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

Abstract

We evaluate the threshold matrix-element for the reaction $pp\to pp{\pi }^0$ 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 $\mathcal{A}=(2.7-i0.3)$ 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 $\omega$ 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, $|\vec{p}|\simeq \sqrt{M{m}_{\pi }}$, with $M$ and $m_{\pi }$ the nucleon and the pion mass, respectively. We furthermore investigate the reaction $pp\to pn{\pi }^{+}$ near threshold within the same approach. We extract from the data the triplet threshold amplitude as $\mathcal{B}=(2.8-i1.5)$ fm${}^4$. Its real part can be well understood from (relativistic) tree level meson-exchange diagrams. In addition, we investigate the process $pp\to pp\eta$ 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, $|\mathcal{C}|=1.32$fm${}^4$. With $g_{\eta N}=5.3$, this value can be reproduced by (relativistic) 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 ${\eta }^{\prime }$-production.

Comments: 28 pp, LaTeX, 9 figs, uses epsf, updated version. To be published in Eur. Phys. J. A (1999). **Title changed again**