Determination of theD0→K+π−relative strong phase using quantum-correlated measurements ine+e−→D0D¯0at CLEO

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Abstract

We exploit the quantum coherence between pair-produced ${D}^{0}$ and ${\overline{D}}^{0}$ in $\ensuremath{\psi}(3770)$ decays to study charm mixing, which is characterized by the parameters $x$ and $y$, and to make a first determination of the relative strong phase $\ensuremath{\delta}$ between doubly Cabibbo-suppressed ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and Cabibbo-favored ${\overline{D}}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. We analyze a sample of $1.0\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${D}^{0}{\overline{D}}^{0}$ pairs from $281\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ collision data collected with the CLEO-c detector at ${E}_{\mathrm{cm}}=3.77\text{ }\text{ }\mathrm{GeV}$. By combining CLEO-c measurements with branching fraction input and time-integrated measurements of ${R}_{\mathrm{M}}\ensuremath{\equiv}({x}^{2}+{y}^{2})/2$ and ${R}_{\mathrm{WS}}\ensuremath{\equiv}\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})/\ensuremath{\Gamma}({\overline{D}}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$ from other experiments, we find $\mathrm{cos}\ensuremath{\delta}={1.03}_{\ensuremath{-}0.17}^{+0.31}\ifmmode\pm\else\textpm\fi{}0.06$, where the uncertainties are statistical and systematic, respectively. In addition, by further including external measurements of charm mixing parameters, we obtain an alternate measurement of $\mathrm{cos}\ensuremath{\delta}=1.10\ifmmode\pm\else\textpm\fi{}0.35\ifmmode\pm\else\textpm\fi{}0.07$, as well as $x\mathrm{sin}\ensuremath{\delta}=({4.4}_{\ensuremath{-}1.8}^{+2.7}\ifmmode\pm\else\textpm\fi{}2.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\ensuremath{\delta}=({22}_{\ensuremath{-}12\ensuremath{-}11}^{+11+9})\ifmmode^\circ\else\textdegree\fi{}$.

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