Precision calculation of $γd\to π^+ nn$ within chiral perturbation theory

Abstract

The reaction $γd\to π^+ nn$ is calculated up to order $χ^{5/2}$ in chiral perturbation theory, where $χ$ denotes the ratio of the pion to the nucleon mass. Special emphasis is put on the role of nucleon--recoil corrections that are the source of contributions with fractional power in $χ$. Using the known near threshold production amplitude for $γp\to π^+ n$ as the only input, the total cross section for $γd\to π^+ nn$ is described very well. A conservative estimate suggests that the theoretical uncertainty for the transition operator amounts to 3 % for the computed amplitude near threshold.