#### ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ MIXING PARAMETERS

For a discussion of ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ mixing see the note on “${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ Mixing” in the ${{\mathit B}^{0}}$ Particle Listings above.
${{\mathit \chi}_{{{d}}}}$ is a measure of the time-integrated ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ mixing probability that a produced ${{\mathit B}^{0}}({{\overline{\mathit B}}^{0}}$) decays as a ${{\overline{\mathit B}}^{0}}({{\mathit B}^{0}}$). Mixing violates $\Delta \mathit B{}\not=$2 rule.
${{\mathit \chi}_{{{d}}}}$ = ${\mathit x{}^{2}_{\mathit d}\over 2(1+\mathit x{}^{2}_{\mathit d})}$

$\mathit x_{\mathit d}$ = ${\Delta {\mathit m}_{{{\mathit B}^{0}}}\over \Gamma _{{{\mathit B}^{0}}}}$ = (${\mathit m}_{{{\mathit B}_{{{H}}}^{0}}}$ $-$ ${\mathit m}_{{{\mathit B}_{{{L}}}^{0}}}){\mathit \tau}_{{{\mathit B}^{0}}}$ ,
where $\mathit H$, $\mathit L$ stand for heavy and light states of two ${{\mathit B}^{0}}$ $\mathit CP$ eigenstates and ${\mathit \tau}_{{{\mathit B}^{0}}}$ = ${1\over 0.5 (\Gamma _{{{\mathit B}_{{{H}}}^{0}}}+\Gamma _{{{\mathit B}_{{{L}}}^{0}}})}$.

#### $\Delta {\mathit m}_{{{\mathit B}^{0}}}$ = ${\mathit m}_{{{\mathit B}_{{{H}}}^{0}}}–{\mathit m}_{{{\mathit B}_{{{L}}}^{0}}}$

$\Delta {\mathit m}_{{{\mathit B}^{0}}}$ is a measure of 2${{\mathit \pi}}$ times the ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ oscillation frequency in time-dependent mixing experiments.

“OUR EVALUATION” is an average using rescaled values of the data listed below. The averaging/rescaling procedure takes into account correlations between the measurements and includes $\Delta {\mathit m}_{{{\mathit d}}}$ calculated from ${{\mathit \chi}_{{{d}}}}$ measured at ${{\mathit \Upsilon}{(4S)}}$.

VALUE ($10^{12}$ $\hbar{}$ s${}^{-1}$) DOCUMENT ID TECN  COMMENT
 $\bf{ 0.5069 \pm0.0019}$ OUR EVALUATION  $~~$(Produced by HFLAV)
$0.516$ $\pm0.008$ $\pm0.005$ 1
 2023 D
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.5050$ $\pm0.0021$ $\pm0.0010$ 2
 2016 AV
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$0.503$ $\pm0.011$ $\pm0.013$ 3
 2013 CF
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$0.5156$ $\pm0.0051$ $\pm0.0033$ 4
 2013 F
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$0.499$ $\pm0.032$ $\pm0.003$ 5
 2012 I
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$0.506$ $\pm0.020$ $\pm0.016$ 6
 2006 W
D0 ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
$0.511$ $\pm0.007$ ${}^{+0.007}_{-0.006}$ 7
 2006 G
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.511$ $\pm0.005$ $\pm0.006$ 8
 2005 B
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.531$ $\pm0.025$ $\pm0.007$ 9
 2003 B
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.492$ $\pm0.018$ $\pm0.013$ 10
 2003 C
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.503$ $\pm0.008$ $\pm0.010$ 11
 2003
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.509$ $\pm0.017$ $\pm0.020$ 12
 2003
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.516$ $\pm0.016$ $\pm0.010$ 13
 2002 I
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.493$ $\pm0.012$ $\pm0.009$ 14
 2002 J
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.497$ $\pm0.024$ $\pm0.025$ 15
 2000 B
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.503$ $\pm0.064$ $\pm0.071$ 16
 1999 K
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$0.500$ $\pm0.052$ $\pm0.043$ 17
 1999 Q
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$0.516$ $\pm0.099$ ${}^{+0.029}_{-0.035}$ 18
 1999 C
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$0.471$ ${}^{+0.078}_{-0.068}$ ${}^{+0.033}_{-0.034}$ 19
 1998 C
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$0.458$ $\pm0.046$ $\pm0.032$ 20
 1998 D
L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.437$ $\pm0.043$ $\pm0.044$ 21
 1998 D
L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.472$ $\pm0.049$ $\pm0.053$ 22
 1998 D
L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.523$ $\pm0.072$ $\pm0.043$ 23
 1997 N
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.493$ $\pm0.042$ $\pm0.027$ 21
 1997 N
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.499$ $\pm0.053$ $\pm0.015$ 24
 1997 N
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.480$ $\pm0.040$ $\pm0.051$ 20
 1997 N
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.444$ $\pm0.029$ ${}^{+0.020}_{-0.017}$ 21
 1997 U
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.430$ $\pm0.043$ ${}^{+0.028}_{-0.030}$ 20
 1997 V
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.482$ $\pm0.044$ $\pm0.024$ 25
 1997 D
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.404$ $\pm0.045$ $\pm0.027$ 21
 1997 D
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.452$ $\pm0.039$ $\pm0.044$ 20
 1997 D
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.539$ $\pm0.060$ $\pm0.024$ 26
 1996 V
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.567$ $\pm0.089$ ${}^{+0.029}_{-0.023}$ 27
 1996 V
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
• • We do not use the following data for averages, fits, limits, etc. • •
$0.516$ $\pm0.016$ $\pm0.010$ 28
 2002 N
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.494$ $\pm0.012$ $\pm0.015$ 29
 2002
BELL Repl. by ABE 2005B
$0.528$ $\pm0.017$ $\pm0.011$ 30
 2002
BELL Repl. by ABE 2005B
$0.463$ $\pm0.008$ $\pm0.016$ 14
 2001 D
BELL Repl. by HASTINGS 2003
$0.444$ $\pm0.028$ $\pm0.028$ 31
 1998 D
L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.497$ $\pm0.035$ 32
 1997 N
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.467$ $\pm0.022$ ${}^{+0.017}_{-0.015}$ 33
 1997 V
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.446$ $\pm0.032$ 34
 1997 D
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.531$ ${}^{+0.050}_{-0.046}$ $\pm0.078$ 35
 1996 Q
DLPH Sup. by ABREU 1997N
$0.496$ ${}^{+0.055}_{-0.051}$ $\pm0.043$ 20
 1996 E
L3 Repl. by ACCIARRI 1998D
$0.548$ $\pm0.050$ ${}^{+0.023}_{-0.019}$ 36
 1996 V
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.496$ $\pm0.046$ 37
 1995 J
OPAL Repl. by ACKERSTAFF 1997V
$0.462$ ${}^{+0.040}_{-0.053}$ ${}^{+0.052}_{-0.035}$ 20
 1995 J
OPAL Repl. by ACKERSTAFF 1997V
$0.50$ $\pm0.12$ $\pm0.06$ 23
 1994 M
DLPH Sup. by ABREU 1997N
$0.508$ $\pm0.075$ $\pm0.025$ 26
 1994 C
OPAL Repl. by ALEXANDER 1996V
$0.57$ $\pm0.11$ $\pm0.02$ 27
 1994 H
OPAL Repl. by ALEXANDER 1996V
$0.50$ ${}^{+0.07}_{-0.06}$ ${}^{+0.11}_{-0.10}$ 20
 1994 B
ALEP Sup. by BUSKULIC 1997D
$0.52$ ${}^{+0.10}_{-0.11}$ ${}^{+0.04}_{-0.03}$ 27
 1993 K
ALEP Sup. by BUSKULIC 1997D
 1 Measured using ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{(*)-}}{{\mathit \pi}^{+}}$ decays.
 2 Uses semileptonic decays of ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{-}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}{{\mathit X}}$ and ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{(*)-}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}{{\mathit X}}$, where the ${{\mathit D}}$ mesons are reconstructed in ${{\mathit D}^{-}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}$ and ${{\mathit D}^{(*)-}}$ $\rightarrow$ ${{\overline{\mathit D}}^{0}}{{\mathit \pi}^{-}}$ with ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$.
 3 Uses semileptonic decays of ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{-}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}{{\mathit X}}$ where the ${{\mathit D}^{-}}$ mesons are reconstructed in ${{\mathit D}^{-}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{-}}$.
 4 Measured using ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{-}}{{\mathit \pi}^{+}}$ and ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}^{*}{(892)}^{0}}$ decays.
 5 Measured using ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{-}}{{\mathit \pi}^{+}}$.
 6 Uses opposite-side flavor-tagging with ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}^{(*)}}{{\mathit \mu}}{{\mathit \nu}_{{{\mu}}}}{{\mathit X}}$ events.
 7 Measured using a simultaneous fit of the ${{\mathit B}^{0}}$ lifetime and ${{\overline{\mathit B}}^{0}}{{\mathit B}^{0}}$ oscillation frequency $\Delta {\mathit m}_{{{\mathit d}}}$ in the partially reconstructed ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit \ell}}{{\mathit \nu}}$ decays.
 8 Measurement performed using a combined fit of $\mathit CP$-violation, mixing and lifetimes.
 9 Events with a high transverse momentum lepton were removed and an inclusively reconstructed vertex was required.
 10 AUBERT 2003C uses a sample of approximately 14,000 exclusively reconstructed ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*}{(2010)}^{-}}{{\mathit \ell}}{{\mathit \nu}}$ and simultaneously measures the lifetime and oscillation frequency.
 11 HASTINGS 2003 measurement based on the time evolution of dilepton events. It also reports $\mathit f_{+}/\mathit f_{0}$ = $1.01$ $\pm0.03$ $\pm0.09$ and $\mathit CPT$ violation parameters in ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ mixing.
 12 ZHENG 2003 data analyzed using partially reconstructed ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit \pi}^{+}}$ decay and a flavor tag based on the charge of the lepton from the accompanying ${{\mathit B}}$ decay.
 13 Uses a tagged sample of fully-reconstructed neutral ${{\mathit B}}$ decays at ${{\mathit \Upsilon}{(4S)}}$.
 14 Measured based on the time evolution of dilepton events in ${{\mathit \Upsilon}{(4S)}}$ decays.
 15 Data analyzed using partially reconstructed ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}}$ decay and a combination of flavor tags from the rest of the event.
 16 Uses di-muon events.
 17 Uses jet-charge and lepton-flavor tagging.
 18 Uses ${{\mathit \ell}^{-}}{{\mathit D}^{*+}}−{{\mathit \ell}}$ events.
 19 Uses ${{\mathit \pi}}-{{\mathit B}}$ in the same side.
 20 Uses ${{\mathit \ell}}-{{\mathit \ell}}$.
 21 Uses ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$.
 22 Uses ${{\mathit \ell}}-{{\mathit \ell}}$ with impact parameters.
 23 Uses ${{\mathit D}^{*\pm}}-\mathit Q_{{\mathrm {hem}}}$.
 24 Uses ${{\mathit \pi}_{{{s}}}^{\pm}}{{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$.
 25 Uses ${{\mathit D}^{*\pm}}-{{\mathit \ell}}/\mathit Q_{{\mathrm {hem}}}$.
 26 Uses ${{\mathit D}^{*\pm}}{{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$.
 27 Uses ${{\mathit D}^{*\pm}}-{{\mathit \ell}}$.
 28 AUBERT 2002N result based on the same analysis and data sample reported in AUBERT 2002I.
 29 Uses a tagged sample of ${{\mathit B}^{0}}$ decays reconstructed in the mode ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit \ell}}{{\mathit \nu}}$.
 30 Uses a tagged sample of fully-reconstructed hadronic ${{\mathit B}^{0}}$ decays at ${{\mathit \Upsilon}{(4S)}}$.
 31 ACCIARRI 1998D combines results from ${{\mathit \ell}}-{{\mathit \ell}}$, ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$, and ${{\mathit \ell}}-{{\mathit \ell}}$ with impact parameters.
 32 ABREU 1997N combines results from ${{\mathit D}^{*\pm}}-\mathit Q_{{\mathrm {hem}}}$, ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$, ${{\mathit \pi}_{{{s}}}^{\pm}}{{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$, and ${{\mathit \ell}}-{{\mathit \ell}}$.
 33 ACKERSTAFF 1997V combines results from ${{\mathit \ell}}-{{\mathit \ell}}$, ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$, ${{\mathit D}^{*}}-{{\mathit \ell}}$, and ${{\mathit D}^{*\pm}}-\mathit Q_{{\mathrm {hem}}}$.
 34 BUSKULIC 1997D combines results from ${{\mathit D}^{*\pm}}-{{\mathit \ell}}/\mathit Q_{{\mathrm {hem}}}$, ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$, and ${{\mathit \ell}}-{{\mathit \ell}}$.
 35 ABREU 1996Q analysis performed using lepton, kaon, and jet-charge tags.
 36 ALEXANDER 1996V combines results from ${{\mathit D}^{*\pm}}-{{\mathit \ell}}$ and ${{\mathit D}^{*\pm}}{{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$.
 37 AKERS 1995J combines results from charge measurement, ${{\mathit D}^{*\pm}}{{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$ and ${{\mathit \ell}}-{{\mathit \ell}}$.
Conservation Laws:
$\Delta \mathit B$ = 2 VIA MIXING
References