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$\mathit CP$ VIOLATION PARAMETERS

sin$(2\beta )$

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 ${{\mathit B}_{{{d}}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit K}_S^0}$ .

VALUE

DOCUMENT ID

TECN

COMMENT

$\bf{ 0.709 \pm0.011}$

OUR EVALUATION $~~$(Produced by HFLAV)

See the ideogram below.

$\bf{ 0.708 \pm0.017}$

OUR AVERAGE Error includes scale factor of 1.5.

See the ideogram below.

$0.724$ $\pm0.014$

LHCB

${{\mathit p}}{{\mathit p}}$ at 7, 8 and 13 TeV

$0.667$ $\pm0.023$ $\pm0.012$

BELL

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.57$ $\pm0.58$ $\pm0.06$

BELL

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(5S)}}$

$0.69$ $\pm0.52$ $\pm0.08$

BABR

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.687$ $\pm0.028$ $\pm0.012$

BABR

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$1.56$ $\pm0.42$ $\pm0.21$

BABR

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.79$ ${}^{+0.41}_{-0.44}$

CDF

${{\mathit p}}{{\overline{\mathit p}}}$ at $1.8$ TeV

$0.84$ ${}^{+0.82}_{-1.04}$ $\pm0.16$

ALEP

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$

$3.2$ ${}^{+1.8}_{-2.0}$ $\pm0.5$

OPAL

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$

• • We do not use the following data for averages, fits, limits, etc. • •

$0.717$ $\pm0.013$ $\pm0.008$

LHCB

${{\mathit p}}{{\mathit p}}$ at 13 TeV

$0.760$ $\pm0.034$

LHCB

${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV

$0.72$ $\pm0.09$ $\pm0.03$

BELL

Repl. by ADACHI 2012A

$0.714$ $\pm0.032$ $\pm0.018$

BABR

Repl. by AUBERT 2009K

$0.642$ $\pm0.031$ $\pm0.017$

BELL

Repl. by ADACHI 2012A

$0.728$ $\pm0.056$ $\pm0.023$

BELL

Repl. by CHEN 2007

$0.722$ $\pm0.040$ $\pm0.023$

BABR

Repl. by AUBERT 2007AY

$0.99$ $\pm0.14$ $\pm0.06$

BELL

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.719$ $\pm0.074$ $\pm0.035$

BELL

Repl. by ABE 2005B

$0.59$ $\pm0.14$ $\pm0.05$

BABR

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$

$0.741$ $\pm0.067$ $\pm0.034$

BABR

Repl. by AUBERT 2005F

$0.58$ ${}^{+0.32}_{-0.34}$ ${}^{+0.09}_{-0.10}$

BELL

Repl. by ABE 2001G

$0.99$ $\pm0.14$ $\pm0.06$

BELL

Repl. by ABE 2002Z

$0.34$ $\pm0.20$ $\pm0.05$

BABR

Repl. by AUBERT 2001B

$0.59$ $\pm0.14$ $\pm0.05$

BABR

Repl. by AUBERT 2002P

$1.8$ $\pm1.1$ $\pm0.3$

CDF

Repl. by AFFOLDER 2000C

¹	A combination of this Run 2 result with the Run 1 result from AAIJ 2017BN is reported with a correlation coefficient of 0.40.

²

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.

³	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.

⁴	Uses Dalitz plot analysis of ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays and the first of two equivalent solutions.

⁵	Measurement based on ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit c}}{{\overline{\mathit c}}}{{\mathit K}^{(*)0}}$ decays.

⁶	Measurement in which the ${{\mathit J / \psi}}$ decays to hadrons or to muons that do not satisfy the standard identification criteria.

⁷	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.

⁸	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.

⁹	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.

¹⁰

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 ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$.

¹¹

AAIJ 2024 provides the correlation coefficient ${{\mathit \rho}}$ = 0.441 between the uncertainties of sin$(2\beta )$ and $\mathit C_{{{\mathit c}} {{\overline{\mathit c}}} {{\mathit K}^{(*)0}} }$ (${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit c}}{{\overline{\mathit c}}}{{\mathit K}^{(*)0}}$ ) measurements.

¹²	AAIJ 2017BN provides the correlation coefficient ${{\mathit \rho}}$ = 0.42 between the uncertainties of sin$(2\beta )$ and cos $(2\beta )$ measurements.

¹³	Based on ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \psi}{(2S)}}{{\mathit K}_S^0}$ decays.

¹⁴	Measurement based on $152 \times 10^{6}{{\mathit B}}{{\overline{\mathit B}}}$ pairs.

¹⁵	Measurement based on $227 \times 10^{6}{{\mathit B}}{{\overline{\mathit B}}}$ pairs.

¹⁶	ABE 2002U result is based on the same analysis and data sample reported in ABE 2001G.

¹⁷	ABE 2002Z result is based on $85 \times 10^{6}{{\mathit B}}{{\overline{\mathit B}}}$ pairs.

¹⁸	AUBERT 2002N result based on the same analysis and data sample reported in AUBERT 2001B.

¹⁹	AUBERT 2002P result is based on $88 \times 10^{6}{{\mathit B}}{{\overline{\mathit B}}}$ pairs.

²⁰	First observation of $\mathit CP$ violation in ${{\mathit B}^{0}}$ meson system.

²¹	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

Except where otherwise noted, content of the 2024 Review of Particle Physics is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. The publication of the Review of Particle Physics is supported by US DOE, MEXT (Japan), INFN (Italy) and CERN. Individual collaborators receive support for their PDG activities from their respective institutes or funding agencies. © 2024. See LBNL disclaimers.