The Eta decay into three neutral pions is mainly electromagnetic

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}).