Determination of the quark mass difference m_u-m_d from eta -> 3 pi
Gilberto Colangelo (Bern)

The decay \(\eta \to 3 \pi\) would not happen if isospin were an exact symmetry. Moreover the contribution from the electromagnetic interaction is suppressed, which makes it a unique source of phenomenological information on the quark mass difference \(m_u-m_d\).
In this talk I will start with general introduction on the problem of the determination of the light quark masses. I will then present a recent dispersive analysis of this decay which is shown to accurately describe the measured Dalitz plot, both of the charged as well as of the neutral channel of this decay.To understand the relation between the two decay channels at the current level of experimental accuracy it is necessary to take into account also electromagnetic corrections, which has also been done. Finally, we rely on chiral perturbation theory to predict the overall normalization of the amplitude and extract from the measurement of the rate the value of the QCD contribution to the kaon mass difference, which is proportional to \(m_u-m_d\).