Low Energy Theorems For Nucleon-Nucleon Scattering

Cohen, Thomas D.; Hansen, James M.

Low Energy Theorems For Nucleon-Nucleon Scattering

Authors

Description

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 $m_π$ 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 $^1S_0$ and $^3S_1$ channels. Analogous theorems are developed for the energy dependence $ε$ parameter which describes $^3S_1 - ^3D_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_π$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_π$ 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