Observation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">CP</mml:mi></mml:math>Violation in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Meson System

We present an updated measurement of time-dependent $\mathrm{CP}$-violating asymmetries in neutral $B$ decays with the BABAR detector at the PEP-II asymmetric $B$ Factory at SLAC. This result uses an additional sample of $\ensuremath{\Upsilon}(4S)$ decays collected in 2001, bringing the data available to $32\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs. We select events in which one neutral $B$ meson is fully reconstructed in a final state containing charmonium and the flavor of the other neutral $B$ meson is determined from its decay products. The amplitude of the $\mathrm{CP}$-violating asymmetry, which in the standard model is proportional to $\mathrm{sin}2\ensuremath{\beta}$, is derived from the decay time distributions in such events. The result $\mathrm{sin}2\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.59\ifmmode\pm\else\textpm\fi{}0.14(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.05(\mathrm{syst})$ establishes $\mathrm{CP}$ violation in the ${B}^{0}$ meson system. We also determine $|\ensuremath{\lambda}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.93\ifmmode\pm\else\textpm\fi{}0.09(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.03(\mathrm{syst})$, consistent with no direct $\mathrm{CP}$ violation.

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