Unitarity constraint for threshold coherent pion photoproduction on the deuteron and chiral perturbation theory

The contribution of the two-step process gamma + d -> p + n -> pi0 + d to the imaginary part of the amplitude for coherent pion production on the deuteron is calculated exploiting unitarity constraints. The result shows that this absorptive process is not negligible and has to be considered in an extraction of the elementary neutron production amplitude from the gamma + d -> pi0 + d cross section at threshold. In addition, it is argued that a consistent calculation of gamma + d -> pi0 + d in baryon chiral perturbation theory beyond next-to-leading order requires the inclusion of this absorptive process.