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

“OUR EVALUATION” is provided by the Heavy Flavor Averaging Group (HFLAV, https://hflav.web.cern.ch/) by taking into account correlations between measurements.

VALUE ($10^{12}$ $\hbar{}$ s${}^{-1}$) CL% DOCUMENT ID TECN  COMMENT
 $\bf{ 17.765 \pm0.006}$ OUR EVALUATION
 $\bf{ 17.765 \pm0.005}$ OUR AVERAGE
$17.7683$ $\pm0.0051$ $\pm0.0032$ 1
 2022 B
LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.757$ $\pm0.007$ $\pm0.008$ 2
 2021 M
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$17.51$ ${}^{+0.10}_{-0.09}$ $\pm0.03$ 3
 2021 E
CMS ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.703$ $\pm0.059$ $\pm0.018$ 4
 2019 Q
LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.768$ $\pm0.023$ $\pm0.006$ 1
 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. • •
$17.711$ ${}^{+0.055}_{-0.057}$ $\pm0.011$ 4
 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 ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{-}}{{\mathit \pi}^{+}}$ decays.
 2 Measured using ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ decays.
 3 Measured using time-dependent angular analysis of ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \phi}}$ decays.
 4 Measured using time-dependent angular analysis of ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ 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:
 AAIJ 2022B
NATP 18 1 Precise determination of the $B_{\mathrm{s}}^0$?$\overline B_{\mathrm{s}}^0$ oscillation frequency
 AAIJ 2021M
JHEP 2103 137 Measurement of the CKM angle $\gamma$ and $B^0_s$-$\bar{B}^0_s$ mixing frequency with $B^0_s \rightarrow D_s^\mp h^\pm \pi^\pm \pi^\mp$ decays
 SIRUNYAN 2021E
PL B816 136188 Measurement of the $CP$-violating phase $\phi_\mathrm{s}$ in the B$^0_\mathrm{s}\to$ J$/\psi\, \phi$(1020) $\to \mu^+\mu^-$K$^+$K$^-$ channel in proton-proton collisions at $\sqrt{s} =$ 13 TeV
 AAIJ 2019Q
EPJ C79 706 Updated measurement of time-dependent {\it CP}-violating observables in $B^{0}_{s}\to J/\psi K^+ K^-$ decays
 Also
EPJ C80 601 (errat.) Updated measurement of time-dependent {\\it CP}-violating observables in $B^{0}_{s}\\to J/\\psi K^+ K^-$ decays
 AAIJ 2015I
PRL 114 041801 Precision Measurement of $\mathit CP$ Violation in ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ Decays
 AAIJ 2013CF
EPJ C73 2655 Observation of ${{\mathit B}_{{s}}^{0}}-{{\overline{\mathit B}}_{{s}}^{0}}$ Mixing and Measurement of Mixing Frequencies using Semileptonic ${{\mathit B}}$ Decays
 AAIJ 2013BI
NJP 15 053021 Precision Measurement of the ${{\mathit B}_{{s}}^{0}}−{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillation Frequency with the Decay ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{-}}{{\mathit \pi}^{+}}$
 AAIJ 2012I
PL B709 177 Measurement of the ${{\mathit B}_{{s}}^{0}}-{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillation Frequency $\mathit \Delta ms$ in ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{-}}$3 ${{\mathit \pi}}$ Decays
 ABAZOV 2006B
PRL 97 021802 Direct Limits on the ${{\mathit B}_{{s}}^{0}}$ Oscillation Frequency
 ABULENCIA 2006Q
PRL 97 062003 Measurement of the ${{\mathit B}_{{s}}^{0}}-{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillation Frequency
 ABULENCIA,A 2006G
PRL 97 242003 Observation of ${{\mathit B}_{{s}}^{0}} - {{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations
 ABDALLAH 2004J
EPJ C35 35 Search for ${{\mathit B}_{{s}}^{0}}\leftrightarrow{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations in Delphi using High-$\mathit p_{T}$ Leptons
 ABDALLAH 2003B
EPJ C28 155 Search for ${{\mathit B}_{{s}}^{0}}\leftrightarrow{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations and a Measurement of ${{\mathit B}_{{d}}^{0}}\leftrightarrow{{\overline{\mathit B}}_{{d}}^{0}}$ Oscillations using Events with an Inclusively Reconstructed Vertex
 ABE 2003
PR D67 012006 Search for Time Dependent ${{\mathit B}_{{s}}^{0}}\leftrightarrow{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations using a Vertex Charge Dipole Technique
 HEISTER 2003E
EPJ C29 143 Improved Search for ${{\mathit B}_{{S}}^{0}}\leftrightarrow{{\overline{\mathit B}}_{{S}}^{0}}$ Oscillations
 ABE 2002V
PR D66 032009 A Search for Time Dependent ${{\mathit B}_{{s}}^{0}}-{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations using Exclusively Reconstructed ${{\mathit D}_{{s}}^{\pm}}$ Mesons
 ABBIENDI 2001D
EPJ C19 241 A Study of ${{\mathit B}_{{s}}^{0}}$ Meson Oscillation using ${{\mathit D}_{{s}}^{-}}$ $−$ ${{\mathit \ell}}$ Correlations
 ABREU 2000Y
EPJ C16 555 Measurement of the ${{\mathit B}_{{s}}^{0}}$ Lifetime and Study of ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations using ${{\mathit D}_{{s}}}{{\mathit \ell}}$ Events
 ABREU,P 2000G
EPJ C18 229 Study of ${{\mathit B}_{{s}}^{0}}{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations and ${{\mathit B}_{{s}}^{0}}$ Lifetimes using Hadronic Decays of ${{\mathit B}_{{s}}^{0}}$ Mesons
 ABBIENDI 1999S
EPJ C11 587 A Study of ${{\mathit B}_{{s}}^{0}}$ Meson Oscillation using Hadronic ${{\mathit Z}^{0}}$ Decays Containing Leptons
 ABE 1999J
PRL 82 3576 A Search for ${{\mathit B}_{{s}}^{0}}−{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations using the Semileptonic Decay ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \ell}^{+}}{{\mathit X}}{{\mathit \nu}}$
 ABE 1999D
PR D59 032004 Measurement of the ${{\mathit B}_{{s}}^{0}}$ Meson Lifetime using Semileptonic Decays
 BARATE 1999J
EPJ C7 553 Search for ${{\mathit B}_{{s}}^{0}}$ Oscillations using Inclusive Lepton Events
 Also
EPJ C12 181 (errat.) Erratum: BARATE 1999J Search for ${{\mathit B}_{{s}}^{0}}$ Oscillations using Inclusive Lepton Events
 BARATE 1998C
EPJ C4 367 Study of ${{\mathit B}_{{s}}}$ Oscillations and Lifetime using Fully Reconstructed ${{\mathit D}_{{s}}^{-}}$ Decays
 ACKERSTAFF 1997U
ZPHY C76 401 A Study of ${{\mathit B}}$ Meson Oscillations using Hadronic ${{\mathit Z}^{0}}$ Decays Containing Leptons
 ACKERSTAFF 1997V
ZPHY C76 417 An Updated Study of ${{\mathit B}}$ Meson Oscillations using Dilepton Events
 ADAM 1997
PL B414 382 Search for ${{\mathit B}_{{s}}^{0}}−{{\overline{\mathit B}}_{{s}}^{0}}$ Oscillations
 BUSKULIC 1996M
PL B377 205 Study of the ${{\mathit B}_{{s}}}{{\overline{\mathit B}}_{{s}}}$ Oscillation Frequency using ${{\mathit D}_{{s}}^{-}}{{\mathit \ell}^{+}}$ Combinations in ${{\mathit Z}}$ Decays
 AKERS 1995J
ZPHY C66 555 A Study of ${{\mathit B}}$ Meson Oscillations using Dilepton Events
 BUSKULIC 1995J
PL B356 409 Limit on ${{\mathit B}_{{s}}}$ Oscillation using a Jet Charge Method
 BUSKULIC 1994B
PL B322 441 An Investigation of ${{\mathit B}_{{d}}^{0}}$ and ${{\mathit B}_{{s}}^{0}}$ Oscillation