Time-independent measurements of $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing and relative strong phases using quantum correlations

Due to the presence of quantum correlations in the $C=-1$ and $C=+1$ $D^0{\overline{D}}^0$ pairs produced in the reactions $e^{+}{e}^{-}\to D^0{\overline{D}}^0(n{\pi }^0)$ and $e^{+}{e}^{-}\to D^0{\overline{D}}^0\gamma (n{\pi }^0)$, respectively, the time-integrated $D^0{\overline{D}}^0$ decay rates are sensitive to interference between amplitudes for indistinguishable final states. The size of this interference is governed by the relevant amplitude ratios and can include contributions from $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing. We present a method for simultaneously measuring the magnitudes and phases of these amplitude ratios and searching for $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing. We make use of fully- and partially-reconstructed $D^0{\overline{D}}^0$ pairs in both $C$ eigenstates, and we estimate experimental sensitivities based on a plausible charm factory data set. Similar analyses can be applied to coherent $K^0{\overline{K}}^0$, $B^0{\overline{B}}^0$, or $B_s^0{\overline{B}}_s^0$ pairs.

Figure 1

Current allowed regions in the plane of $y_{K\pi }^{\prime }$ versus $x_{K\pi }^{\prime }$ [24, 25, 27, 29, 30, 31, 32, 33, 34, 35], assuming ${\delta }_{K\pi }=0$. A nonzero value for ${\delta }_{K\pi }$ would rotate the $\Delta \Gamma$ confidence region clockwise about the origin by an angle ${\delta }_{K\pi }$.

Figure 2

Current allowed regions in the plane of $y$ versus $x$ [24, 25, 27, 29, 30, 35], with our 95% C.L. contour for ${\Gamma }_{D^0{\overline{D}}^0}^{C=-1}=10·{\Gamma }_{D^0{\overline{D}}^0}^{C=+1}=3\times {10}^6$ superimposed.