# ${{\boldsymbol D}^{0}}$ $\rightarrow$ ${{\boldsymbol K}^{-}}{{\boldsymbol \pi}^{-}}$2 ${{\boldsymbol \pi}^{+}}$ COHERENCE FACTOR $\boldsymbol R_{ {{\boldsymbol K}}3 {{\boldsymbol \pi}} }$ INSPIRE search

See the note on `${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing' for the definition. $\mathit R_{ {{\mathit K}}3 {{\mathit \pi}} }$ can have any value between 0 and 1. A value near 1 indicates the decay is dominated by a few intermediate states with limited interference.
VALUE EVTS DOCUMENT ID TECN  COMMENT
$0.53$ ${}^{+0.18}_{-0.21}$ 1, 2, 3
 2016
${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at ${{\mathit \psi}{(3770)}}$, ${{\mathit p}}{{\mathit p}}$ at 7,8 TeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.458$ $\pm0.010$ $\pm0.023$ 0.9M,3k 4
 2018 AI
LHCB amplitude models
$0.32$ ${}^{+0.20}_{-0.28}$ 1, 3
 2014
Repl. by EVANS 2016
$0.36$ ${}^{+0.24}_{-0.30}$ 5
 2009
CLEO Repl. by LIBBY 2014
1  Uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$, where the decay rates of $\mathit CP$-tagged ${{\mathit K}^{-}}{{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}$ final states depend on $\mathit R_{ {{\mathit K}}3 {{\mathit \pi}} }$ and $\delta {}^{ {{\mathit K}}3 {{\mathit \pi}} }$.
2  A combined fit with a recent LHCB ${{\mathit D}^{0}}$ ${{\overline{\mathit D}}^{0}}$ mixing results in AAIJ 2016F is also reported, to be $0.43$ ${}^{+0.17}_{-0.13}$.
3  Obtained by analyzing CLEO-c data but not authored by the CLEO Collaboration.
4  Calculated from amplitude models to ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{-}}$ and cc. Reports $0.458$ $\pm0.010$ $\pm0.012$ $\pm0.020$ value where the 3rd uncertainty is the model uncertainty. We combined both systematic uncertainties in quadrature. Because of the importance of model independence in the practical use of the coherence factor, we do not include model-derived results in the average.
5  LOWREY 2009 uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$, where the decay rates of $\mathit CP$-tagged ${{\mathit K}^{-}}{{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}$ final states depend on $\mathit R_{ {{\mathit K}}3 {{\mathit \pi}} }$ and $\delta {}^{ {{\mathit K}}3 {{\mathit \pi}} }$. A fit that includes external measurements of charm mixing parameters gets $\mathit R_{ {{\mathit K}}3 {{\mathit \pi}} }$ = $0.33$ ${}^{+0.26}_{-0.23}$.
References:
 AAIJ 2018AI
EPJ C78 443 Studies of the resonance structure in $D^{0} \rightarrow K^\mp \pi ^\pm \pi ^\pm \pi ^\mp$ decays
 EVANS 2016
PL B757 520 Improved Determination of the ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Coherence Factor and Associated Hadronic Parameters from a Combination of ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \psi}{(3770)}}$ $\rightarrow$ ${{\mathit c}}{{\overline{\mathit c}}}$ and ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit c}}{{\overline{\mathit c}}}{{\mathit X}}$ Data
 LIBBY 2014
PL B731 197 New Determination of the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Coherence Factors and Average Strong-Phase Differences
 LOWREY 2009
PR D80 031105 Determination of the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Coherence Factors and Average Strong-Phase Differences using Quantum-Correlated Measurements