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
1
S
0
and
3
S
1
channels. Analogous theorems are developed for the energy dependence
ϵ
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
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.