Updated measurement of the strong phase inD0→K+π−decay using quantum correlations ine+e−→D0D¯0at CLEO

We analyze a sample of $3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ quantum-correlated ${D}^{0}{\overline{D}}^{0}$ pairs from $818\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ collision data collected with the CLEO-c detector at ${E}_{\mathrm{cm}}=3.77\text{ }\text{ }\mathrm{GeV}$, to give an updated measurement of $\mathrm{cos}\ensuremath{\delta}$ and a first determination of $\mathrm{sin}\ensuremath{\delta}$, where $\ensuremath{\delta}$ is the relative strong phase between doubly Cabibbo-suppressed ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and Cabibbo-favored ${\overline{D}}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay amplitudes. With no inputs from other experiments, we find $\mathrm{cos}\ensuremath{\delta}={0.81}_{\ensuremath{-}0.18\ensuremath{-}0.05}^{+0.22+0.07}$, $\mathrm{sin}\ensuremath{\delta}=\ensuremath{-}0.01\ifmmode\pm\else\textpm\fi{}0.41\ifmmode\pm\else\textpm\fi{}0.04$, and $|\ensuremath{\delta}|=({10}_{\ensuremath{-}53\ensuremath{-}0}^{+28+13})\ifmmode^\circ\else\textdegree\fi{}$. By including external measurements of mixing parameters, we find alternative values of $\mathrm{cos}\ensuremath{\delta}={1.15}_{\ensuremath{-}0.17\ensuremath{-}0.08}^{+0.19+0.00}$, $\mathrm{sin}\ensuremath{\delta}={0.56}_{\ensuremath{-}0.31\ensuremath{-}0.20}^{+0.32+0.21}$, and $\ensuremath{\delta}=({18}_{\ensuremath{-}17}^{+11})\ifmmode^\circ\else\textdegree\fi{}$. Our results can be used to improve the world average uncertainty on the mixing parameter $y$ by approximately 10%.