# cos $\delta$ INSPIRE search

$\delta$ is the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ relative strong phase.
VALUE DOCUMENT ID TECN  COMMENT
$\bf{ 0.97 \pm0.11}$ OUR AVERAGE
$1.02$ $\pm0.11$ $\pm0.06$ 1
 2014 C
BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ , 3.77 GeV
$0.81$ ${}^{+0.22}_{-0.18}$ ${}^{+0.07}_{-0.05}$ 2
 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. • • •
$1.03$ ${}^{+0.31}_{-0.17}$ $\pm0.06$ 3
 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 ($12.7$ $\pm1.3$ $\pm0.7)\%$. 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 ${{\mathit \psi}{(3770)}}$, 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 $\vert \delta \vert$ = ($18$ ${}^{+11}_{-17})^\circ{}$.
3  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 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