A next-to-next-to-leading-order pp to ppπ⁰ transition operator in chiral perturbation theory

We present a systematic analysis of next-to-next-to-leading-order diagrams that contribute to the $pp \to pp\pi^0$ production at threshold. Analytic expressions are given for the effective transition operators, and the relative importance of various types of diagrams is discussed. The vertex-correction-type graphs are found to give only small corrections to lower order graphs in conformity with expectations. By contrast, we find very large contributions from the two-pion graphs which can be interpreted as a part of effective $\sigma$-meson exchange diagrams. The recoil correction to the pion rescattering diagram also turns out to be large.