Year: 2008
Type: article
Abstract: The contribution of the box and crossed two-pion-exchange diagrams to proton-proton scattering at ${90}_{\mathrm{c}.\mathrm{m}.}^{○}$ 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 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, it was observed 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 better for pion-nucleon pseudovector vis \`a vis pseudoscalar coupling although potentially important corrections for inelastic effects are lacking. 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. The imaginary part of the amplitude arising from the form factor remains to be understood. It seems that the importance of the exchange of color singlets may extend higher in energy than expected.
Source: Physical Review C
Authors: W. R. Gibbs, B. Loiseau
Institution: New Mexico State University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1973366684