Measurement of the $D\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $D\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^0$ coherence factors and average strong-phase differences in quantum-correlated $D\bar{D}$ decays

Abstract

The decays $D\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $D\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^0$ are studied in a sample of quantum-correlated $D\bar{D}$ pairs produced through the process $e^{+}{e}^{-}\to \ddot{I}ˆ(3770)\to D\bar{D}$, exploiting a data set collected by the BESIII experiment that corresponds to an integrated luminosity of 2.93 fb${}^{-1}$. Here $D$ indicates a quantum superposition of a $D^0$ and a ${\bar{D}}^0$ meson. By reconstructing one neutral charm meson in a signal decay, and the other in the same or a different final state, observables are measured that contain information on the coherence factors and average strong-phase differences of each of the signal modes. These parameters are critical inputs in the measurement of the angle ${\hat{I}}^3$ of the Unitarity Triangle in $B^{-}\to D{K}^{-}$ decays at the LHCb and Belle II experiments. The coherence factors are determined to be $R_{K3\ddot{I}€}=0.52_{-0.10}^{+0.12}$ and $R_{K\ddot{I}€\ddot{I}{€}^0}=0.78\pm 0.04$, with values for the average strong-phase differences that are $\hat{I}{´}_D^{K3\ddot{I}€}={\left(167_{-19}^{+31}\right)}^{\circ }$ and $\hat{I}{´}_D^{K\ddot{I}€\ddot{I}{€}^0}={\left(196_{-15}^{+14}\right)}^{\circ }$, where the uncertainties include both statistical and systematic contributions. The analysis is re-performed in four bins of the phase-space of the $D\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ to yield results that will allow for a more sensitive measurement of ${\hat{I}}^3$ with this mode, to which the BESIII inputs will contribute an uncertainty of around 6${}^{\circ }$.

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