Two-Pion-Exchange Contribution to Nucleon-Nucleon Scattering on the Basis of Pion-Pion Dynamics

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Abstract
Calculation of nucleon-nucleon scattering is presented as a completion of our works on the systematic studies of low energy strong interactions. The essential part of the present work is a quantitative evaluation of the two-pion-exchange contribution to nucleon-nucleon scattering, starting from the pion-pion scattering phase shifts in the I = L = 0 and I = L = 1 states. In this calculation, the parameters for the two-pion contribution with I = L = 1 state are predetermined from the iso-vector part of the nucleon electromagnetic form factors. For the I = L = 0 state, both cases of the up-down and the down-up solutions for S-wave pion-pion scattering are examined. The I = 0 S-wave pion-pion phase shift δ0(0) in the former case shows a very broad enhancement below 1 GeV region, whereas δ0(0) in the latter case contains a sharp resonance in the neighbourhood of the ρ-meson mass. For the higher angular momentum two-pion states L ≥2, pion-pion correlations are neglected. In addition to these two-pion contributions and the one-pion contribution, inclusion of the ω- and the η-meson contributions leads us to the results which agree well with the experimentally determined nucleon-nucleon scattering amplitudes, when we take the up-down solution for δ0(0). However, the down-up solution for δ0(0) makes the I = L = 0 part of the two-pion contribution too large and we cannot obtain reasonable fit with the experiment on nucleon-nucleon scattering for the latter case. From the present analysis we may conclude that the up-down solution for S-wave pion-pion scattering is superior to the down-up solution. This gives another indication to the importance of the non-resonant part of two-pion contribution as well as that given by the analysis of the nucleon electromagnetic form factors. It is also shown that in the present treatment the η-meson contribution becomes rather large.

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