Model-independent determination of the strong-phase difference between $D^0$ and ${\bar{D}}^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays

Abstract

Measurements of the strong-phase difference between $D^0$ and ${\bar{D}}^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ are performed in bins of phase space. The study exploits a sample of quantum-correlated $D\bar{D}$ mesons collected by the BESIII experiment in $e^{+}{e}^{-}$ collisions at a center-of-mass energy of 3.773~GeV, corresponding to an integrated luminosity of 2.93~fb${}^{-1}$. Here, $D$ denotes a neutral charm meson in a superposition of flavor eigenstates. The reported results are valuable for measurements of the $CP$-violating phase ${\hat{I}}^3$ (also denoted $\ddot{I}{•}_3$) in $B^{\pm }\to D{K}^{\pm }$, $D\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays, and the binning schemes are designed to provide good statistical sensitivity to this parameter. The expected uncertainty on ${\hat{I}}^3$ arising from the precision of the strong-phase measurements, when applied to very large samples of $B$-meson decays, is around $1.5^{\circ }$ or $2^{\circ }$, depending on the binning scheme. The binned strong-phase parameters are combined to give a value of $F_{+}^{4\ddot{I}€}=0.746\pm 0.010\pm 0.004$ for the $CP$-even fraction of $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays, which is around 30\% more precise than the previous best measurement of this quantity.