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${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}$ AVERAGE RELATIVE STRONG PHASE $\delta {}^{ {{\mathit K}}3 {{\mathit \pi}} }$

INSPIRE   PDGID:

S032SP2

The quoted value of $\delta $ is based on the same sign $\mathit CP$ phase of ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ convention.

VALUE ($^\circ{}$) EVTS DOCUMENT ID TECN  COMMENT $\bf{ 149 {}^{+26}_{-16}}$ OUR AVERAGE  Error includes scale factor of 1.4. $167$ ${}^{+31}_{-19}$ 8.6k 1 ABLIKIM 2021 AA BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at ${{\mathit \psi}{(3770)}}$ $125$ ${}^{+22}_{-14}$ 1, 2, 3 EVANS 2016 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at ${{\mathit \psi}{(3770)}}$ • • We do not use the following data for averages, fits, limits, etc. • • $255$ ${}^{+21}_{-78}$ 1, 3 LIBBY 2014 Repl. by EVANS 2016 $118$ ${}^{+62}_{-53}$ 4 LOWREY 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 ($128$ ${}^{+28}_{-17})^\circ{}$. 3  Obtained by analyzing CLEO-c data but not authored by the CLEO Collaboration. 4  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 $\delta {}^{ {{\mathit K}}3 {{\mathit \pi}} }$ = ($114$ ${}^{+26}_{-23})^\circ{}$.

References:

ABLIKIM 2021AA JHEP 2105 164 Measurement of the $D \to K^-\pi^+\pi^+\pi^-$ and $D \to K^-\pi^+\pi^0$ coherence factors and average strong-phase differences in quantum-correlated ${D\bar{D}}$ 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 Also PL B765 402 (errat.) 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