Rare Kaon Decays in the $1/N_c$-Expansion

Abstract

We study the unknown coupling constants that appear at order $p^4$ in the Chiral Perturbation Theory analysis of $K \to πγ^* \to πl^+ l^-$, $K^{+-} \to π^{+-} γγ$ and $K \to ππγ$ decays. To that end, we compute the chiral realization of the $ΔS \, = \, 1$ Hamiltonian in the framework of the $1/N_c$-expansion of the low-energy action. The phenomenological implications are also discussed.