This ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ mixing parameter is the probability (integrated over time) that a produced ${{\mathit B}^{0}}$ (or ${{\overline{\mathit B}}^{0}}$) decays as a ${{\overline{\mathit B}}^{0}}$ (or ${{\mathit B}^{0}}$), e.g. for inclusive lepton decays

$\chi _{\mathit d}$

= $\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \ell}^{-}} X (via {{\overline{\mathit B}}^{0}}))}/\Gamma\mathrm {( {{\mathit B}^{0}} \rightarrow {{\mathit \ell}^{\pm}} X)}$

= $\Gamma\mathrm {( {{\overline{\mathit B}}^{0}} \rightarrow {{\mathit \ell}^{+}} X (via {{\mathit B}^{0}}))}/\Gamma\mathrm {( {{\overline{\mathit B}}^{0}} \rightarrow {{\mathit \ell}^{\pm}} X)}$

Where experiments have measured the parameter $\mathit r$ = $\chi /(1−\chi $), we have converted to $\chi $. Mixing violates the $\Delta \mathit B{}\not=$2 rule.

Note that the measurement of $\chi $ at energies higher than the ${{\mathit \Upsilon}{(4S)}}$ have not separated $\chi _{\mathit d}$ from $\chi _{\mathit s}$ where the subscripts indicate ${{\mathit B}^{0}}({\mathit {\overline{\mathit b}}}{\mathit {\mathit d}}$) or ${{\mathit B}_{{s}}^{0}}({\mathit {\overline{\mathit b}}}{\mathit {\mathit s}}$). They are listed in the ${{\mathit B}^{\pm}}/{{\mathit B}^{0}}/{{\mathit B}_{{s}}^{0}}/{\mathit {\mathit b}}$-baryon ADMIXTURE section.

The experiments at ${{\mathit \Upsilon}{(4S)}}$ make an assumption about the ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ fraction and about the ratio of the ${{\mathit B}^{\pm}}$ and ${{\mathit B}^{0}}$ semileptonic branching ratios (usually that it equals one).

“OUR EVALUATION” is an average using rescaled values of the data listed below. The average and rescaling were performed by the Heavy Flavor Averaging Group (HFLAV) and are described at https://hflav.web.cern.ch/. The averaging/rescaling procedure takes into account correlations between the measurements, includes ${{\mathit \chi}_{{d}}}$ calculated from $\Delta {\mathit m}_{{{\mathit B}^{0}}}$ and $\tau _{{{\mathit B}^{0}}}$.

VALUE CL% DOCUMENT ID TECN  COMMENT $\bf{ 0.1858 \pm0.0011}$ OUR EVALUATION $\bf{ 0.182 \pm0.015}$ OUR AVERAGE $0.198$ $\pm0.013$ $\pm0.014$ 1 BEHRENS 2000 B CLE2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.16$ $\pm0.04$ $\pm0.04$ 2 ALBRECHT 1994 ARG ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.149$ $\pm0.023$ $\pm0.022$ 3 BARTELT 1993 CLE2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.171$ $\pm0.048$ 4 ALBRECHT 1992 L ARG ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ • • We do not use the following data for averages, fits, limits, etc. • • $0.20$ $\pm0.13$ $\pm0.12$ 5 ALBRECHT 1996 D ARG ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.19$ $\pm0.07$ $\pm0.09$ 6 ALBRECHT 1996 D ARG ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.24$ $\pm0.12$ 7 ELSEN 1990 JADE ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $35 - 44$ GeV $0.158$ ${}^{+0.052}_{-0.059}$ ARTUSO 1989 CLEO ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.17$ $\pm0.05$ 8 ALBRECHT 1987 I ARG ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $<0.19$ 90 9 BEAN 1987 B CLEO ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $<0.27$ 90 10 AVERY 1984 CLEO ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ 1  BEHRENS 2000B uses high-momentum lepton tags and partially reconstructed ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \pi}^{-}}$ , ${{\mathit \rho}^{-}}$ decays to determine the flavor of the ${{\mathit B}}~$meson. 2  ALBRECHT 1994 reports $\mathit r=0.194$ $\pm0.062$ $\pm0.054$. We convert to $\chi $ for comparison. Uses tagged events (lepton + pion from ${{\mathit D}^{*}}$). 3  BARTELT 1993 analysis performed using tagged events (lepton+pion from ${{\mathit D}^{*}}$). Using dilepton events they obtain $0.157$ $\pm0.016$ ${}^{+0.033}_{-0.028}$. 4  ALBRECHT 1992L is a combined measurement employing several lepton-based techniques. It uses all previous ARGUS data in addition to new data and therefore supersedes ALBRECHT 1987I. A value of $\mathit r$ = $20.6$ $\pm7.0\%$ is directly measured. The value can be used to measure $\mathit x$ = $\Delta \mathit M/\Gamma $ = $0.72$ $\pm0.15$ for the ${{\mathit B}_{{d}}}$ meson. Assumes $\mathit f_{+−}/\mathit f_{0}$ = $1.0$ $\pm0.05$ and uses ${\mathit \tau}_{{{\mathit B}^{\pm}}}/{\mathit \tau}_{{{\mathit B}^{0}}}$ = ($0.95$ $\pm0.14$) ($\mathit f_{+−}/\mathit f_{0}$). 5  Uses ${{\mathit D}^{*+}}{{\mathit K}^{\pm}}$ correlations. 6  Uses ( ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}$ ) ${{\mathit K}^{\pm}}$ correlations. 7  These experiments see a combination of ${{\mathit B}_{{s}}}$ and ${{\mathit B}_{{d}}}$ mesons. 8  ALBRECHT 1987I is inclusive measurement with like-sign dileptons, with tagged ${{\mathit B}}$ decays plus leptons, and one fully reconstructed event. Measures $\mathit r=0.21$ $\pm0.08$. We convert to $\chi $ for comparison. Superseded by ALBRECHT 1992L. 9  BEAN 1987B measured $\mathit r$ $<$ $0.24$; we converted to $\chi $. 10  Same-sign dilepton events. Limit assumes semileptonic BR for ${{\mathit B}^{+}}$ and ${{\mathit B}^{0}}$ equal. If ${{\mathit B}^{0}}/{{\mathit B}^{\pm}}$ ratio $<$0.58, no limit exists. The limit was corrected in BEAN 1987B from $\mathit r$ $<$ $0.30$ to $\mathit r$ $<$ $0.37$. We converted this limit to $\chi $.

Conservation Laws:

$\Delta \mathit B$ = 2 VIA MIXING

References:

BEHRENS 2000B PL B490 36 Precise Measurement of ${{\mathit B}^{0}}$ $\leftrightarrow$ ${{\overline{\mathit B}}^{0}}$ Mixing Parameters at the ${{\mathit \Upsilon}{(4S)}}$ ALBRECHT 1996D PL B374 256 Two Measurements of ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ Mixing using Kaon Tagging ALBRECHT 1994 PL B324 249 A Study of ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}}$ and ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ Mixing using Partial ${{\mathit D}^{*+}}$ Reconstruction BARTELT 1993 PRL 71 1680 Two Measurements of ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ Mixing ALBRECHT 1992L ZPHY C55 357 A New Determination of the ${{\mathit B}^{0}}$ $\leftrightarrow$ ${{\overline{\mathit B}}^{0}}$ Oscillation Strength ELSEN 1990 ZPHY C46 349 A Measurement of the Weak Axial Couplings of the ${\mathit {\mathit b}}$ and ${\mathit {\mathit c}}$ Quarks ARTUSO 1989 PRL 62 2233 ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ Mixing at the ${{\mathit \Upsilon}{(4S)}}$ ALBRECHT 1987I PL B192 245 Observation of ${{\mathit B}^{0}}$ $−$ ${{\overline{\mathit B}}^{0}}$ Mixing BEAN 1987B PRL 58 183 Limits on ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ Mixing and ${\mathit \tau}_{{{\mathit B}^{0}}}/{\mathit \tau}_{{{\mathit B}^{+}}}$ AVERY 1984 PRL 53 1309 Upper Limit on Flavour Changing Neutral Current Decays of the ${\mathit {\mathit b}}$ Quark