dorsal/arxiv
View SchemaNovel approach to pion and eta production in proton-proton collisions near threshold
| Authors | V. Bernard, N. Kaiser, Ulf-G. Meißner |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9806013 |
| URL | https://arxiv.org/abs/nucl-th/9806013 |
| DOI | 10.1007/s100500050229 |
| Journal | Eur.Phys.J. A4 (1999) 259-275 |
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 ${\cal A} = (2.7 - i 0.3)$ 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 $\omega$ 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, $|\vec p | \simeq \sqrt {Mm_\pi}$, 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 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 $pp \to pp \eta$ 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 (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 $\eta'$-production.
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"abstract": "We evaluate the threshold matrix-element for the reaction $pp \\to pp\\pi^0$ in\na fully relativistic Feynman diagrammatic approach. We employ a simple\neffective range approximation to take care of the S-wave $pp$ final-state\ninteraction. The experimental value for the threshold amplitude ${\\cal A} =\n(2.7 - i 0.3)$ fm$^4$ can be reproduced by contributions from tree level chiral\n(long-range) pion exchange and short-range effects related to vector meson\nexchanges, with $\\omega$ exchange giving the largest individual contribution.\nPion loop effects appear to be small. We stress that the commonly used heavy\nbaryon formalism is not applicable in the NN-system above the pion production\nthreshold due to the large external momentum, $|\\vec p | \\simeq \\sqrt\n{Mm_\\pi}$, with $M$ and $m_\\pi$ the nucleon and the pion mass, respectively. We\nfurthermore investigate the reaction $pp\\to p n \\pi^+$ near threshold within\nthe same approach. We extract from the data the triplet threshold amplitude as\n${\\cal B}= (2.8 -i 1.5)$ fm$^4$. Its real part can be well understood from\n(relativistic) tree level meson-exchange diagrams. In addition, we investigate\nthe process $pp \\to pp \\eta$ near threshold. We use a simple factorization\nansatz for the $pp\\eta$ final-state interaction and extract from the data the\nmodulus of the threshold amplitude, $|{\\cal C}| = 1.32 $fm$^4$. With $g_{\\eta\nN}=5.3$, this value can be reproduced by (relativistic) tree level\nmeson-exchange diagrams and $\\eta$-rescattering, whose strength is fixed by the\n$\\eta N$ scattering length. We also comment on the recent near threshold data\nfor $\\eta\u0027$-production.",
"arxiv_id": "nucl-th/9806013",
"authors": [
"V. Bernard",
"N. Kaiser",
"Ulf-G. Mei\u00dfner"
],
"categories": [
"nucl-th"
],
"doi": "10.1007/s100500050229",
"journal_ref": "Eur.Phys.J. A4 (1999) 259-275",
"title": "Novel approach to pion and eta production in proton-proton collisions near threshold",
"url": "https://arxiv.org/abs/nucl-th/9806013"
},
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