Dispersive evaluation of the second-class amplitude $\ddot{I}„\to \hat{I}\cdot \ddot{I}€\hat{I}{½}_{\ddot{I}}„$ in the standard model

Abstract

We reevaluate the two form factors relevant for the $\hat{I}\cdot \ddot{I}€$ second-class $\ddot{I}„$ decay mode, making systematic use of analyticity, unitarity, combined with updated inputs to the NLO chiral constraints. We focus, in particular, on the shape of the $\ddot{I}$ resonance peak which is a background-free signature of a second-class current. Its dispersive construction requires the $\hat{I}\cdot \ddot{I}€\to \ddot{I}€\ddot{I}€$ scattering amplitude which we derive from a family of Khuri-Treiman equations solutions constrained with accurate recent results on the $\hat{I}\cdot \to 3\ddot{I}€$ Dalitz plot.

Presented at the 12th International workshop on Tau lepton physics (TAU2012) in Nagoya, Japan