${{\mathit \delta}}({{\mathit K}}{{\mathit \pi}}$) - relative strong phase

INSPIRE   JSON  (beta) PDGID:
S032DPH
${{\mathit \delta}}({{\mathit K}}{{\mathit \pi}}$) is the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ relative strong phase between DCS and CF decays, with the convention $\mathit CP~|{{\mathit D}^{0}}>$ = $|{{\overline{\mathit D}}^{0}}>$.
S032DPH
VALUE (degrees) DOCUMENT ID TECN  COMMENT
$\bf{ 191 {}^{+6}_{-7}}$ OUR AVERAGE
$189.2$ ${}^{+6.9}_{-7.4}$ ${}^{+3.4}_{-3.8}$ 1
ABLIKIM
2025CM
 
BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$, $4.13 - 4.23$ GeV and 3.773 GeV
$198$ ${}^{+11}_{-17}$ 2, 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. • •
$192.8$ ${}^{+11.0}_{-12.4}$ ${}^{+1.9}_{-2.4}$ 4
ABLIKIM
2025CM
 
BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$, $4.13 - 4.23$ GeV
$187.6$ ${}^{+8.9}_{-9.7}$ ${}^{+5.4}_{-6.4}$ 5
ABLIKIM
2022BM
 
BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$, 3.77 GeV
6, 3
ABLIKIM
2014C
 
BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$, 3.77 GeV
$202$ ${}^{+11}_{-12}$ ${}^{+9}_{-11}$ 7, 3
ASNER
2008
 
CLEO Repl. by ASNER 2012
1  The reported value is a combination with that in ABLIKIM 2022BM.
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 $ = ($10$ ${}^{+28}_{-53}{}^{+13}_{-0})^\circ{}$ 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  The value reported here has been rotated by 180 deg with respect to the value quoted in the paper, where the convention $\mathit CP~|{{\mathit D}^{0}}>$ = $−|{{\overline{\mathit D}}^{0}}>$ is used.
4  Uses quantum correlations in ${{\mathit D}}{{\overline{\mathit D}}}$ produced in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}}{{\overline{\mathit D}}}$, ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\overline{\mathit D}}}$ and ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\overline{\mathit D}}^{*}}$ 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. The fit includes external measurements of charm mixing parameters.
5  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.
6  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 of cos($\delta $) = $1.02$ $\pm0.11$ $\pm0.06$ $\pm0.01$ where the third uncertainty is due to errors introduced by external inputs.
7  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