Three-body final state interaction in $\hat{I}\cdot \to 3\ddot{I}€$ updated

Abstract

In view of the recent high-statistic KLOE data for the $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ decay, a new determination of the quark mass double ratio has been done. Our approach relies on a dispersive model that takes into account rescattering effects between three pions via subenergy unitarity. The latter is essential to reproduce the Dalitz plot distribution. A simultaneous description of the KLOE and WASA-at-COSY data is achieved in terms of just two real parameters. From a global fit, we determine $Q=21.6\pm 1.1$. The predicted slope parameter for the neutral channel $\hat{I}\pm =-0.025\pm 0.004$ is in reasonable agreement with the PDG average value.

7 pages, 2 figures