Weak $K$--Amplitudes in the Chiral and $1/N_c$--Expansions

Abstract

It is shown that there exist symmetry constraints for non--leptonic weak amplitudes which emerge when the $1/N_c$--expansion restricted to the leading and next--to--leading approximations only is systematically combined with $\chi$PT limited to the lowest non--trivial order. We discuss these constraints for the couplings $\mbox{\bf g}_8$ and $\mbox{\bf g}_{27}$ of $\Delta S=1$ transitions and the $\mbox{\bf B}_{K}$--parameter of $K^0-{\bar K}^0$ mixing.