η→3π: Study of the Dalitz plot and extraction of the Quark Mass Ratio Q [The decay η→3π: Study of the Dalitz plot and extraction of the quark mass ratio Q

The η→3π amplitude is sensitive to the quark mass difference m_u−m_d and offers a unique way to determine the quark mass ratio Q²≡(m_s²−m_ud²)/(m_d²−m_u²) from experiment. We calculate the amplitude dispersively and fit the KLOE data on the charged mode, varying the subtraction constants in the range allowed by chiral perturbation theory. The parameter-free predictions obtained for the neutral Dalitz plot and the neutral-to-charged branching ratio are in excellent agreement with experiment. Lastly, our representation of the transition amplitude implies Q=22.0±0.7.