SU(3) and Nonet Breaking Effects in $K_L \to γγ$ 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 $K_L \to γγ$ in the Standard Model. We find that this interaction can induce new sizeable SU(3) and U(3) nonet breaking effects in $K_L - η, η&#39;$ transitions and therefore in $K_L\to γγ$ due to large matrix elements of $<η(η&#39;)|α_s G^a_{μν} \tilde G_a^{μν}|0>$ 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 $Δm_{K_L-K_S}$.