## 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

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 $$m_u-m_d$$.
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 $$Q=22.0(7)$$.