$\vert{}{\mathit m}_{{{\mathit D}_{{{1}}}^{0}}}–{\mathit m}_{{{\mathit D}_{{{2}}}^{0}}}\vert{}$ = $x$ $\Gamma $

INSPIRE   PDGID:
S032D
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. The experiments usually present $x$ ${}\equiv$ $\Delta \mathit m/\Gamma $. Then $\Delta \mathit m$ = $x$ $\Gamma $ = $x$ $\hbar{}/\tau $.
VALUE ($ 10^{10} $ $\hbar{}$ s${}^{-1}$) CL% DOCUMENT ID TECN  COMMENT
$\bf{ 0.997 \pm0.116}$ OUR EVALUATION  $~~$(Produced by HFLAV)
$\bf{ 0.94 \pm0.11}$ OUR AVERAGE
$1.05$ $\pm0.36$ $\pm0.06$ 1
AAIJ
2023BC
 LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV, ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$0.97$ ${}^{+0.14}_{-0.13}$ 2
AAIJ
2021AB
 LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV, ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$0.66$ ${}^{+0.41}_{-0.37}$ 3
AAIJ
2019X
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV, ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
4
AAIJ
2018K
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$-2.10$ $\pm1.29$ $\pm0.41$ 5
AAIJ
2016V
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$3.7$ $\pm2.9$ $\pm1.5$ 6
LEES
2016D
 BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$, 10.6 GeV
7
KO
2014
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$
$1.37$ $\pm0.46$ ${}^{+0.18}_{-0.28}$ 8
PENG
2014
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$
9
AALTONEN
2013AE
 CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
$0.39$ $\pm0.56$ $\pm0.35$ 10
DEL-AMO-SANCH..
2010D
 BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$, 10.6 GeV
• • We do not use the following data for averages, fits, limits, etc. • •
11
AAIJ
2017AO
 LHCB Repl. by AAIJ 2018K
12
AAIJ
2013CE
 LHCB Repl. by AAIJ 2017AO
13
AAIJ
2013N
 LHCB Repl. by AAIJ 2013CE
$6.4$ ${}^{+1.4}_{-1.7}$ $\pm1.0$ 14
AUBERT
2009AN
 BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at 10.58 GeV
$-2$ ${}^{+7}_{-6}$ 15
LOWREY
2009
CLEO ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \psi}{(3770)}}$
$1.98$ $\pm0.73$ ${}^{+0.32}_{-0.41}$ 16
ZHANG
2007B
 BELL Repl. by PENG 2014
$<7$ 95 17
ZHANG
2006
BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$
$-11\text{ to }+22 $ 16
ASNER
2005
CLEO ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ 10 GeV
$<11$ 90
BITENC
2005
BELL
$<30$ 90
CAWLFIELD
2005
CLEO
$<7$ 95 17
LI
2005A
 BELL See ZHANG 2006
$<22$ 95 18
LINK
2005H
 FOCS ${{\mathit \gamma}}$ nucleus
$<23$ 95
AUBERT
2004Q
 BABR
$<11$ 95 17
AUBERT
2003Z
 BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$, 10.6~GeV
$<7$ 95 19
GODANG
2000
CLE2 ${{\mathit e}^{+}}{{\mathit e}^{-}}$
$<32$ 90 20, 21
AITALA
1998
E791 ${{\mathit \pi}^{-}}$ nucleus, 500 GeV
$<24$ 90 22
AITALA
1996C
 E791 ${{\mathit \pi}^{-}}$ nucleus, 500 GeV
$<21$ 90 21, 23
ANJOS
1988C
 E691 Photoproduction
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 2021AB measurement allows for $\mathit CP$ violation (none seen).
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).
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 $), ${{\mathit y}^{\,'}}$ = ${{\mathit y}}$
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.
6  Time-dependent amplitude analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$.
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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 $\Delta \mathit m$.
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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.
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
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.
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${}^{-1}$.
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 $\Delta \mathit m$.
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.
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$\%$.
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.
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.
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.
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.
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.
Conservation Laws:
$\Delta \mathit C$ = 2 VIA MIXING
References