¹ Uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$ to measure the asymmetry of the branching fraction of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ in $\mathit CP$-odd and $\mathit CP$-even eigenstates to be ($13.2$ $\pm1.1$ $\pm0.7)\%$ and ($13.0$ $\pm1.2$ $\pm0.8)\%$ when using the predominantly $\mathit CP$-even tag ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$. A fit that includes external measurements of charm mixing parameters finds the value quoted above.

² Uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$ to measure the asymmetry of the branching fraction of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ in $\mathit CP$-odd and $\mathit CP$-even eigenstates to be ($12.7$ $\pm1.3$ $\pm0.7)\%$. A fit that includes external measurements of charm mixing parameters finds the value quoted above.

³ Uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$, where decay rates of $\mathit CP$-tagged ${{\mathit K}}{{\mathit \pi}}$ final states depend on the strong phases between the decays of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$. The measurements obtained sin($\delta $) = $-0.01$ $\pm0.41$ $\pm0.04$ and $\vert \delta \vert $ = ()$^\circ{}$ as well. A fit that includes external measurements of charm mixing parameters finds cos($\delta $) = $1.15$ ${}^{+0.19}_{-0.17}{}^{+0.00}_{-0.08}$, sin($\delta $) = $0.56$ ${}^{+0.32}_{-0.31}{}^{+0.21}_{-0.20}$, and $\vert \delta \vert $ = ($18$ ${}^{+11}_{-17})^\circ{}$.

⁴ ASNER 2008 uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$, where decay rates of $\mathit CP$-tagged ${{\mathit K}}{{\mathit \pi}}$ final states depend on cos $ \delta $ because of interfering amplitudes. The above measurement implies $\vert \delta \vert $ $<$ 75$^\circ{}$ with a confidence level of 95$\%$. A fit that includes external measurements of charm mixing parameters finds cos $ \delta $ = $1.10$ $\pm0.35$ $\pm0.07$. See also the note on ``${{\mathit D}^{0}}-$ ${{\overline{\mathit D}}^{0}}$ Mixing'' p. 783 in our 2008 Review (PDG 2008).

References:

ABLIKIM

2022BM

EPJ C82 1009

Improved measurement of the strong-phase difference $\delta _D^{K\pi }$ in quantum-correlated $D{\bar{D}}$ decays

ABLIKIM

2014C

PL B734 227

Measurement of the ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ Strong Phase Difference in ${{\mathit \psi}{(3770)}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$

ASNER

2012

PR D86 112001

Updated Measurement of the Strong Phase in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ Decay using Quantum Correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at CLEO

ASNER

2008

PR D78 012001

Determination of the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ Relative Strong Phase Using Quantum-Correlated Measurements in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at CLEO