For a discussion of $\mathit CP$ violation, see the review on “$\mathit CP$ Violation” in the Reviews section. sin$(2\beta )$ is a measure of the $\mathit CP$-violating amplitude in the ${{\mathit B}_{{d}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit K}_S^0}$ .

“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.

VALUE DOCUMENT ID TECN  COMMENT $\bf{ 0.699 \pm0.017}$ OUR EVALUATION  See the ideogram below. $\bf{ 0.698 \pm0.027}$ OUR AVERAGE  Error includes scale factor of 1.6.  See the ideogram below. $0.760$ $\pm0.034$ 1, 2 AAIJ 2017 BN LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV $0.667$ $\pm0.023$ $\pm0.012$ 3 ADACHI 2012 A BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.57$ $\pm0.58$ $\pm0.06$ 4 SATO 2012 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(5S)}}$ $0.69$ $\pm0.52$ $\pm0.08$ 5 AUBERT 2009 AU BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.687$ $\pm0.028$ $\pm0.012$ 6 AUBERT 2009 K BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $1.56$ $\pm0.42$ $\pm0.21$ 7 AUBERT 2004 R BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.79$ ${}^{+0.41}_{-0.44}$ 8 AFFOLDER 2000 C CDF ${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV $0.84$ ${}^{+0.82}_{-1.04}$ $\pm0.16$ 9 BARATE 2000 Q ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$ $3.2$ ${}^{+1.8}_{-2.0}$ $\pm0.5$ 10 ACKERSTAFF 1998 Z OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$ • • We do not use the following data for averages, fits, limits, etc. • • $0.72$ $\pm0.09$ $\pm0.03$ 11 SAHOO 2008 BELL Repl. by ADACHI 2012A $0.714$ $\pm0.032$ $\pm0.018$ 6 AUBERT 2007 AY BABR Repl. by AUBERT 2009K $0.642$ $\pm0.031$ $\pm0.017$ CHEN 2007 BELL Repl. by ADACHI 2012A $0.728$ $\pm0.056$ $\pm0.023$ 12 ABE 2005 B BELL Repl. by CHEN 2007 $0.722$ $\pm0.040$ $\pm0.023$ 13 AUBERT 2005 F BABR Repl. by AUBERT 2007AY $0.99$ $\pm0.14$ $\pm0.06$ 14 ABE 2002 U BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.719$ $\pm0.074$ $\pm0.035$ 15 ABE 2002 Z BELL Repl. by ABE 2005B $0.59$ $\pm0.14$ $\pm0.05$ 16 AUBERT 2002 N BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $0.741$ $\pm0.067$ $\pm0.034$ 17 AUBERT 2002 P BABR Repl. by AUBERT 2005F $0.58$ ${}^{+0.32}_{-0.34}$ ${}^{+0.09}_{-0.10}$ ABASHIAN 2001 BELL Repl. by ABE 2001G $0.99$ $\pm0.14$ $\pm0.06$ 18 ABE 2001 G BELL Repl. by ABE 2002Z $0.34$ $\pm0.20$ $\pm0.05$ AUBERT 2001 BABR Repl. by AUBERT 2001B $0.59$ $\pm0.14$ $\pm0.05$ 18 AUBERT 2001 B BABR Repl. by AUBERT 2002P $1.8$ $\pm1.1$ $\pm0.3$ 19 ABE 1998 U CDF Repl. by AFFOLDER 2000C 1  Measurement based on ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}_S^0}$ , ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \psi}{(2S)}}{{\mathit K}_S^0}$ with ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ and ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ . 2  AAIJ 2017BN provides the correlation coefficient ${{\mathit \rho}}$ = 0.42 between the uncertainties of sin$(2\beta )$ and cos $(2\beta )$ measurements. 3  Measurement based on ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}_S^0}$ , ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \psi}{(2S)}}{{\mathit K}_S^0}$ , ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}_L^0}$ , and ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \chi}_{{c1}}{(1P)}}{{\mathit K}_S^0}$ decays. 4  SATO 2012 uses 121 fb${}^{-1}$ data collected on ${{\mathit Y}{(5S)}}$ resonance. Uses the ''${{\mathit B}}−{{\mathit \pi}}$ tagging'' where ${{\mathit B}}{{\mathit \pi}^{+}}$ and ${{\mathit B}}{{\mathit \pi}^{-}}$ tagged ${{\mathit J / \psi}}{{\mathit K}_S^0}$ events are compared. 5  Uses Dalitz plot analysis of ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays and the first of two equivalent solutions. 6  Measurement based on ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit c}}{{\overline{\mathit c}}}{{\mathit K}^{(*)0}}$ decays. 7  Measurement in which the ${{\mathit J / \psi}}$ decays to hadrons or to muons that do not satisfy the standard identification criteria. 8  AFFOLDER 2000C uses about 400 ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit K}_S^0}$ events. The production flavor of ${{\mathit B}^{0}}$ was determined using three tagging algorithms: a same-side tag, a jet-charge tag, and a soft-lepton tag. 9  BARATE 2000Q uses 23 candidates for ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit K}_S^0}$ decays. A combination of jet-charge, vertex-charge, and same-side tagging techniques were used to determine the ${{\mathit B}^{0}}$ production flavor. 10  ACKERSTAFF 1998Z uses 24 candidates for ${{\mathit B}_{{d}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit K}_S^0}$ decay. A combination of jet-charge and vertex-charge techniques were used to tag the ${{\mathit B}_{{d}}^{0}}$ production flavor. 11  Based on ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \psi}{(2S)}}{{\mathit K}_S^0}$ decays. 12  Measurement based on $152 \times 10^{6}$ ${{\mathit B}}{{\overline{\mathit B}}}$ pairs. 13  Measurement based on $227 \times 10^{6}$ ${{\mathit B}}{{\overline{\mathit B}}}$ pairs. 14  ABE 2002U result is based on the same analysis and data sample reported in ABE 2001G. 15  ABE 2002Z result is based on $85 \times 10^{6}$ ${{\mathit B}}{{\overline{\mathit B}}}$ pairs. 16  AUBERT 2002N result based on the same analysis and data sample reported in AUBERT 2001B. 17  AUBERT 2002P result is based on $88 \times 10^{6}$ ${{\mathit B}}{{\overline{\mathit B}}}$ pairs. 18  First observation of $\mathit CP$ violation in ${{\mathit B}^{0}}$ meson system. 19  ABE 1998U uses $198$ $\pm17$ ${{\mathit B}_{{d}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit K}^{0}}$ events. The production flavor of ${{\mathit B}^{0}}$ was determined using the same side tagging technique.

sin$(2\beta )$

Conservation Laws:

$\mathit CP$ VIOLATION OBSERVED

References:

AAIJ 2017BN JHEP 1711 170 Measurement of $\mathit CP$ Violation in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}_S^0}$ and ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \psi}{(2S)}}{{\mathit K}_S^0}$ Decays ADACHI 2012A PRL 108 171802 Precise Measurement of the $\mathit CP$ Violation Parameter sin2$\mathit \phi _{1}$ in ${{\mathit B}^{0}}$ $\rightarrow$ ( ${{\mathit c}}{{\overline{\mathit c}}}$) ${{\mathit K}^{0}}$ Decays SATO 2012 PRL 108 171801 Measurement of the $\mathit CP$-Violation Parameter sin2$\mathit \phi _{1}$ with a New Tagging Method at the ${{\mathit \Upsilon}{(5S)}}$ Resonance AUBERT 2009AU PR D80 112001 Time-Dependent Amplitude Analysis of ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ AUBERT 2009K PR D79 072009 Measurement of Time-Dependent $\mathit CP$ Asymmetry in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit c}}{{\overline{\mathit c}}}{{\mathit K}^{(*)0}}$ Decays SAHOO 2008 PR D77 091103 Measurements of Time-Dependent $\mathit CP$ Violation in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \psi}{(2S)}}{{\mathit K}_S^0}$ Decays AUBERT 2007AY PRL 99 171803 Improved Measurement of $\mathit CP$ Violation in Neutral ${{\mathit B}}$ Decays to ${\mathit {\mathit c}}{\mathit {\overline{\mathit c}}}{\mathit {\mathit s}}$ CHEN 2007 PRL 98 031802 Observation of Time-Dependent $\mathit CP$ Violation in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit K}^{0}}$ Decays and Improved Measurements of $\mathit CP$ Asymmetries in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit K}^{0}}$ , ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ and ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}^{0}}$ Decays ABE 2005B PR D71 072003 Improved Measurement of $\mathit CP$ Violation Parameters sin2$\phi _{1}$ and $\vert {{\mathit \lambda}}\vert $, ${{\mathit B}}$ Meson Lifetimes, and ${{\mathit B}^{0}}−{{\overline{\mathit B}}^{0}}$ Mixing Parameter $\Delta {{\mathit m}_{{d}}}$ Also PR D71 079903 (errat.) Publisher's Note to ABE 2005B. Improved Measurement of $\mathit CP$ Violation Parameters sin2$\phi _{1}$ and $\vert \lambda \vert $, ${{\mathit B}}$ Meson Lifetimes, and ${{\mathit B}^{0}}−{{\overline{\mathit B}}^{0}}$ Mixing Parameter $\Delta {\mathit m}_{{{\mathit d}}}$ AUBERT 2005F PRL 94 161803 Improved Measurement of $\mathit CP$ Asymmetries in ${{\mathit B}^{0}}$ $\rightarrow$ ( ${{\mathit c}}{{\overline{\mathit c}}}$) ${{\mathit K}}{}^{0(*)}$ Decays AUBERT 2004R PR D69 052001 Measurement of sin2$\beta $ with Hadronic and Previously Unused Muonic ${{\mathit J / \psi}}$ Decays ABE 2002Z PR D66 071102 An Improved Measurement of Mixing Induced $\mathit CP$ Violation in the Neutral ${{\mathit B}}$ Meson System ABE 2002U PR D66 032007 Observation of Mixing Induced $\mathit CP$ Violation in the Neutral ${{\mathit B}}$ Meson System AUBERT 2002N PR D66 032003 A Study of Time Dependent $\mathit CP$ Violating Asymetries and Flavor Oscillations in Neutral ${{\mathit B}}$ Decays at the ${{\mathit \Upsilon}{(4S)}}$ AUBERT 2002P PRL 89 201802 Measurement of the $\mathit CP$ Violating Asymmetry Amplitude sin2$\beta $ ABASHIAN 2001 PRL 86 2509 Measurement of the $\mathit CP$ Violation Parameter sin$2\phi _{1}$ in ${{\mathit B}_{{d}}^{0}}$ Meson Decays ABE 2001G PRL 87 091802 Observation of Large $\mathit CP$ Violation in the Neutral ${{\mathit B}}$ Meson System AUBERT 2001B PRL 87 091801 Observation of $\mathit CP$ Violation in the ${{\mathit B}^{0}}$ Meson System AUBERT 2001 PRL 86 2515 Measurement of $\mathit CP$ Violating Asymmetries in ${{\mathit B}^{0}}$ Decays to $\mathit CP$ Eigenstates AFFOLDER 2000C PR D61 072005 A Measurement of sin$^2\beta $ from ${{\mathit B}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}_S^0}$ with the CDF Detector BARATE 2000Q PL B492 259 Study of the $\mathit CP$ Asymmetry of ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}_S^0}$ Decays in ALEPH ABE 1998U PRL 81 5513 Measurement of the $\mathit CP$ Violation Parameter sin(2$\beta $) in ${{\mathit B}_{{d}}^{0}}/{{\overline{\mathit B}}_{{d}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit K}_S^0}$ Decays ACKERSTAFF 1998Z EPJ C5 379 Investigation of $\mathit CP$ Violation in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}_S^0}$ Decays at LEP