$\mathit CP$ impurity in ${{\mathit B}_{{d}}^{0}}$ system. It is obtained from either $\mathit a_{ {{\mathit \ell}} {{\mathit \ell}} }$, the charge asymmetry in like-sign dilepton events or $\mathit a_{ {{\mathit c}} {{\mathit p}} }$, the time-dependent asymmetry of inclusive ${{\mathit B}^{0}}$ and ${{\overline{\mathit B}}^{0}}$ decays.

"OUR EVALUATION" is an average obtained by the Heavy Flavor Averaging Group (HFLAV) and described at https://hflav.web.cern.ch/. It is the result of a fit to ${{\mathit B}_{{d}}}$ and ${{\mathit B}_{{s}}}$ $\mathit CP$ asymmetries, which includes the ${{\mathit B}_{{d}}}$ measurements listed below and the ${{\mathit B}_{{s}}}$ measurements listed in the ${{\mathit B}_{{s}}}$ section, taking into account correlations between those measurements.

VALUE ($ 10^{-3} $) DOCUMENT ID TECN  COMMENT $\bf{ -0.5 \pm0.4}$ OUR EVALUATION $\bf{ -0.1 \pm0.4}$ OUR AVERAGE $-0.05$ $\pm0.48$ $\pm0.75$ 1 AAIJ 2015 F LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV $-0.975$ $\pm0.875$ $\pm0.475$ 2 LEES 2015 A BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $1.55$ $\pm1.05$ 3 ABAZOV 2014 D0 ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV $0.15$ $\pm0.42$ ${}^{+0.94}_{-0.81}$ 4 LEES 2013 N BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $-1.7$ $\pm1.1$ $\pm0.4$ 5 ABAZOV 2012 AC D0 ${{\mathit p}}{{\overline{\mathit p}}}$ at 1.96 TeV $0.4$ $\pm1.3$ $\pm0.9$ 6 AUBERT 2006 T BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $-0.3$ $\pm2.0$ $\pm2.1$ 7 NAKANO 2006 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $3.5$ $\pm10.3$ $\pm1.5$ 8 JAFFE 2001 CLE2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ • • We do not use the following data for averages, fits, limits, etc. • • $-0.3$ $\pm1.3$ 9 ABAZOV 2011 U D0 Repl. by ABAZOV 2014 $-2.3$ $\pm1.1$ $\pm0.8$ 10 ABAZOV 2006 S D0 Repl. by ABAZOV 2011U $-14.7$ $\pm6.7$ $\pm5.7$ 11 AUBERT,B 2004 C BABR Repl. by AUBERT 2006T $1.2$ $\pm2.9$ $\pm3.6$ 2 AUBERT 2002 K BABR Repl. by LEES 2015A $-3.2$ $\pm6.5$ 12 BARATE 2001 D ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$ $4$ $\pm18$ $\pm3$ 13 BEHRENS 2000 B CLE2 Repl. by JAFFE 2001 $1.2$ $\pm13.8$ $\pm3.2$ 14 ABBIENDI 1999 J OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$ $2$ $\pm7$ $\pm3$ 15 ACKERSTAFF 1997 U OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$ $<45$ 16 BARTELT 1993 CLE2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ 1  AAIJ 2015F uses semileptonic ${{\mathit B}^{0}}$ decays in the inclusive final states ${{\mathit D}^{-}}{{\mathit \mu}^{+}}$ and ${{\mathit D}^{*-}}{{\mathit \mu}^{+}}$ , where the ${{\mathit D}^{-}}$ meson decays into the ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}$ final state, and the ${{\mathit D}^{*-}}$ meson into the ${{\overline{\mathit D}}^{0}}$( $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ )${{\mathit \pi}^{-}}$ final state. Reports ${{\mathit A}_{{{SL}}}^{d}}$ = ($-0.02$ $\pm0.19$ $\pm0.30)\%$, which equals to 4${\mathrm {Re}}(\epsilon _{{{\mathit B}^{0}}})/(1+\vert \epsilon _{{{\mathit B}^{0}}}\vert ^2$). 2  Uses the charge asymmetry in like-sign dilepton events. LEES 2015A reports ${{\mathit A}_{{{SL}}}^{d}}$ = ($-3.9$ $\pm3.5$ $\pm1.9$) $ \times 10^{-3}$. 3  ABAZOV 2014 uses the dimuon charge asymmetry with different impact parameters from which it reports ${{\mathit A}_{{{SL}}}^{d}}$ = $-0.0062$ $\pm0.0042$. 4  Uses ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit X}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ and a kaon-tagged sample which yields measurement of ${{\mathit A}_{{SL}}^{d}}$ = ($0.06$ $\pm0.17$ ${}^{+0.38}_{-0.32})\%$, corresponding to $\Delta _{CP}$ = 1$−\vert $q/p$\vert $ = ($0.29$ $\pm0.84$ ${}^{+1.88}_{-1.61}$) $ \times 10^{-3}$. 5  ABAZOV 2012AC uses ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{-}}{{\mathit \mu}^{+}}{{\mathit X}}$ and ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*}{(2010)}^{-}}{{\mathit \mu}^{+}}{{\mathit X}}$ decays without initial state flavor tagging which yields measurement of A${}^{d}_{SL}$ = ($6.8$ $\pm4.5$ $\pm1.4$) $ \times 10^{-3}$. 6  AUBERT 2006T reports $\vert $q/p$\vert −1=(-0.8$ $\pm2.7$ $\pm1.9$) $ \times 10^{-3}$. We convert to (1$−\vert $q/p$\vert {}^{2}$)/4. 7  Uses the charge asymmetry in like-sign dilepton events and reports $\vert $q/p$\vert $ = $1.0005$ $\pm0.0040$ $\pm0.0043$. 8  JAFFE 2001 finds ${{\mathit a}}_{ {{\mathit \ell}} {{\mathit \ell}} }$ = $0.013$ $\pm0.050$ $\pm0.005$ and combines with the previous BEHRENS 2000B independent measurement. 9  ABAZOV 2011U uses the dimuon charge asymmetry with different impact parameters from which it reports ${{\mathit A}_{{SL}}^{d}}$ = ($-1.2$ $\pm5.2$) $ \times 10^{-3}$. 10  Uses the dimuon charge asymmetry. 11  AUBERT 2004C reports $\vert $q/p$\vert $ = $1.029$ $\pm0.013$ $\pm0.011$ and we converted it to (1- $\vert $q/p$\vert {}^{2}$)/4. 12  BARATE 2001D measured by investigating time-dependent asymmetries in semileptonic and fully inclusive ${{\mathit B}_{{d}}^{0}}$ decays. 13  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. 14  Data analyzed using the time-dependent asymmetry of inclusive ${{\mathit B}^{0}}$ decay. The production flavor of ${{\mathit B}^{0}}$ mesons is determined using both the jet charge and the charge of secondary vertex in the opposite hemisphere. 15  ACKERSTAFF 1997U assumes $\mathit CPT$ and is based on measuring the charge asymmetry in a sample of ${{\mathit B}^{0}}$ decays defined by lepton and $\mathit Q_{{\mathrm {hem}}}$ tags. If $\mathit CPT$ is not invoked, Re(${{\mathit \epsilon}_{{B}}}$) = $-0.006$ $\pm0.010$ $\pm0.006$ is found. The indirect $\mathit CPT$ violation parameter is determined to Im( ${{\mathit \delta}}{{\mathit B}}$ ) = $-0.020$ $\pm0.016$ $\pm0.006$. 16  BARTELT 1993 finds $\mathit a_{ {{\mathit \ell}} {{\mathit \ell}} }$ = $0.031$ $\pm0.096$ $\pm0.032$ which corresponds to $\vert \mathit a_{ {{\mathit \ell}} {{\mathit \ell}} }\vert <0.18$, which yields the above $\vert {\mathrm {Re}}(\epsilon _{{{\mathit B}^{0}}})/(1+\vert \epsilon _{{{\mathit B}^{0}}}\vert ^2)\vert $.

Conservation Laws:

$\mathit CP$ INVARIANCE

References:

AAIJ 2015F PRL 114 041601 Measurement of the Semileptonic $\mathit CP$ Asymmetry in ${{\mathit B}^{0}}−{{\overline{\mathit B}}^{0}}$ Mixing LEES 2015A PRL 114 081801 Study of $\mathit CP$ Asymmetry in ${{\mathit B}^{0}}−{{\overline{\mathit B}}^{0}}$ Mixing with Inclusive Dilepton Events ABAZOV 2014 PR D89 012002 Study of $\mathit CP$-Violating Charge Asymmetries of Single Muons and Like-Sign Dimuons in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions LEES 2013N PRL 111 101802 Search for $\mathit CP$ Violation in ${{\mathit B}^{0}}−{{\overline{\mathit B}}^{0}}$ Mixing using Partial Reconstruction of ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit \Xi}^{+}}$ nu and a Kaon Tag Also PRL 111 159901(errat.) Publisher's Note: Search for $\mathit CP$ Violation in ${{\mathit B}^{0}}−{{\overline{\mathit B}}^{0}}$ Mixing Using Partial Reconstruction of ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*-}}{{\mathit X}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ and a Kaon Tag. LEES 2013N Also PR D93 032001 Search for Mixing-Induced $\mathit CP$ Violation using Partial Reconstruction of ${{\overline{\mathit B}}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit X}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}_{{{{\mathit \ell}}}}}$ and Kaon Tagging ABAZOV 2012AC PR D86 072009 Measurement of the Semileptonic Charge Asymmetry in ${{\mathit B}^{0}}$ Meson Mixing with the ${D0}$ Detector ABAZOV 2011U PR D84 052007 Measurement of the Anomalous Like-Sign Dimuon Charge Asymmetry with 9 fb${}^{-1}$ of ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions ABAZOV 2006S PR D74 092001 Measurement of the $\mathit CP$-violation Parameter of ${{\mathit B}^{0}}$ Mixing and Decay with ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \mu}}{{\mathit X}}$ Data AUBERT 2006T PRL 96 251802 Search for $\mathit T$, $\mathit CP$, and $\mathit CPT$ Violation in ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ Mixing with Inclusive Dilepton Events NAKANO 2006 PR D73 112002 Charge Asymmetry of Same-Sign Dileptons in ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ Mixing AUBERT,B 2004C PR D70 012007 Limits on the Decay Rate Difference of Neutral ${{\mathit B}}$ Mesons and on $\mathit CP$, $\mathit T$, and $\mathit CPT$ Violation in ${{\mathit B}^{0}}\leftrightarrow{{\overline{\mathit B}}^{0}}$ Oscillations Also PRL 92 181801 Limits on the Decay Rate Difference of Neutral ${{\mathit B}}$ Mesons and on $\mathit CP$, $\mathit T$, and $\mathit CPT$ Violation in ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ Oscillations AUBERT 2002K PRL 88 231801 Search for $\mathit T$ and $\mathit CP$ Violation in ${{\mathit B}^{0}}-{{\overline{\mathit B}}^{0}}$ Mixing with Inclusive Dilapton Events BARATE 2001D EPJ C20 431 Investigation of Inclusive $\mathit CP$ Asymmetries in ${{\mathit B}^{0}}$ Decays JAFFE 2001 PRL 86 5000 Bounds on the $\mathit CP$ Asymmetry in Like Sign Dileptons from ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ Meson Decays BEHRENS 2000B PL B490 36 Precise Measurement of ${{\mathit B}^{0}}$ $\leftrightarrow$ ${{\overline{\mathit B}}^{0}}$ Mixing Parameters at the ${{\mathit \Upsilon}{(4S)}}$ ABBIENDI 1999J EPJ C12 609 Measurement of the ${{\mathit B}^{+}}$ and ${{\mathit B}^{0}}$ Lifetimes and Search for $\mathit CP(T)$ Violation using Reconstructed Secondary Vertices ACKERSTAFF 1997U ZPHY C76 401 A Study of ${{\mathit B}}$ Meson Oscillations using Hadronic ${{\mathit Z}^{0}}$ Decays Containing Leptons BARTELT 1993 PRL 71 1680 Two Measurements of ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ Mixing