Large-$N_c$ Higher Order Weak Chiral Lagrangians for Nonleptonic and Radiative Kaon Decays

In pure chiral perturbation theory (ChPT) the couplings of higher order Lagrangian terms are running parameters and hence can be determined only empirically from various low-energy hadronic processes. While this scenario works well for strong interactions, it is unsatisfactory for nonleptonic and radiative nonleptonic weak interactions: It is impossible, from the outset, to determine all unknown higher-order chiral couplings by experiment; theory is tested only by certain chiral constraints rather than by its quantitative predictions. Based on a QCD-motivated model for $p^4$ strong chiral Lagrangian valid in the limit of large $N_c$, one can derive large-$N_c$ fourth-order effective chiral Lagrangians for $\Delta S=1$ nonleptonic weak interactions and radiative weak transitions. Applications to $K\ri\pi\pi\pi,~K\ri\pi\gamma\gamma$, and $K\ri\pi\pi\gamma$ are discussed.