Interplay of the Chiral and Large N_c Limits in pi N Scattering

Light-quark hadronic physics admits two useful systematic expansions, the chiral and 1/N_c expansions. Their respective limits do not commute, making such cases where both expansions may be considered to be especially interesting. We first study pi N scattering lengths, showing that (as expected for such soft-pion quantities) the chiral expansion converges more rapidly than the 1/N_c expansion, although the latter nevertheless continues to hold. We also study the Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules of pi N scattering, finding that both fail if the large N_c limit is taken prior to the chiral limit.