dorsal/arxiv
View SchemaTwo-Pion Exchange in Proton-Proton Scattering
| Authors | W. R. Gibbs, B. Loiseau |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0606045 |
| URL | https://arxiv.org/abs/nucl-th/0606045 |
| DOI | 10.1103/PhysRevC.77.014003 |
| Journal | Phys.Rev.C77:014003,2008 |
Abstract
The contribution of the box and crossed two-pion-exchange diagrams to proton-proton scattering at 90$^{\circ}_{c.m.}$ is calculated in the laboratory momentum range up to 12 GeV/c. Relativistic form factors related to the nucleon and pion size and representing the pion source distribution based on the quark structure of the hadronic core are included at each vertex of the pion-nucleon interaction. These form factors depend on the four-momenta of the exchanged pions and scattering nucleons. Feynman-diagram amplitudes calculated without form factors are checked against those derived from dispersion relations. In this comparison, one notices that a very short-range part of the crossed diagram, neglected in dispersion-relation calculations of the two-pion-exchange nucleon-nucleon potential, gives a sizable contribution. In the Feynman-diagram calculation with form factors the agreement with measured spin-separated cross sections, as well as amplitudes in the lower part of the energy range considered, is much better for pion-nucleon pseudo-vector vis \`a vis pseudo-scalar coupling. While strengths of the box and crossed diagrams are comparable for laboratory momenta below 2 GeV/c, the crossed diagram dominates for larger momenta, largely due to the kinematics of the crossed diagram allowing a smaller momentum transfer in the nucleon center of mass. An important contribution arises from the principal-value part of the integrals which is non-zero when form factors are included. It seems that the importance of the exchange of color singlets may extend higher in energy than expected.
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"abstract": "The contribution of the box and crossed two-pion-exchange diagrams to\nproton-proton scattering at 90$^{\\circ}_{c.m.}$ is calculated in the laboratory\nmomentum range up to 12 GeV/c. Relativistic form factors related to the nucleon\nand pion size and representing the pion source distribution based on the quark\nstructure of the hadronic core are included at each vertex of the pion-nucleon\ninteraction. These form factors depend on the four-momenta of the exchanged\npions and scattering nucleons. Feynman-diagram amplitudes calculated without\nform factors are checked against those derived from dispersion relations. In\nthis comparison, one notices that a very short-range part of the crossed\ndiagram, neglected in dispersion-relation calculations of the two-pion-exchange\nnucleon-nucleon potential, gives a sizable contribution. In the Feynman-diagram\ncalculation with form factors the agreement with measured spin-separated cross\nsections, as well as amplitudes in the lower part of the energy range\nconsidered, is much better for pion-nucleon pseudo-vector vis \\`a vis\npseudo-scalar coupling. While strengths of the box and crossed diagrams are\ncomparable for laboratory momenta below 2 GeV/c, the crossed diagram dominates\nfor larger momenta, largely due to the kinematics of the crossed diagram\nallowing a smaller momentum transfer in the nucleon center of mass. An\nimportant contribution arises from the principal-value part of the integrals\nwhich is non-zero when form factors are included. It seems that the importance\nof the exchange of color singlets may extend higher in energy than expected.",
"arxiv_id": "nucl-th/0606045",
"authors": [
"W. R. Gibbs",
"B. Loiseau"
],
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"doi": "10.1103/PhysRevC.77.014003",
"journal_ref": "Phys.Rev.C77:014003,2008",
"title": "Two-Pion Exchange in Proton-Proton Scattering",
"url": "https://arxiv.org/abs/nucl-th/0606045"
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