Dispersive Approach to Abelian Axial Anomaly and $\eta-\eta'$ Mixing

Abstract

We investigate what can be learnt about the $\eta$ -$\eta'$ mixing by means of dispersive representation of axial anomaly. We show that our method leads to the strong bounds for the $\eta-\eta'$ mixing angle: $\theta = -15.3^o \pm 1^o$. Moreover, our result manifests also a dramatic dependence of the width $\Gamma_{\eta\to 2\gamma}$ on the mixing angle $\theta$. This property explains how the relatively small mixing strongly effects the decay width.