The decay $\eta \to 3\pi$: study of the Dalitz plot and extraction of the quark mass ratio $Q$

Abstract

The $\eta \to 3\pi$ amplitude is sensitive to the quark mass difference $m_u-m_d$ and offers a unique way to determine the quark mass ratio $Q^2\equiv (m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$ 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. Our representation of the transition amplitude implies $Q=22.0\pm 0.7$.

Comments: 5 pages, 1 figure, v2 = published version. Slightly shorter and with minor changes