Large $N_c$ Expansion and the Parity Violating $\pi, N, \Delta$ Couplings

In the limit of large $N_c$ we first consider the $N_c$ ordering of the various parity violating $\pi, N, \Delta$ couplings. Then we derive the relations among these couplings and consistency relations from the stability of these couplings under the chiral loop corrections with and without the mass splitting between $N$ and $\Delta$. Especially we find that $h_\Delta =-{3\over \sqrt{5}}h_\pi$ in the large $N_c$ limit, which correctly reproduces the relative sign and magnitude of the "DDH" values for these PV couplings.