The 1/Nc Expansion in Hadron Effective Field Theory

We study the N-c scalings of pion-nucleon and nucleon-nucleon scatterings in hadron effective field theory. By assuming Witten's counting rules are applied to matrix elements or scattering amplitudes, which use the relativistic normalization for the nucleons, we find that the nucleon axial coupling g(A) A is of order N-c(0), and a consistent large N-c counting can be established for the pion-nucleon and nucleon-nucleon scatterings. We also justify the nonperturbative treatment of the low energy nucleon-nucleon interaction with the large N-c analysis and find that the deuteron binding energy is of order 1/N-c.