Improved measurement of the strong-phase difference $\hat{I}{´}_D^{K\ddot{I}€}$ in quantum-correlated $D\bar{D}$ decays

Abstract

The decay $D\to K^{-}\ddot{I}{€}^{+}$ is studied in a sample of quantum-correlated $D\bar{D}$ pairs, based on a data set corresponding to an integrated luminosity of 2.93\,fb${}^{-1}$ collected at the $\ddot{I}ˆ(3770)$ resonance by the BESIII experiment. The asymmetry between $CP$-odd and $CP$-even eigenstate decays into $K^{-}\ddot{I}{€}^{+}$ is determined to be ${\mathcal{A}}_{K\ddot{I}€}=0.132\pm 0.011\pm 0.007$, where the first uncertainty is statistical and the second is systematic. This measurement is an update of an earlier study exploiting additional tagging modes, including several decay modes involving a $K_L^0$ meson. The branching fractions of the $K_L^0$ modes are determined as input to the analysis in a manner that is independent of any strong phase uncertainty. Using the predominantly $CP$-even tag $D\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ and the ensemble of $CP$-odd eigenstate tags, the observable ${\mathcal{A}}_{K\ddot{I}€}^{\ddot{I}€\ddot{I}€\ddot{I}{€}^0}$ is measured to be $0.130\pm 0.012\pm 0.008$. The two asymmetries are sensitive to $r_D^{K\ddot{I}€}\cos \hat{I}{´}_D^{K\ddot{I}€}$, where $r_D^{K\ddot{I}€}$ and $\hat{I}{´}_D^{K\ddot{I}€}$ are the ratio of amplitudes and phase difference, respectively, between the doubly Cabibbo-suppressed and Cabibbo-favoured decays. In addition, events containing $D\to K^{-}\ddot{I}{€}^{+}$ tagged by $D\to K_{S,L}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ are studied in bins of phase space of the three-body decays. This analysis has sensitivity to both $r_D^{K\ddot{I}€}\cos \hat{I}{´}_D^{K\ddot{I}€}$ and $r_D^{K\ddot{I}€}\sin \hat{I}{´}_D^{K\ddot{I}€}$. A fit to ${\mathcal{A}}_{K\ddot{I}€}$, ${\mathcal{A}}_{K\ddot{I}€}^{\ddot{I}€\ddot{I}€\ddot{I}{€}^0}$ and the phase-space distribution of the $D\to K_{S,L}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ tags yields $\hat{I}{´}_D^{K\ddot{I}€}=\left(187.6{}_{-9.7}^{+8.9}{}_{-6.4}^{+5.4}\right)$ degrees, where external constraints are applied for $r_D^{K\ddot{I}€}$ and other relevant parameters. This is the most precise measurement of $\hat{I}{´}_D^{K\ddot{I}€}$ in quantum-correlated $D\bar{D}$ decays.

Submitted to EPJC