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

TL;DR

This paper calculates electromagnetic corrections to the ta 3 decay within chiral perturbation theory, showing significant violations of Sutherland's theorem and implications for quark mass determinations.

Contribution

It provides the first detailed calculation of electromagnetic effects on ta decay, challenging the assumption that these effects are negligible.

Findings

Electromagnetic corrections are about 17% of the strong interaction correction.

Sutherland's theorem is strongly violated when electromagnetic effects are included.

Electromagnetic interactions must be considered in light quark mass extractions from this 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.