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

TL;DR

This paper uses a dispersive approach to axial anomaly to tightly constrain the $ heta$ mixing angle between $ ext{eta}$ and $ ext{eta'}$, revealing its significant impact on decay widths.

Contribution

It introduces a dispersive method to analyze the $ ext{eta}$-$ ext{eta'}$ mixing, providing precise bounds on the mixing angle and its influence on decay processes.

Findings

The mixing angle $ heta$ is approximately -15.3 degrees with 1 degree uncertainty.

The decay width $ ext{Gamma}_{ ext{eta} o 2 ext{gamma}}$ is highly sensitive to the mixing angle.

Strong bounds on $ heta$ improve understanding of $ ext{eta}$-$ ext{eta'}$ mixing dynamics.

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.