Interplay of the chiral and large Nc limits in πn scattering

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