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

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

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

#### $\Delta {\mathit m}_{{{\mathit B}_{{{s}}}^{0}}}$ = ${\mathit m}_{\mathrm {{{\mathit B}}{}^{0}_{{{\mathit s}} {{\mathit H}}}}}$ $-$ ${\mathit m}_{\mathrm {{{\mathit B}}{}^{0}_{{{\mathit s}} {{\mathit L}}}}}$

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

VALUE ($10^{12}$ $\hbar{}$ s${}^{-1}$) CL% DOCUMENT ID TECN  COMMENT
 $\bf{ 17.765 \pm0.006}$ OUR EVALUATION  $~~$(Produced by HFLAV)
 $\bf{ 17.765 \pm0.005}$ OUR AVERAGE
$17.743$ $\pm0.033$ $\pm0.009$ 1
 2024 A
LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.7683$ $\pm0.0051$ $\pm0.0032$ 2
 2022 B
LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.757$ $\pm0.007$ $\pm0.008$ 3
 2021 M
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$17.51$ ${}^{+0.10}_{-0.09}$ $\pm0.03$ 4
 2021 E
CMS ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.768$ $\pm0.023$ $\pm0.006$ 2
 2013 BI
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$17.93$ $\pm0.22$ $\pm0.15$ 5
 2013 CF
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$17.77$ $\pm0.10$ $\pm0.07$ 6
 2006 G
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
• • We do not use the following data for averages, fits, limits, etc. • •
$17.703$ $\pm0.059$ $\pm0.018$ 1
 2019 Q
LHCB Repl. by AAIJ 2024A
$17.711$ ${}^{+0.055}_{-0.057}$ $\pm0.011$ 1
 2015 I
LHCB Repl. by AAIJ 2019Q
$17.63$ $\pm0.11$ $\pm0.02$ 7
 2012 I
LHCB Repl. by AAIJ 2021M
$\text{17 - 21}$ 90 8
 2006 B
D0 ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
$17.31$ ${}^{+0.33}_{-0.18}$ $\pm0.07$ 9
 2006 Q
CDF Repl. by ABULENCIA,A 2006G
$>8.0$ 95 10
 2004 J
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}^{0}}$
$>4.9$ 95 11
 2004 J
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}^{0}}$
$>8.5$ 95 12
 2004 J
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}^{0}}$
$>5.0$ 95 13
 2003 B
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>10.3$ 95 14
 2003
SLD ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>10.9$ 95 15
 2003 E
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>5.3$ 95 16
 2002 V
SLD ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>1.0$ 95 17
 2001 D
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>7.4$ 95 18
 2000 Y
DLPH Repl. by ABDALLAH 2004J
$>4.0$ 95 19
 2000 G
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>5.2$ 95 20
 1999 S
OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$<96$ 95 21
 1999 D
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$>5.8$ 95 22
 1999 J
CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$>9.6$ 95 23
 1999 J
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>7.9$ 95 24
 1998 C
ALEP Repl. by BARATE 1999J
$>3.1$ 95 25
 1997 U
OPAL Repl. by ABBIENDI 1999S
$>2.2$ 95 26
 1997 V
OPAL Repl. by ABBIENDI 1999S
$>6.5$ 95 27
 1997
DLPH Repl. by ABREU 2000Y
$>6.6$ 95 28
 1996 M
ALEP Repl. by BARATE 1998C
$>2.2$ 95 26
 1995 J
OPAL Sup. by ACKERSTAFF 1997V
$>5.7$ 95 29
 1995 J
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>1.8$ 95 26
 1994 B
ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
 1 Measured using time-dependent angular analysis of ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ decays.
 2 Measured using ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{-}}{{\mathit \pi}^{+}}$ decays.
 3 Measured using ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ decays.
 4 Measured using time-dependent angular analysis of ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \phi}}$ decays.
 5 Measured using ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{-}}{{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}{{\mathit X}}$ decays.
 6 Significance of oscillation signal is 5.4 $\sigma$. Also reports $\vert \mathit V_{\mathit td}$ $/$ $\mathit V_{\mathit ts}\vert$ = $0.2060$ $\pm0.0007$ ${}^{+0.0081}_{-0.0060}$.
 7 Measured using ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{-}}{{\mathit \pi}^{+}}$ and ${{\mathit D}_{{{s}}}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ decays.
 8 A likelihood scan over the oscillation frequency, $\Delta \mathit m_{s}$, gives a most probable value of 19$~$ps${}^{-1}$ and a range of 17$<\Delta \mathit m_{s}<21~$(ps${}^{-1}$) at 90$\%$ C.L. assuming Gaussian uncertainties. Also excludes $\Delta \mathit m_{s}<14.8~$ps${}^{-1}$ at 95$\%$ C.L
 9 Significance of oscillation signal is 0.2$\%$. Also reported the value $\vert \mathit V_{\mathit td}$ $/$ $\mathit V_{\mathit ts}\vert$ = $0.208$ ${}^{+0.001}_{-0.002}{}^{+0.008}_{-0.006}$.
 10 Uses leptons emitted with large momentum transverse to a jet and improved techniques for vertexing and flavor-tagging.
 11 Updates of ${{\mathit D}_{{{s}}}}$-lepton analysis.
 12 Combined results from all Delphi analyses.
 13 Events with a high transverse momentum lepton were removed and an inclusively reconstructed vertex was required.
 14 ABE 2003 uses the novel charge dipole'' technique to reconstruct separate secondary and tertiary vertices originating from the ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}}$ decay chain. The analysis excludes $\Delta {\mathit m}_{{{\mathit s}}}<4.9~$ps${}^{-1}$ and 7.9$<\Delta {\mathit m}_{{{\mathit s}}}<10.3~$ps${}^{-1}$.
 15 Three analyses based on complementary event selections: (1) fully-reconstructed hadronic decays; (2) semileptonic decays with ${{\mathit D}_{{{s}}}}$ exclusively reconstructed; (3) inclusive semileptonic decays.
 16 ABE 2002V uses exclusively reconstructed ${{\mathit D}_{{{s-}}}}$ mesons and excludes $\Delta {\mathit m}_{{{\mathit s}}}<1.4~$ps${}^{-1}$ and 2.4$<\Delta {\mathit m}_{{{\mathit s}}}<5.3~$ps${}^{-1}$ at 95$\%$CL.
 17 Uses fully or partially reconstructed ${{\mathit D}_{{{s}}}}{{\mathit \ell}}$ vertices and a mixing tag as a flavor tagging.
 18 Replaced by ABDALLAH 2004A. Uses ${{\mathit D}_{{{s}}}^{-}}{{\mathit \ell}^{+}}$, and ${{\mathit \phi}}{{\mathit \ell}^{+}}$ vertices, and a multi-variable discriminant as a flavor tagging.
 19 Uses inclusive ${{\mathit D}_{{{s}}}}$ vertices and fully reconstructed ${{\mathit B}_{{{s}}}}$ decays and a multi-variable discriminant as a flavor tagging.
 20 Uses ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$ and ${{\mathit \ell}}-{{\mathit \ell}}$.
 21 ABE 1999D assumes $\tau _{{{\mathit B}_{{{s}}}^{0}}}$= $1.55$ $\pm0.05~$ps and $\Delta \Gamma /\Delta \mathit m$= ($5.6$ $\pm2.6$) $\times 10^{-3}$.
 22 ABE 1999J uses $\phi$ ${{\mathit \ell}}-{{\mathit \ell}}$ correlation.
 23 BARATE 1999J uses combination of an inclusive lepton and ${{\mathit D}_{{{s}}}^{-}}$-based analyses.
 24 BARATE 1998C combines results from ${{\mathit D}_{{{s}}}}{{\mathit h}}-{{\mathit \ell}}/\mathit Q_{{\mathrm {hem}}}$, ${{\mathit D}_{{{s}}}}{{\mathit h}}-{{\mathit K}}$ in the same side, ${{\mathit D}_{{{s}}}}{{\mathit \ell}}-{{\mathit \ell}}/\mathit Q_{{\mathrm {hem}}}$ and ${{\mathit D}_{{{s}}}}{{\mathit \ell}}-{{\mathit K}}$ in the same side.
 25 Uses ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$.
 26 Uses ${{\mathit \ell}}-{{\mathit \ell}}$.
 27 ADAM 1997 combines results from ${{\mathit D}_{{{s}}}}{{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$, ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$, and ${{\mathit \ell}}-{{\mathit \ell}}$.
 28 BUSKULIC 1996M uses ${{\mathit D}_{{{s}}}}$ lepton correlations and lepton, kaon, and jet charge tags.
 29 BUSKULIC 1995J uses ${{\mathit \ell}}-\mathit Q_{{\mathrm {hem}}}$. They find $\Delta {\mathit m}_{{{\mathit s}}}>5.6$ [$>6.1$] for ${{\mathit f}_{{{s}}}}=10\%$ [12$\%$]. We interpolate to our central value ${{\mathit f}_{{{s}}}}=10.5\%$.
Conservation Laws:
$\Delta \mathit B$ = 2 VIA MIXING
References