Electromagnetic Corrections to the (\eta\rightarrow 3\pi) Neutral Decay

Abstract

Sutherland's theorem dictates that the contribution of the electromagnetic interaction to the decay process (\eta\rightarrow 3\pi^{0}) is neglected with respect to the one coming from the difference between the up and down quark masses. In the framework of chiral perturbation theory including virtual photons, we calculated the main diagram concerning the exchange of a virtual photon between two intermediate charged pions. The correction induced by this diagram on the slope parameter amounts to (17%) of the correction induced by the pure strong interaction at one-loop level. If this result is maintained when considering all the diagrams at the chiral order we are working, we can say without any doubt that Sutherland's theorem is strongly violated. As a direct consequence, any determination of light quark masses from the present decay \textit{should} take into account the electromagnetic interaction.