Revisiting $C$ and $CP$ Violation in $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ Decay

Abstract

The decay $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ is an ideal process in which to study flavor-conserving $C$ and $CP$ violation beyond the Standard Model. We deduce the $C$- and $CP$-odd quark operators that contribute to $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ originating from the mass-dimension 6 Standard Model effective field theory. The corresponding hadron-level operators that generate a non-vanishing $I=0$ amplitude at order $p^6$ in the chiral effective theory are presented for the first time, in addition to the leading order operatorsascribed to the $I=2$ final state. By fitting the KLOE-2 and the most recent BESIII experimental data, we determine the coefficients of the lowest order $I=0$ and $I=2$ amplitudes and estimate the potential new physics energy scale. We also perform an impact study of the future $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ experiments.

11 pages, 4 figures. Updated version matched to the one submitted to PRD