The ${{\mathit D}_{{1}}^{0}}$ and ${{\mathit D}_{{2}}^{0}}$ are the mass eigenstates of the ${{\mathit D}^{0}}$ meson, as described in the note on “${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing,” above.

Due to the strong phase difference between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ , we exclude from the average those measurements of ${{\mathit y}^{\,'}}$ that are inferred from the ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ mixing ratio $\Gamma $( ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ via ${{\overline{\mathit D}}^{0}}$) $/$ $\Gamma $( ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ) given near the end of this ${{\mathit D}^{0}}$ Listings. OUR AVERAGE assumes $\mathit CP$ conservation, though this is disfavored by data.

In the absence of $\mathit CP$ violation, the experimental measurement of the observable y$_{CP}$ corresponds to y. In the presence of $\mathit CP$ violation, y$_{CP}$ is approximately equal to y up to a $\mathit CP$-violating weak phase cosine, that is very close to unity, and higher order $\mathit CP$-violating effects. Many experiments measure y$_{CP}$ with respect to a reference channel, such that the quoted results below are often y$_{CP}\pm{}$y$_{CP}$(reference). We denote the actual observable and the reference channel below for those experiments with sufficient sensitivity such that y$_{CP}$(reference) cannot be neglected.

Some early results have been omitted. See our 2006 $\mathit Review$ (Journal of Physics G33 1 (2006)).

“OUR EVALUATION” comes from CPV allowing averages provided by the Heavy Flavor Averaging Group, see the note on “${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing.''

VALUE ($ 10^{-2} $) EVTS DOCUMENT ID TECN  COMMENT $\bf{ 1.394 \pm0.056}$ OUR EVALUATION  See the ideogram below. $\bf{ 1.34 \pm0.08}$ OUR AVERAGE  Error includes scale factor of 1.4.  See the ideogram below. $1.392$ $\pm0.052$ $\pm0.026$ 1 AAIJ 2022 O LHCB y$_{CP}$ $−$ y$_{CP}$( ${{\mathit K}}{{\mathit \pi}}$ ) , ${{\mathit p}}{{\mathit p}}$ at 13 TeV $0.92$ ${}^{+0.30}_{-0.28}$ 30.6M 2 AAIJ 2021 AB LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV $1.92$ $\pm1.82$ ${}^{+1.29}_{-1.24}$ 91k 3 NAYAK 2020 BELL ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \omega}}$ $1.14$ $\pm0.26$ $\pm0.18$ 4 AAIJ 2019 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV $1.48$ $\pm0.74$ 2.3M 5 AAIJ 2019 X LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ 6 AAIJ 2018 K LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV $0.06$ $\pm0.92$ $\pm0.26$ 7 AAIJ 2016 V LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV $0.4$ $\pm1.8$ $\pm1.0$ 8 LEES 2016 D BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , 10.6 GeV $2.22$ $\pm0.44$ $\pm0.18$ 9 STARIC 2016 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$ $-4.0$ $\pm2.6$ $\pm1.4$ 10 ABLIKIM 2015 D BES3 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \psi}{(3770)}}$ 11 KO 2014 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$ $0.60$ $\pm0.30$ ${}^{+0.10}_{-0.17}$ 12 PENG 2014 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$ 13 AALTONEN 2013 AE CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV $1.44$ $\pm0.36$ $\pm0.24$ 14 LEES 2013 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.55$ $\pm0.63$ $\pm0.41$ 15 AAIJ 2012 K LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV $1.14$ $\pm0.40$ $\pm0.30$ 16 DEL-AMO-SANCH.. 2010 D BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , 10.6 GeV $0.22$ $\pm1.22$ $\pm1.04$ 17 ZUPANC 2009 BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ $-1.0$ $\pm2.0$ ${}^{+1.4}_{-1.6}$ 18k 18 ABE 2002 I BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ $-2.4$ $\pm5.0$ $\pm2.8$ 3393 19 CSORNA 2002 CLE2 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ $6.84$ $\pm2.78$ $\pm1.48$ 10k 18 LINK 2000 FOCS ${{\mathit \gamma}}$ nucleus $+1.6$ $\pm5.8$ $\pm2.1$ 18 AITALA 1999 E E791 ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{+}}{{\mathit K}^{-}}$ • • We do not use the following data for averages, fits, limits, etc. • • 20 AAIJ 2017 AO LHCB Repl. by AAIJ 2018K 21 AAIJ 2013 CE LHCB Repl. by AAIJ 2017AO 22 AAIJ 2013 N LHCB Repl. by AAIJ 2013CE $2.32$ $\pm0.44$ $\pm0.36$ 23 AUBERT 2009 AI BABR See LEES 2013 $-0.12$ ${}^{+1.10}_{-1.28}$ $\pm0.68$ 24 AUBERT 2009 AN BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at 10.58 GeV $1.4$ ${}^{+4.8}_{-5.4}$ 25 LOWREY 2009 CLEO ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \psi}{(3770)}}$ $1.70$ $\pm1.52$ 13k 26 AALTONEN 2008 E CDF ${{\mathit p}}{{\overline{\mathit p}}}$ , $\sqrt {s }$ = 1.96 TeV $2.06$ $\pm0.66$ $\pm0.38$ 27 AUBERT 2008 U BABR See AUBERT 2009AI $1.94$ $\pm0.88$ $\pm0.62$ 4k 26 AUBERT 2007 W BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ 10.6 GeV $2.62$ $\pm0.64$ $\pm0.50$ 160k 28 STARIC 2007 BELL Repl. by STARIC 2016 $0.74$ $\pm0.50$ ${}^{+0.20}_{-0.31}$ 534k 29 ZHANG 2007 B BELL Repl. by PENG 2014 $-0.7$ $\pm4.9$ 4k 30, 26 ZHANG 2006 BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $-3.0$ ${}^{+5.0}_{-4.8}$ ${}^{+1.6}_{-0.8}$ 29 ASNER 2005 CLEO ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ 10 GeV $-0.3$ $\pm5.7$ 30, 26 LI 2005 A BELL See ZHANG 2006 $-5.2$ ${}^{+18.4}_{-16.8}$ 30, 26 LINK 2005 H FOCS ${{\mathit \gamma}}$ nucleus $1.6$ $\pm0.8$ ${}^{+1.0}_{-0.8}$ 450k 31 AUBERT 2003 P BABR See AUBERT 2008U $1.6$ ${}^{+6.2}_{-12.8}$ 30, 26 AUBERT 2003 Z BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , 10.6~GeV $-5.0$ ${}^{+2.8}_{-3.2}$ $\pm0.6$ 26 GODANG 2000 CLE2 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ 1  AAIJ 2022O is the combination of the measurement in the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ channel and the one in the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}$ channel, that are ($1.314$ $\pm0.106$ $\pm0.032)\%$ and ($1.416$ $\pm0.060$ $\pm0.028)\%$ respectively, assuming fully correlated systematics except those related to peaking backgrounds. 2  AAIJ 2021AB analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ events allows for $\mathit CP$ violation (none seen). 3  NAYAK 2020 reports $0.0192$ $\pm0.0182$ $\pm0.0124$ ${}^{+0.0034}_{-0.0000}$ where the last uncertainty is due to possible presence of $\mathit CP$-even decays in the data sample. Extracts $\mathit y_{CP}=(\Gamma _{CP+}$ $−$ $\Gamma _{CP-}$) $/$ ($\Gamma _{CP+}$ + $\Gamma _{CP-}$) in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \omega}}$ versus ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \omega}}$ , by measuring the decay lifetime of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \omega}}$ with ${{\mathit \omega}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ versus ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ . We list 2$\mathit y_{CP}$ = 2$\mathit y$ (= $\Delta \Gamma /\Gamma $) in the absence of $\mathit CP$ violation. 4  Based on 3 fb${}^{-1}$ of data collected at $\sqrt {s }$ = 7, 8 TeV. Measures the lifetime difference between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ ($\mathit CP~$even) decays and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ ($\mathit CP~$mixed) decays, or $\mathit y_{\mathit CP}=(\Gamma _{CP+}$ $−$ $\Gamma _{CP-}$) $/$ ($\Gamma _{CP+}$ + $\Gamma _{CP-}$). The ${{\mathit D}^{0}}$ mesons are required to originate from semimuonic decays of ${{\mathit B}}$ mesons. We list 2$\mathit y_{\mathit CP}$ = $\Delta \Gamma /\Gamma $. 5  AAIJ 2019X ${{\mathit D}^{0}}$ come from ${{\mathit D}^{*+}}$ and ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \mu}^{-}}{{\mathit X}}$ decays (and c.c.) in ${{\mathit p}}{{\mathit p}}$ collisions at 7 and 8 TeV. Measurement allows for $\mathit CP$ violation (none seen). 6  The result was established with ${{\mathit D}^{0}}$ from prompt and secondary ${{\mathit D}^{*}}$. Based on 5 fb${}^{-1}$ of data collected at $\sqrt {s }$ = 7, 8, 13 TeV. Assumes no $\mathit CP$ violation. Reported ${{\mathit x}^{'2}}$ = ($3.9$ $\pm2.7$) $ \times 10^{-5}$ and ${{\mathit y}^{\,'}}$ = ($5.28$ $\pm0.52$) $ \times 10^{-3}$, where ${{\mathit x}^{\,'}}$ = ${{\mathit x}}$ cos($\delta $) + ${{\mathit y}}$ sin($\delta $), ${{\mathit y}^{\,'}}$ = ${{\mathit y}}$ cos($\delta $) $−$ ${{\mathit x}}$ sin($\delta $) and $\delta $ is the strong phase between the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ . 7  Model-independent measurement of the charm mixing parameters in the decay ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ using 1.0 ${\mathrm {fb}}{}^{-1}$ of LHCb data at $\sqrt {s }$ = 7 TeV. 8  Time-dependent amplitude analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ . 9  An improved measurement of ${{\overline{\mathit D}}^{0}}−{{\mathit D}^{0}}$ mixing and a search for $\mathit CP$ violation in ${{\mathit D}^{0}}$ decays to $\mathit CP$-even final states ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ using the final Belle data sample of 976 fb${}^{-1}$. 10  ABLIKIM 2015D uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$. 11  Based on 976 fb${}^{-1}$ of data collected at ${{\mathit Y}{(nS)}}$ resonances. Assumes no $\mathit CP$ violation. Reported ${{\mathit x}^{'2}}$ = ($0.09$ $\pm0.22$) $ \times 10^{-3}$ and ${{\mathit y}^{\,'}}$ = ($4.6$ $\pm3.4$) $ \times 10^{-3}$, where ${{\mathit x}^{\,'}}$ = x$~$cos($\delta $) + y$~$sin($\delta $), ${{\mathit y}^{\,'}}$ = y$~$cos($\delta $) $−$ x$~$sin($\delta $) and $\delta $ is the strong phase between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ . 12  The time-dependent Dalitz-plot analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ is emplored. Decay-time information and interference on the Dalitz plot are used to distinguish doubly Cabibbo-suppressed decays from mixing and to measure the relative phase between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{*+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{*+}}{{\mathit \pi}^{-}}$ . This value allows $\mathit CP$ violation and is sensitive to the sign of $\Delta \mathit m$. 13  Based on 9.6 fb${}^{-1}$ of data collected at the Tevatron. Assumes no $\mathit CP$ violation. Reported ${{\mathit x}^{'2}}$ = ($0.08$ $\pm0.18$) $ \times 10^{-3}$ and ${{\mathit y}^{\,'}}$ = ($4.3$ $\pm4.3$) $ \times 10^{-3}$, where ${{\mathit x}^{\,'}}$ = ${{\mathit x}}$ cos($\delta $) + ${{\mathit y}}$ sin($\delta $), ${{\mathit y}^{\,'}}$ = ${{\mathit y}}$ cos($\delta $) $−$ ${{\mathit x}}$ sin($\delta $) and $\delta $ is the strong phase between the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ . 14  Obtained ${{\mathit y}_{{CP}}}$ = ($0.72$ $\pm0.18$ $\pm0.12)\%$ based on three effective ${{\mathit D}^{0}}$ lifetimes measured in ${{\mathit K}^{\mp}}{{\mathit \pi}^{\pm}}$ , ${{\mathit K}^{-}}{{\mathit K}^{+}}$ , and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ . We list 2${{\mathit y}_{{CP}}}$ = $\Delta \Gamma /\Gamma $. 15  Compared the lifetimes of ${{\mathit D}^{0}}$ decay to the $\mathit CP$ eigenstate ${{\mathit K}^{+}}{{\mathit K}^{-}}$ with ${{\mathit D}^{0}}$ decay to ${{\mathit \pi}^{+}}{{\mathit K}^{-}}$ . The values here assume no $\mathit CP$ violation. 16  DEL-AMO-SANCHEZ 2010D uses 540,800$\pm800$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and 79,900$\pm300$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ events in a time-dependent amplitude analyses of the ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ Dalitz plots. No evidence was found for $\mathit CP$ violation, and the values here assume no such violation. 17  ZUPANC 2009 uses a method based on measuring the mean decay time of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ events for different ${{\mathit K}^{+}}{{\mathit K}^{-}}$ mass intervals. 18  LINK 2000 , AITALA 1999E, and ABE 2002I measure the lifetime difference between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}$ ($\mathit CP~$even) decays and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ ($\mathit CP~$mixed) decays, or $\mathit y_{\mathit CP}$= [$\Gamma\mathrm {(\mathit CP+)}−\Gamma\mathrm {(\mathit CP−)}]/[\Gamma\mathrm {(\mathit CP+)}+\Gamma\mathrm {(\mathit CP−)}$]. We list 2$\mathit y_{\mathit CP}=\Delta \Gamma /\Gamma $. 19  CSORNA 2002 measures the lifetime difference between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}$ and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ ($\mathit CP~$even) decays and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ ($\mathit CP~$mixed) decays, or $\mathit y_{\mathit CP}$= [$\Gamma\mathrm {(\mathit CP+)}−\Gamma\mathrm {(\mathit CP−)}]/[\Gamma\mathrm {(\mathit CP+)}+\Gamma\mathrm {(\mathit CP−)}$]. We list 2$\mathit y_{\mathit CP}=\Delta \Gamma /\Gamma $. 20  The result was established with ${{\mathit D}^{0}}$ from prompt and secondary ${{\mathit D}^{*}}$. Based on 3 fb${}^{-1}$ of data collected at $\sqrt {s }$ = 7, 8 TeV. Assumes no $\mathit CP$ violation. Reported ${{\mathit x}^{'2}}$ = ($3.6$ $\pm4.3$) $ \times 10^{-5}$ and ${{\mathit y}^{\,'}}$ = ($5.23$ $\pm0.84$) $ \times 10^{-3}$, where ${{\mathit x}^{\,'}}$ = ${{\mathit x}}$ cos($\delta $) + ${{\mathit y}}$ sin($\delta $), ${{\mathit y}^{\,'}}$ = ${{\mathit y}}$ cos($\delta $) $−$ ${{\mathit x}}$ sin($\delta $) and $\delta $ is the strong phase between the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ . 21  Based on 3 fb${}^{-1}$ of data collected at $\sqrt {s }$ = 7, 8 TeV. Assumes no $\mathit CP$ violation. Reported ${{\mathit x}^{'2}}$ = ($5.5$ $\pm4.9$) $ \times 10^{-4}$ and ${{\mathit y}^{\,'}}$ = ($4.8$ $\pm1.0$) $ \times 10^{-3}$, where ${{\mathit x}^{\,'}}$ = ${{\mathit x}}$ cos($\delta $) + ${{\mathit y}}$ sin($\delta $), ${{\mathit y}^{\,'}}$ = ${{\mathit y}}$ cos($\delta $) $−$ ${{\mathit x}}$ sin($\delta $) and $\delta $ is the strong phase between the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ . 22  Based on 1 fb${}^{-1}$ of data collected at $\sqrt {s }$ = 7 TeV in 2011. Assumes no $\mathit CP$ violation. Reported ${{\mathit x}^{'2}}$ = ($-0.9$ $\pm1.3$) $ \times 10^{-4}$ and ${{\mathit y}^{\,'}}$ = ($7.2$ $\pm2.4$) $ \times 10^{-3}$, where ${{\mathit x}^{\,'}}$ = ${{\mathit x}}$ cos($\delta $) + ${{\mathit y}}$ sin($\delta $), ${{\mathit y}^{\,'}}$ = ${{\mathit y}}$ cos($\delta $) $−$ ${{\mathit x}}$ sin($\delta $) and $\delta $ is the strong phase between the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ . 23  This combines the $\mathit y_{CP}$ = (${\mathit \tau}_{ {{\mathit K}} {{\mathit \pi}} }/{\mathit \tau}_{ {{\mathit K}} {{\mathit K}} })−$1 using untagged ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ and ${{\mathit K}^{-}}{{\mathit K}^{+}}$ events of AUBERT 2009AI with the disjoint $\mathit y_{CP}$ using tagged ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{-}}{{\mathit K}^{+}}$ , and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ events of AUBERT 2008U. 24  The AUBERT 2009AN values are inferred from the branching ratio $\Gamma($ ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ via ${{\overline{\mathit D}}^{0}})/\Gamma($ ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ $)$ given near the end of this Listings. Mixing is distinguished from DCS decays using decay-time information. Interference between mixing and DCS is allowed. The phase between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ is assumed to be small. The width difference here is ${{\mathit y}^{''}}$, which is not the same as ${{\mathit y}_{{CP}}}$ in the note on ${{\mathit D}^{0}}--{{\overline{\mathit D}}^{0}}$ mixing. 25  LOWREY 2009 uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$. See below for coherence factors and average relative strong phases for both ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}$ . A fit that includes external measurements of charm mixing parameters gets 2$\mathit y$ = $0.0162$ $\pm0.0032$. 26  The GODANG 2000 , AUBERT 2003Z, LINK 2005H, LI 2005A, ZHANG 2006 , AUBERT 2007W, and AALTONEN 2008E limits are inferred from the ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ mixing ratio $\Gamma\mathrm {( {{\mathit K}^{+}} {{\mathit \pi}^{-}} (via {{\overline{\mathit D}}^{0}}))}/\Gamma\mathrm {( {{\mathit K}^{-}} {{\mathit \pi}^{+}} )}$ given near the end of this ${{\mathit D}^{0}}$ Listings. Decay-time information is used to distinguish DCS decays from ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ mixing. The limits allow interference between the DCS and mixing ratios, and all except AUBERT 2007W and AALTONEN 2008E also allow $\mathit CP$ violation. The phase between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ is assumed to be small. This is a measurement of ${{\mathit y}^{\,'}}$ and is not the same as the $\mathit y_{\mathit CP}$ of our note above on ``${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing.'' 27  This value combines the results of AUBERT 2008U and AUBERT 2003P. 28  STARIC 2007 compares the lifetimes of ${{\mathit D}^{0}}$ decay to the $\mathit CP$ eigenstates ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ with ${{\mathit D}^{0}}$ decay to ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ . 29  The ASNER 2005 and ZHANG 2007B values are from the time-dependent Dalitz-plot analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ . Decay-time information and interference on the Dalitz plot are used to distinguish doubly Cabibbo-suppressed decays from mixing and to measure the relative phase between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{*+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{*+}}{{\mathit \pi}^{-}}$ . This limit allows $\mathit CP$ violation. 30  The ranges of AUBERT 2003Z, LINK 2005H, LI 2005A, and ZHANG 2006 measurements are for 95$\%$ confidence level. 31  AUBERT 2003P measures Y${}\equiv$ 2 ${{\mathit \tau}^{0}}$ $/$ (${{\mathit \tau}^{+}}$ + ${{\mathit \tau}^{-}}$) $\text{-}$ 1, where ${{\mathit \tau}^{0}}$ is the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ (and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ ) lifetime, and ${{\mathit \tau}^{+}}$ and ${{\mathit \tau}^{-}}$ are the ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ lifetimes to $\mathit CP$-even states (here ${{\mathit K}^{-}}{{\mathit K}^{+}}$ and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ ). In the limit of $\mathit CP$ conservation, Y~=~y${}\equiv\Delta \Gamma $ $/$ 2 $\Gamma $ (we list 2y = $\Delta \Gamma /\Gamma $). AUBERT 2003P also uses ${{\mathit \tau}^{+}}\text{-}{{\mathit \tau}^{-}}$ to get $\Delta $Y = $-0.008$ $\pm0.006$ $\pm0.002$.

($\Gamma _{1}$ $-$ $\Gamma _{2})/\Gamma $ = 2$\mathit y$

Conservation Laws:

$\Delta \mathit C$ = 2 VIA MIXING

References:

AAIJ 2022O PR D105 092013 Measurement of the charm mixing parameter $y_{CP} - y_{CP}^{K\pi}$ using two-body $D^0$ meson decays AAIJ 2021AB PRL 127 111801 Observation of the Mass Difference Between Neutral Charm-Meson Eigenstates NAYAK 2020 PR D102 071102 Measurement of the charm-mixing parameter $y_{CP}$ in $D^{0}\to K^{0}_{S}\omega$ decays at Belle AAIJ 2019X PRL 122 231802 Measurement of the mass difference between neutral charm-meson eigenstates AAIJ 2019 PRL 122 011802 Measurement of the charm-mixing parameter $y_{CP}$ AAIJ 2018K PR D97 031101 Updated determination of $D^0$-$\overline{D}{}^0$ mixing and CP violation parameters with $D^0\to K^+\pi^-$ decays AAIJ 2017AO PR D95 052004 Measurements of Charm Mixing and $\mathit CP$ Violation using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}$ Decays Also PR D96 099907 (errat.) Erratum to AAIJ 2017AO: Measurements of Charm Mixing and $\mathit CP$ Violation using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}$ Decays AAIJ 2016V JHEP 1604 033 Model-independent Measurement of Mixing Parameters in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays LEES 2016D PR D93 112014 Measurement of the Neutral ${{\mathit D}}$ Meson Mixing Parameters in a Time-Dependent Amplitude Analysis of the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Decay STARIC 2016 PL B753 412 Measurement of ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing and Search for $\mathit CP$ Violation in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ , ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays with the Full Belle Data Set ABLIKIM 2015D PL B744 339 Measurement of $\mathit y_{CP}$ in ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Oscillation using Quantum Correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at $\sqrt {s }$ = 3.773 GeV KO 2014 PRL 112 111801 Observation of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions PENG 2014 PR D89 091103 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing and Search for Indirect $\mathit CP$ Violation using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays AAIJ 2013N PRL 110 101802 Observation of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Oscillations AAIJ 2013CE PRL 111 251801 Measurement of ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing Parameters and Search for $\mathit CP$ Violation using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ Decays AALTONEN 2013AE PRL 111 231802 Observation of ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing Using the CDFII Detector LEES 2013 PR D87 012004 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing and $\mathit CP$ Violation in Two-Body ${{\mathit D}^{0}}$ Decays AAIJ 2012K JHEP 1204 129 Measurement of Mixing and $\mathit CP$ Violation Parameters in Two-Body Charm Decays DEL-AMO-SANCHEZ 2010D PRL 105 081803 Measurement of ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing Parameters using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ Decays AUBERT 2009AN PRL 103 211801 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing from a Time-Dependent Amplitude Analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Decays AUBERT 2009AI PR D80 071103 Measurement of ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ Mixing using the Ratio of Lifetimes for the Decays ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ and ${{\mathit K}^{+}}{{\mathit K}^{-}}$ 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 ZUPANC 2009 PR D80 052006 Measurement of $\mathit y_{CP}$ in ${{\mathit D}^{0}}$ Meson Decays to the ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ Final State AALTONEN 2008E PRL 100 121802 Evidence for ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing Using the CDF II Detector AUBERT 2008U PR D78 011105 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing using the Ratio of Lifetimes for the Decays ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{-}}{{\mathit K}^{+}}$ , and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ AUBERT 2007W PRL 98 211802 Evidence for ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing STARIC 2007 PRL 98 211803 Evidence for ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing ZHANG 2007B PRL 99 131803 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing Parameters in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays ZHANG 2006 PRL 96 151801 Improved Constraints on ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ Decays from the Belle Detector ASNER 2005 PR D72 012001 Search for ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing in the Dalitz Plot Analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ LI 2005A PRL 94 071801 Search for ${{\mathit D}^{0}}\leftrightarrow{{\overline{\mathit D}}^{0}}$ Mixing in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ Decays and Measurement of the Doubly-Cabibbo-Suppressed Decay Rate LINK 2005H PL B618 23 Measurement of the Doubly Cabibbo Suppressed Decay ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and a Search for Charm Mixing AUBERT 2003P PRL 91 121801 Limits on ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ Mixing and $\mathit CP$ Violation from the Ratio of Lifetimes for Decay to ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{-}}{{\mathit K}^{+}}$ and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ AUBERT 2003Z PRL 91 171801 Search for ${{\mathit D}^{0}}\leftrightarrow{{\overline{\mathit D}}^{0}}$ Nixing and a Measurement of the Doubly Cabibbo Suppressed Decay Rate in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}}{{\mathit \pi}}$ Decays ABE 2002I PRL 88 162001 A Measurement of Lifetime Difference in ${{\mathit D}^{0}}$ Meson Decays CSORNA 2002 PR D65 092001 Lifetime Differences, Direct $\mathit CP$ Violation and Partial Width in ${{\mathit D}^{0}}$ Meson Decays to ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ GODANG 2000 PRL 84 5038 Search for ${{\mathit D}^{0}}$ $\leftrightarrow$ ${{\overline{\mathit D}}^{0}}$ Mixing LINK 2000 PL B485 62 A Measurement of Lifetime Differences in the Neutral ${{\mathit D}}$-Meson System AITALA 1999E PRL 83 32 Measurements of Lifetimes and a Limit on the Lifetime Difference in the Neutral ${{\mathit D}}$ Meson System