Determination of the quark mass difference m_u-m_d from \eta \to 3 \pi

Who: Gilberto Colangelo (Universität Bern)
When: Monday, December 3, 2018 at 14:15
Where: The CP³ meeting room

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The decay \(\eta \to 3 \pi\) would not happen if isospin were an exact symmetry. Moreover, since the contribution from the electromagnetic interaction is suppressed this decay is 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 we have taken into account also electromagnetic corrections.
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 \(m_u-m_d\). An outcome of this analysis is a measure of Dashen’s-theorem violations, which turn out to be large. By invoking a low-energy theorem we determine the quark mass ratio \(Q^2=(m_s^2-\hat{m}^2)/(m_d^2-m_u^2)\) to be \(Q=22.0(7)\).
A comparison and some tension to lattice determinations of quark masses and their ratios will also be discussed.