SU(3) and Nonet Breaking Effects in $K_L\to \gamma \gamma$ Induced by $s\to d+2gluon$ due to Anomaly

In this paper we study the effects of $s\to d+2gluon$ on $K_L \to \gamma\gamma$ in the Standard Model. We find that this interaction can induce new sizeable SU(3) and U(3) nonet breaking effects in $K_L-\eta ,{\eta }^{\mathrm{\prime }}$ transitions and therefore in $K_L\to \gamma \gamma$ due to large matrix elements of $<\eta ({\eta }^{\mathrm{\prime }})\mathrm{\mid }{\alpha }_s{G}_{\mu \nu }^a{\tilde{G}}_a^{\mu \nu }\mathrm{\mid }0>$ from QCD anomaly. These new effects play an important role in explaining the observed value. We also study the effects of this interaction on the contribution to $\mathrm{\Delta }{m}_{K_L-K_S}$.