Dispersive Approach to Abelian Axial Anomaly and $\eta -{\eta }^{\prime }$ Mixing

Abstract

We investigate what can be learnt about the $\eta$ -${\eta }^{\prime }$ mixing by means of dispersive representation of axial anomaly. We show that our method leads to the strong bounds for the $\eta -{\eta }^{\prime }$ 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.

11 pages, 4 figures