interest for the evaluation of the systematic uncertainties caused by the use of different elementary operators in the analyses of γd → π⁰d measurements to extract information on the free neutron amplitude from deuteron data. (author)