Measurement of the $CP$-even fraction of $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$

Abstract

A measurement of the $CP$-even fraction of the decay $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ is performed with a quantum-correlated $\ddot{I}ˆ(3770)\to D\bar{D}$ data sample collected by the BESIII experiment, corresponding to an integrated luminosity of 2.93 ${\text{fb}}^{-1}$. Using a combination of $CP$ eigenstates, $D\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ and $D\to K_{S,L}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ as tagging modes, the $CP$-even fraction is measured to be $F_{+}^{4\ddot{I}€}=0.735\pm 0.015\pm 0.005$, where the first uncertainty is statistical and the second is systematic. This is the most precise determination of this quantity to date. It provides valuable model-independent input for the measurement of the CKM angle ${\hat{I}}^3$ with $B^{\pm }\to D{K}^{\pm }$ decays, and for time-dependent studies of $CP$ violation and mixing in the $D^0$-${\bar{D}}^0$ system.

15 pages, 4 figures