Model-independent determination of the relative strong-phase difference between $D^0$ and ${\bar{D}}^0\to K_{S,L}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and its impact on the measurement of the CKM angle ${\hat{I}}^3/\ddot{I}{•}_3$

Abstract

Crucial inputs for a variety of $CP$-violation studies can be determined through the analysis of pairs of quantum-entangled neutral $D$ mesons, which are produced in the decay of the $\ddot{I}ˆ(3770)$ resonance. The relative strong-phase parameters between $D^0$ and ${\bar{D}}^0$ in the decays $D^0\to K_{S,L}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ are studied using 2.93~${\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data delivered by the BEPCII collider and collected by the BESIII detector at a center-of-mass energy of 3.773 GeV. Results are presented in regions of the phase space of the decay. These are the most precise measurements to date of the strong-phase parameters in $D\to K_{S,L}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays. Using these parameters, the associated uncertainty on the Cabibbo-Kobayashi-Maskawa angle ${\hat{I}}^3/\ddot{I}{•}_3$ is expected to be between $0.7^{\circ }$ and $1.2^{\circ }$, for an analysis using the decay $B^{\pm }\to D{K}^{\pm }$, $D\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, where $D$ represents a superposition of $D^0$ and $\overline{D^0}$ states. This is a factor of three smaller than that achievable with previous measurements. Furthermore, these results provide valuable input for charm-mixing studies, other measurements of $CP$ violation, and the measurement of strong-phase parameters for other $D$-decay modes.

34 pages, 10 figures