Novel approach to pion and eta production in proton-proton collisions

We evaluate the threshold matrix-element for the reaction $pp \to pp\pi^0$ 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 ${\cal A} = (2.7 - i 0.3)$ fm$^4$ 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 very 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, $|\vec p | \simeq \sqrt {m M_\pi}$, with $m$ and $M_\pi$ the nucleon and the pion mass, respectively. We furthermore investigate the reaction $pp\to p n \pi^+$ near threshold within the same approach. We extract from the data the triplet threshold amplitude, ${\cal B}= (3.9 -i 2.1)$ fm$^4$, which comes out too small by a factor of two from tree level diagrams. A reason why this approach works well for $pp\to pp \pi^0$ and less well for $pp \to pn \pi^+$ is the relative strength of initial-state interactions. In addition, we investigate the process $pp \to pp \eta$ near threshold. We use a simple factorization ansatz for the $pp\eta$ final-state interaction and extract from the data the modulus of the threshold amplitude, $|{\cal C}| = 1.32 $fm$^4$. With $g_{\eta N}=5.3$, this value can be reproduced by tree level meson exchange diagrams and $\eta$-rescattering, whose strength is fixed by the $\eta N$ scattering length. We also comment on the recent near threshold data for $\eta '$-production.