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

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

INSPIRE   PDGID:
S086D
$\Delta {\mathit m}_{{{\mathit B}_{{s}}^{0}}}$ 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
AAIJ
2022B
 LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.757$ $\pm0.007$ $\pm0.008$ 2
AAIJ
2021M
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$17.51$ ${}^{+0.10}_{-0.09}$ $\pm0.03$ 3
SIRUNYAN
2021E
 CMS ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.703$ $\pm0.059$ $\pm0.018$ 4
AAIJ
2019Q
 LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV
$17.768$ $\pm0.023$ $\pm0.006$ 1
AAIJ
2013BI
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$17.93$ $\pm0.22$ $\pm0.15$ 5
AAIJ
2013CF
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$17.77$ $\pm0.10$ $\pm0.07$ 6
ABULENCIA,A
2006G
 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
AAIJ
2015I
 LHCB Repl. by AAIJ 2019Q
$17.63$ $\pm0.11$ $\pm0.02$ 7
AAIJ
2012I
 LHCB Repl. by AAIJ 2021M
$\text{17 - 21}$ 90 8
ABAZOV
2006B
 D0 ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV
$17.31$ ${}^{+0.33}_{-0.18}$ $\pm0.07$ 9
ABULENCIA
2006Q
 CDF Repl. by ABULENCIA,A 2006G
$>8.0$ 95 10
ABDALLAH
2004J
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}^{0}}$
$>4.9$ 95 11
ABDALLAH
2004J
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}^{0}}$
$>8.5$ 95 12
ABDALLAH
2004J
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}^{0}}$
$>5.0$ 95 13
ABDALLAH
2003B
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>10.3$ 95 14
ABE
2003
SLD ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>10.9$ 95 15
HEISTER
2003E
 ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>5.3$ 95 16
ABE
2002V
 SLD ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>1.0$ 95 17
ABBIENDI
2001D
 OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>7.4$ 95 18
ABREU
2000Y
 DLPH Repl. by ABDALLAH 2004J
$>4.0$ 95 19
ABREU,P
2000G
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>5.2$ 95 20
ABBIENDI
1999S
 OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$<96$ 95 21
ABE
1999D
 CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$>5.8$ 95 22
ABE
1999J
 CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV
$>9.6$ 95 23
BARATE
1999J
 ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>7.9$ 95 24
BARATE
1998C
 ALEP Repl. by BARATE 1999J
$>3.1$ 95 25
ACKERSTAFF
1997U
 OPAL Repl. by ABBIENDI 1999S
$>2.2$ 95 26
ACKERSTAFF
1997V
 OPAL Repl. by ABBIENDI 1999S
$>6.5$ 95 27
ADAM
1997
DLPH Repl. by ABREU 2000Y
$>6.6$ 95 28
BUSKULIC
1996M
 ALEP Repl. by BARATE 1998C
$>2.2$ 95 26
AKERS
1995J
 OPAL Sup. by ACKERSTAFF 1997V
$>5.7$ 95 29
BUSKULIC
1995J
 ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$
$>1.8$ 95 26
BUSKULIC
1994B
 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