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

Abstract

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 $h_{\Delta }=-\frac{3}{\sqrt{5}}{h}_{\pi }$ in the large $N_c$ limit, which correctly reproduces the relative sign and magnitude of the "DDH" values for these PV couplings.