Low energy theorems for nucleon-nucleon scattering

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 S-1(0) and S-3(1) channels. Analogous theorems are developed for the energy dependence epsilon parameter which describes S-3(1)-D-3(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. [S0556-2813(99)03501-3].