Abstract
In the phenomenological description of the nuclear interaction a crucial role is traditionally played by the exchange of a scalar I=0 meson, the sigma, of mass 500-600 MeV, which however is not seen clearly in the particle spectrum and which has a very ambiguous status in QCD. I show that a remarkably simple and reasonably controlled combination of ingredients can reproduce the features of this part of the nuclear force. The use of chiral perturbation theory calculations for two pion exchange supplemented by the Omnes function for pion rescattering suffices to reproduce the magnitude and shape of the exchange of a supposed $\sigma$ particle, even though no such particle is present in this calculation. I also show how these ingredients can describe the contact interaction that enters more modern descriptions of the internucleon interaction.
Highlights
When describing QCD to non-physicists, we generally say that it is the theory that accounts for nuclear binding
At low energy the result of the exchange of a heavy particle can be described by a local interaction
This is consistent with the potential description because, as the mass m gets large, the Yukawa potential forms a representation of a delta function
Summary
When describing QCD to non-physicists, we generally say that it is the theory that accounts for nuclear binding. After discussing the potential treatment, I will attempt to make contact with this effective field theory description. Because ρS describes physical on-shell intermediate states, this formalism provides a well defined tool either for the analysis of nucleon scattering or for theoretical attempts to describe the nuclear interaction.
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