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 $\text{mbox}{\mathbf{g}}_8$ and $\text{mbox}{\mathbf{g}}_{27}$ of $\Delta S=1$ transitions and the $\text{mbox}{\mathbf{B}}_K$--parameter of $K^0-{\bar{K}}^0$ mixing.

Comments: 11 pages, latex, 1 figure (included in a separate ps file)