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)).

VALUE ($ 10^{-2} $) EVTS DOCUMENT ID TECN  COMMENT $\bf{ 1.394 \pm0.056}$ OUR EVALUATION  $~~$(Produced by HFLAV)  See the ideogram below. $\bf{ 1.35 \pm0.08}$ OUR AVERAGE  Error includes scale factor of 1.5.  See the ideogram below. $2.52$ $\pm0.62$ $\pm0.17$ 1 AAIJ 2023 BC LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV, ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $1.392$ $\pm0.052$ $\pm0.026$ 2 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 3 AAIJ 2021 AB LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV $1.92$ $\pm1.82$ ${}^{+1.29}_{-1.24}$ 91k 4 NAYAK 2020 BELL ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \omega}}$ $1.14$ $\pm0.26$ $\pm0.18$ 5 AAIJ 2019 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV $1.48$ $\pm0.74$ 2.3M 6 AAIJ 2019 X LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ 7 AAIJ 2018 K LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV $0.06$ $\pm0.92$ $\pm0.26$ 8 AAIJ 2016 V LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV $0.4$ $\pm1.8$ $\pm1.0$ 9 LEES 2016 D BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$, 10.6 GeV $2.22$ $\pm0.44$ $\pm0.18$ 10 STARIC 2016 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$ $-4.0$ $\pm2.6$ $\pm1.4$ 11 ABLIKIM 2015 D BES3 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \psi}{(3770)}}$ 12 KO 2014 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$ $0.60$ $\pm0.30$ ${}^{+0.10}_{-0.17}$ 13 PENG 2014 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$ 14 AALTONEN 2013 AE CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV $1.44$ $\pm0.36$ $\pm0.24$ 15 LEES 2013 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.55$ $\pm0.63$ $\pm0.41$ 16 AAIJ 2012 K LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV $1.14$ $\pm0.40$ $\pm0.30$ 17 DEL-AMO-SANCH.. 2010 D BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$, 10.6 GeV $0.22$ $\pm1.22$ $\pm1.04$ 18 ZUPANC 2009 BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ $-1.0$ $\pm2.0$ ${}^{+1.4}_{-1.6}$ 18k 19 ABE 2002 I BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ $-2.4$ $\pm5.0$ $\pm2.8$ 3393 20 CSORNA 2002 CLE2 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ $6.84$ $\pm2.78$ $\pm1.48$ 10k 19 LINK 2000 FOCS ${{\mathit \gamma}}$ nucleus $+1.6$ $\pm5.8$ $\pm2.1$ 19 AITALA 1999 E E791 ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$, ${{\mathit K}^{+}}{{\mathit K}^{-}}$ • • We do not use the following data for averages, fits, limits, etc. • • 21 AAIJ 2017 AO LHCB Repl. by AAIJ 2018K 22 AAIJ 2013 CE LHCB Repl. by AAIJ 2017AO 23 AAIJ 2013 N LHCB Repl. by AAIJ 2013CE $2.32$ $\pm0.44$ $\pm0.36$ 24 AUBERT 2009 AI BABR See LEES 2013 $-0.12$ ${}^{+1.10}_{-1.28}$ $\pm0.68$ 25 AUBERT 2009 AN BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at 10.58 GeV $1.4$ ${}^{+4.8}_{-5.4}$ 26 LOWREY 2009 CLEO ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \psi}{(3770)}}$ $1.70$ $\pm1.52$ 13k 27 AALTONEN 2008 E CDF ${{\mathit p}}{{\overline{\mathit p}}}$, $\sqrt {s }$ = 1.96 TeV $2.06$ $\pm0.66$ $\pm0.38$ 28 AUBERT 2008 U BABR See AUBERT 2009AI $1.94$ $\pm0.88$ $\pm0.62$ 4k 27 AUBERT 2007 W BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ 10.6 GeV $2.62$ $\pm0.64$ $\pm0.50$ 160k 29 STARIC 2007 BELL Repl. by STARIC 2016 $0.74$ $\pm0.50$ ${}^{+0.20}_{-0.31}$ 534k 30 ZHANG 2007 B BELL Repl. by PENG 2014 $-0.7$ $\pm4.9$ 4k 31, 27 ZHANG 2006 BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $-3.0$ ${}^{+5.0}_{-4.8}$ ${}^{+1.6}_{-0.8}$ 30 ASNER 2005 CLEO ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ 10 GeV $-0.3$ $\pm5.7$ 31, 27 LI 2005 A BELL See ZHANG 2006 $-5.2$ ${}^{+18.4}_{-16.8}$ 31, 27 LINK 2005 H FOCS ${{\mathit \gamma}}$ nucleus $1.6$ $\pm0.8$ ${}^{+1.0}_{-0.8}$ 450k 32 AUBERT 2003 P BABR See AUBERT 2008U $1.6$ ${}^{+6.2}_{-12.8}$ 31, 27 AUBERT 2003 Z BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$, 10.6~GeV $-5.0$ ${}^{+2.8}_{-3.2}$ $\pm0.6$ 27 GODANG 2000 CLE2 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ 1  AAIJ 2023BC analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ from ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \mu}}{{\mathit \nu}}{{\mathit X}}$ events allows for $\mathit CP$ violation (none seen). 2  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. 3  AAIJ 2021AB analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ events allows for $\mathit CP$ violation (none seen). 4  NAYAK 2020 reports ($1.92$ $\pm1.82$ $\pm1.24$ ${}^{+0.34}_{-0.00}$) $ \times 10^{-2}$ 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. 5  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 $. 6  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). 7  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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$. 8  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. 9  Time-dependent amplitude analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$. 10  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${}^{-1}$. 11  ABLIKIM 2015D uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$. 12  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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$. 13  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 $\Delta \mathit m$. 14  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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$. 15  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 $. 16  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. 17  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. 18  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. 19  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 $. 20  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 $. 21  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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$. 22  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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$. 23  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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$. 24  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. 25  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. 26  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$\mathit y$ = ($1.62$ $\pm0.32$) $ \times 10^{-2}$. 27  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.'' 28  This value combines the results of AUBERT 2008U and AUBERT 2003P. 29  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 ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$. 30  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. 31  The ranges of AUBERT 2003Z, LINK 2005H, LI 2005A, and ZHANG 2006 measurements are for 95$\%$ confidence level. 32  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