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cos $ \delta $

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S032DKP

$\delta $ is the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ relative strong phase.

VALUE DOCUMENT ID TECN  COMMENT $\bf{ 0.990 \pm0.025}$ OUR AVERAGE $0.991$ ${}^{+0.021}_{-0.022}$ ${}^{+0.012}_{-0.015}$ 1 ABLIKIM 2022 BM BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ , 3.77 GeV $1.02$ $\pm0.11$ $\pm0.06$ 2 ABLIKIM 2014 C BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ , 3.77 GeV $0.81$ ${}^{+0.22}_{-0.18}$ ${}^{+0.07}_{-0.05}$ 3 ASNER 2012 CLEO ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ , 3.77 GeV • • We do not use the following data for averages, fits, limits, etc. • • $1.03$ ${}^{+0.31}_{-0.17}$ $\pm0.06$ 4 ASNER 2008 CLEO Repl. by ASNER 2012 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