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

Abstract

We evaluate the threshold matrix-element for the reaction $pp \to ppπ^0$ 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 vector meson exchanges, with $ω$ exchange giving the largest individual contribution. 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, $|\vec p | \simeq \sqrt {Mm_π}$, with $M$ and $m_π$ the nucleon and the pion mass, respectively. We furthermore investigate the reaction $pp\to p n π^+$ near threshold within the same approach. We extract from the data the triplet threshold amplitude as ${\cal B}= (2.8 -i 1.5)$ fm$^4$. Its real part can be well understood from (relativistic) tree level meson-exchange diagrams. In addition, we investigate the process $pp \to pp η$ 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, $|{\cal C}| = 1.32 $fm$^4$. With $g_{ηN}=5.3$, this value can be reproduced by (relativistic) 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.