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

Abstract

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 $K_L-\eta ,{\eta }^{\prime }$ transitions and therefore in $K_L\to \gamma \gamma$ due to large matrix elements of $<\eta ({\eta }^{\prime })|{\alpha }_s{G}_{\mu \nu }^a{\tilde{G}}_a^{\mu \nu }|0>$ 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 $\Delta m_{K_L-K_S}$.

Comments: RevTex, 12 Pages, no figures. Version to be published in PRD