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Register a new userElectromagnetic Corrections to the (etarightarrow 3pi) Neutral Decay
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Sutherlands theorem dictates that the contribution of the electromagnetic interaction to the decay process (etarightarrow 3pi^{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 Sutherlands 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.
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We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant $g_A$ in the neutron $beta$-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function $g_1$, we determine the contribution from the $gamma W$-box diagram to a precision better than $10^{-4}$. Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron $beta$-decay are almost identical, i.e. the ratio $lambda=g_A/g_V$ is almost unrenormalized. With this result, we predict the bare axial coupling constant to be {$mathring{g}_A=-1.2754(13)_mathrm{exp}(2)_mathrm{RC}$} based on the PDG average $lambda=-1.2756(13)$
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 (etarightarrow 3pi^{0}) amounts to (-0.0221pm 0.0034). When compared with the experimental value, (alpha =-0.0317pm 0.0016), on the one hand, and with the contribution of the up and down quark mass difference, (+0.013pm 0.032), on the other hand, our result leads to the direct conclusion: textit{The} (etarightarrow 3pi^{0}) textit{decay uline{cannot} be used to determine} (m_{d}-m_{u}).
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