Low Energy Theorems For Nucleon-Nucleon Scattering
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by
Thomas D. Cohen, James M. Hansen
1998
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_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.
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