1 7 A pr 2 00 7 Two - pion - exchange contributions to the pp → ppπ 0 reaction

Our previous study of the near-threshold pp → ppπ reaction based on a hybrid nuclear effective field theory is further elaborated by examining the momentum dependence of the relevant transition operators. We show that the two-pion exchange diagrams give much larger contributions than the one-pion exchange diagram, even though the former is of higher order in the Weinberg counting scheme. The relation between our results and an alternative counting scheme, the momentum counting scheme, is also discussed. In the standard nuclear physics approach (SNPA), a nuclear reaction amplitude is calculated with the use of the transition operator derived from a phenomenological Lagrangian and nuclear wave functions generated by a high-precision phenomenological NN potential. SNPA has been enormously successful in explaining a vast range of nuclear phenomena. Meanwhile, a nuclear chiral perturbation approach based on heavy-baryon chiral perturbation theory (HBχPT) is gaining ground as a powerful tool for addressing issues that cannot be readily settled in SNPA. HBχPT is a lowenergy effective field theory of QCD, based on a systematic expansion in terms of the expansion parameter ǫ ≡ Q/Λχ ≪ 1, where Q is a typical energy-momentum involved in a process under study or the pion mass mπ, and the chiral scale Λχ ≃ 4πfπ ≃ 1 GeV. HBχPT has been applied with great success to low-energy processes including e.g., pion-nucleon scattering and electroweak reactions on a nucleon and in fewnucleon systems. Our present work is concerned with a HBχPT study of the nearthreshold pp→ppπ0 reaction. A motivation of this study may be stated in reference to the generic NN→NNπ processes near threshold. Although HBχPT presupposes the small size of its expansion parameter Q/Λχ, the pion-production reactions involve somewhat large energyand three-momentum transfers even at threshold. Therefore the application of HBχPT to the NN→NNπ reactions may involve some delicate aspects, but this also means that these processes may serve as a good test case for probing the limit of applicability of HBχPT. Apart from this general issue to be investigated, a specific aspect of the pp→ppπ0 reaction makes its study particularly interesting. For most isospin channels, the NN→NNπ amplitude near threshold is dominated by the pion rescattering diagram where the πN scattering vertex is given by the Weinberg-Tomozawa term, which represents the lowest chiral order contribution. However, a quantitatively reliable description of the NN→NNπ reactions obviously requires detailed examinations of the corrections to this dominant amplitude. Meanwhile, since the Weinberg-Tomozawa vertex does not contribute to the pion-nucleon rescattering diagram for pp→ppπ0, this reaction is particularly sensitive to higher chiral-order contributions and hence its study is expected to provide valuable information to guide us in formulating a quantitative description of all the NN→NNπ reactions (including the channels that involve a deuteron). The first HBχPT-based study of the near-threshold pp→ppπ0 reaction was made in Refs. [1, 2]. In HBχPT one naturally expects a small cross section for this reaction since, for s-wave pion production, the pion-nucleon vertex in the impulse approximation (IA) diagram and the pion-rescattering vertex in the one-pion-exchange rescattering (1π-Resc) diagram arise from the next-to-leading-order (NLO) chiral lagrangian. A remarkable feature found in Refs. [1, 2] is that a drastic cancellation