${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ 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 ${\mathit \tau}_{{{\mathit B}^{0}}}$ = ${1\over 0.5 (\Gamma _{{{\mathit B}_{{{H}}}^{0}}}+\Gamma _{{{\mathit B}_{{{L}}}^{0}}})}$.

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

INSPIRE   PDGID:
S042D
$\Delta {\mathit m}_{{{\mathit B}^{0}}}$ 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
ABUDINEN
2023D
 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.5050$ $\pm0.0021$ $\pm0.0010$ 2
AAIJ
2016AV
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$0.503$ $\pm0.011$ $\pm0.013$ 3
AAIJ
2013CF
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$0.5156$ $\pm0.0051$ $\pm0.0033$ 4
AAIJ
2013F
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$0.499$ $\pm0.032$ $\pm0.003$ 5
AAIJ
2012I
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$0.506$ $\pm0.020$ $\pm0.016$ 6
ABAZOV
2006W
 D0 ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
$0.511$ $\pm0.007$ ${}^{+0.007}_{-0.006}$ 7
AUBERT
2006G
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.511$ $\pm0.005$ $\pm0.006$ 8
ABE
2005B
 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.531$ $\pm0.025$ $\pm0.007$ 9
ABDALLAH
2003B
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.492$ $\pm0.018$ $\pm0.013$ 10
AUBERT
2003C
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.503$ $\pm0.008$ $\pm0.010$ 11
HASTINGS
2003
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.509$ $\pm0.017$ $\pm0.020$ 12
ZHENG
2003
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.516$ $\pm0.016$ $\pm0.010$ 13
AUBERT
2002I
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.493$ $\pm0.012$ $\pm0.009$ 14
AUBERT
2002J
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.497$ $\pm0.024$ $\pm0.025$ 15
ABBIENDI,G
2000B
 OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.503$ $\pm0.064$ $\pm0.071$ 16
ABE
1999K
 CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$0.500$ $\pm0.052$ $\pm0.043$ 17
ABE
1999Q
 CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$0.516$ $\pm0.099$ ${}^{+0.029}_{-0.035}$ 18
AFFOLDER
1999C
 CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$0.471$ ${}^{+0.078}_{-0.068}$ ${}^{+0.033}_{-0.034}$ 19
ABE
1998C
 CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$0.458$ $\pm0.046$ $\pm0.032$ 20
ACCIARRI
1998D
 L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.437$ $\pm0.043$ $\pm0.044$ 21
ACCIARRI
1998D
 L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.472$ $\pm0.049$ $\pm0.053$ 22
ACCIARRI
1998D
 L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.523$ $\pm0.072$ $\pm0.043$ 23
ABREU
1997N
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.493$ $\pm0.042$ $\pm0.027$ 21
ABREU
1997N
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.499$ $\pm0.053$ $\pm0.015$ 24
ABREU
1997N
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.480$ $\pm0.040$ $\pm0.051$ 20
ABREU
1997N
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.444$ $\pm0.029$ ${}^{+0.020}_{-0.017}$ 21
ACKERSTAFF
1997U
 OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.430$ $\pm0.043$ ${}^{+0.028}_{-0.030}$ 20
ACKERSTAFF
1997V
 OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.482$ $\pm0.044$ $\pm0.024$ 25
BUSKULIC
1997D
 ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.404$ $\pm0.045$ $\pm0.027$ 21
BUSKULIC
1997D
 ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.452$ $\pm0.039$ $\pm0.044$ 20
BUSKULIC
1997D
 ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.539$ $\pm0.060$ $\pm0.024$ 26
ALEXANDER
1996V
 OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.567$ $\pm0.089$ ${}^{+0.029}_{-0.023}$ 27
ALEXANDER
1996V
 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
AUBERT
2002N
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.494$ $\pm0.012$ $\pm0.015$ 29
HARA
2002
BELL Repl. by ABE 2005B
$0.528$ $\pm0.017$ $\pm0.011$ 30
TOMURA
2002
BELL Repl. by ABE 2005B
$0.463$ $\pm0.008$ $\pm0.016$ 14
ABE
2001D
 BELL Repl. by HASTINGS 2003
$0.444$ $\pm0.028$ $\pm0.028$ 31
ACCIARRI
1998D
 L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.497$ $\pm0.035$ 32
ABREU
1997N
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.467$ $\pm0.022$ ${}^{+0.017}_{-0.015}$ 33
ACKERSTAFF
1997V
 OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.446$ $\pm0.032$ 34
BUSKULIC
1997D
 ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.531$ ${}^{+0.050}_{-0.046}$ $\pm0.078$ 35
ABREU
1996Q
 DLPH Sup. by ABREU 1997N
$0.496$ ${}^{+0.055}_{-0.051}$ $\pm0.043$ 20
ACCIARRI
1996E
 L3 Repl. by ACCIARRI 1998D
$0.548$ $\pm0.050$ ${}^{+0.023}_{-0.019}$ 36
ALEXANDER
1996V
 OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$0.496$ $\pm0.046$ 37
AKERS
1995J
 OPAL Repl. by ACKERSTAFF 1997V
$0.462$ ${}^{+0.040}_{-0.053}$ ${}^{+0.052}_{-0.035}$ 20
AKERS
1995J
 OPAL Repl. by ACKERSTAFF 1997V
$0.50$ $\pm0.12$ $\pm0.06$ 23
ABREU
1994M
 DLPH Sup. by ABREU 1997N
$0.508$ $\pm0.075$ $\pm0.025$ 26
AKERS
1994C
 OPAL Repl. by ALEXANDER 1996V
$0.57$ $\pm0.11$ $\pm0.02$ 27
AKERS
1994H
 OPAL Repl. by ALEXANDER 1996V
$0.50$ ${}^{+0.07}_{-0.06}$ ${}^{+0.11}_{-0.10}$ 20
BUSKULIC
1994B
 ALEP Sup. by BUSKULIC 1997D
$0.52$ ${}^{+0.10}_{-0.11}$ ${}^{+0.04}_{-0.03}$ 27
BUSKULIC
1993K
 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