Large $N_c$ Expansion and the Parity Violating $π, N, Δ$ Couplings

Abstract

In the limit of large $N_c$ we first consider the $N_c$ ordering of the various parity violating $π, N, Δ$ 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 $Δ$. Especially we find that $h_Δ=-{3\over \sqrt{5}}h_π$ in the large $N_c$ limit, which correctly reproduces the relative sign and magnitude of the "DDH" values for these PV couplings.