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

Abstract

In this paper we study the effects of $s\to d + 2{gluon}$ 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 $K_L - \eta, \eta'$ transitions and therefore in $K_L\to \gamma\gamma$ due to large matrix elements of $<\eta(\eta')|\alpha_s G^a_{\mu\nu} \tilde G_a^{\mu\nu}|0>$ 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 $\Delta m_{K_L-K_S}$.