Simple diagrammatic approach to pion and eta production in proton-proton collisions

We evaluate the threshold matrix–element for the reaction pp → ppπ0 in a fully relativistic Feynman diagrammatic approach. We employ a simple effective range approximation to take care of the S–wave pp final–state interaction. The experimental value for the threshold amplitude A = (2.7− i 0.3) fm4 can be reproduced by contributions from tree level chiral (long–range) pion exchange and short–range effects related to heavy meson exchanges, with these two different contributions of roughly the same size. Pion loop effects appear to be small. We stress that the commonly used heavy baryon formalism is not applicable in the NN–system above the pion production threshold due to the large external momentum, |~ p | ≃ √ mMπ, with m and Mπ the nucleon and the pion mass, respectively. We furthermore investigate the reaction pp → pnπ+ near threshold within the same approach. We extract from the data the triplet threshold amplitude as B = (2.8 − i 1.5) fm4. Its real part can be well understood from tree level meson exchange diagrams. In addition, we investigate the process pp → ppη near threshold. We use a simple factorization ansatz for the ppη final–state interaction and extract from the data the modulus of the threshold amplitude, |C| = 1.32 fm4. With gηN = 5.3, this value can be reproduced by tree level meson exchange diagrams and η–rescattering, whose strength is fixed by the ηN scattering length. We also comment on the recent near threshold data for η′–production.