| $\bf{
0.997 \pm0.116}$
|
OUR EVALUATION
$~~$(Produced by HFLAV)
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| $\bf{
0.94 \pm0.11}$
|
OUR AVERAGE
|
| $1.05$ $\pm0.36$ $\pm0.06$ |
|
1 |
|
LHCB |
| $0.97$ ${}^{+0.14}_{-0.13}$ |
|
2 |
|
LHCB |
| $0.66$ ${}^{+0.41}_{-0.37}$ |
|
3 |
|
LHCB |
|
|
4 |
|
LHCB |
| $-2.10$ $\pm1.29$ $\pm0.41$ |
|
5 |
|
LHCB |
| $3.7$ $\pm2.9$ $\pm1.5$ |
|
6 |
|
BABR |
|
|
7 |
|
BELL |
| $1.37$ $\pm0.46$ ${}^{+0.18}_{-0.28}$ |
|
8 |
|
BELL |
|
|
9 |
|
CDF |
| $0.39$ $\pm0.56$ $\pm0.35$ |
|
10 |
|
BABR |
| • • • We do not use the following data for averages, fits, limits, etc. • • • |
|
|
11 |
|
LHCB |
|
|
12 |
|
LHCB |
|
|
13 |
|
LHCB |
| $6.4$ ${}^{+1.4}_{-1.7}$ $\pm1.0$ |
|
14 |
|
BABR |
| $-2$ ${}^{+7}_{-6}$ |
|
15 |
|
CLEO |
| $1.98$ $\pm0.73$ ${}^{+0.32}_{-0.41}$ |
|
16 |
|
BELL |
| $<7$ |
95 |
17 |
|
BELL |
| $-11\text{ to }+22 $ |
|
16 |
|
CLEO |
| $<11$ |
90 |
|
|
BELL |
| $<30$ |
90 |
|
|
CLEO |
| $<7$ |
95 |
17 |
|
BELL |
| $<22$ |
95 |
18 |
|
FOCS |
| $<23$ |
95 |
|
|
BABR |
| $<11$ |
95 |
17 |
|
BABR |
| $<7$ |
95 |
19 |
|
CLE2 |
| $<32$ |
90 |
20, 21 |
|
E791 |
| $<24$ |
90 |
22 |
|
E791 |
| $<21$ |
90 |
21, 23 |
|
E691 |
|
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).
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2
AAIJ 2021AB measurement allows for $\mathit CP$ violation (none seen).
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3
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.). Measurement allows for $\mathit CP$ violation (none seen).
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4
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 $), ${{\mathit y}^{\,'}}$ = ${{\mathit y}}$
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5
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.
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6
Time-dependent amplitude analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$.
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7
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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8
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 $\Delta \mathit m$.
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9
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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10
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 analysis 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.
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11
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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12
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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13
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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14
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.
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15
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 $\Delta \mathit m$ = ($23.4$ $\pm6.1$) $ \times 10^{9}$ $\hbar{}~$s${}^{-1}$.
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16
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 value allows $\mathit CP$ violation and is sensitive to the sign of $\Delta \mathit m$.
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17
The AUBERT 2003Z, LI 2005A, and ZHANG 2006 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 limit allows interference between the DCS and mixing ratios, and also allows $\mathit CP$ violation. AUBERT 2003Z assumes the strong phase between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ amplitudes is small; if an arbitrary phase is allowed, the limit degrades by 20$\%$. The LI 2005A and ZHANG 2006 limits are valid for an arbitrary strong phase.
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18
This LINK 2005H limit is 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 limit allows interference between the DCS and mixing ratios, and also allows $\mathit CP$ violation. The strong 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. If an arbitrary relative strong phase is allowed, the limit degrades by 25$\%$.
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19
This GODANG 2000 limit is 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 limit allows interference between the DCS and mixing ratios, and also allows $\mathit CP$ violation. The strong 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. If an arbitrary relative strong phase is allowed, the limit degrades by a factor of two.
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20
AITALA 1998 allows interference between the doubly Cabibbo-suppressed and mixing amplitudes, and also allows $\mathit CP$ violation in this term, but assumes that $\mathit A_{{{\mathit D}}}=\mathit A_{\mathit R}$=0. See the note on ``${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing,'' above.
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21
This limit is inferred from $\mathit R_{\mathit M}$ for $\mathit f$ = ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and $\mathit f$ = ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$. See the note on ``${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing,'' above. Decay-time information is used to distinguish doubly Cabibbo-suppressed decays from ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ mixing.
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22
This limit is inferred from $\mathit R_{\mathit M}$ for $\mathit f$ = ${{\mathit K}^{+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{{\mathit \ell}}}}}}$. See the note on ``${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing,'' above.
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23
ANJOS 1988C assumes that $\mathit y$ = 0. See the note on ``${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing,'' above. Without this assumption, the limit degrades by about a factor of two.
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