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 ${m}_{\ensuremath{\pi}}$ 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 ${}^{1}{S}_{0} \mathrm{and}{ }^{3}{S}_{1}$ channels. Analogous theorems are developed for the energy dependence $\ensuremath{\epsilon}$ parameter which describes ${}^{3}{S}_{1}{\ensuremath{-}}^{3}{D}_{1}$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of ${m}_{\ensuremath{\pi}}$ is too large for the chiral expansion to be valid in this context. Comparisons of ${m}_{\ensuremath{\pi}}$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.