Low Energy Theorems For Nucleon-Nucleon Scattering

Abstract

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both $m_{\pi }$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the ${}^1{S}_0$ and ${}^3{S}_1$ channels. Analogous theorems are developed for the energy dependence $\epsilon$ parameter which describes ${}^3{S}_1{-}^3{D}_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_{\pi }$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_{\pi }$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.

12 pages, 1 figure, 1 table; appendix added to discuss behavior in chiral limit; minor revisions including revised figure reference to recent work added

References in corpus (4)

• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Nucleon-Deuteron Scattering from an Effective Field Theory
• The potential of effective field theory in NN scattering

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