The Eta decay into three neutral pions is mainly electromagnetic

TL;DR

This study uses Chiral Perturbation Theory with photons to analyze the eta decay into three neutral pions, revealing that electromagnetic effects dominate and the decay cannot reliably determine quark mass differences.

Contribution

The paper demonstrates that electromagnetic interactions significantly influence eta decay and clarifies that this decay is unsuitable for measuring quark mass differences.

Findings

Photon exchange contributes -0.0221 to the slope parameter.

Electromagnetic effects dominate the eta decay process.

Decay cannot be used to determine quark mass differences.

Abstract

In the framework of Chiral Perturbation Theory including photons, we found that the contribution of the photon exchange between two intermediate charged Kaons to the slope parameter of the decay (\eta\rightarrow 3\pi^{0}) amounts to (-0.0221\pm 0.0034). When compared with the experimental value, (\alpha =-0.0317\pm 0.0016), on the one hand, and with the contribution of the up and down quark mass difference, (+0.013\pm 0.032), on the other hand, our result leads to the direct conclusion: \textit{The} (\eta\rightarrow 3\pi^{0}) \textit{decay \uline{cannot} be used to determine} (m_{d}-m_{u}).