Measurement ofCP-Violating Asymmetries inB0Decays toCPEigenstates

We present measurements of time-dependent $\mathrm{CP}$-violating asymmetries in neutral $B$ decays to several $\mathrm{CP}$ eigenstates. The measurement uses a data sample of $23\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ decays collected by the BABAR detector at the PEP-II asymmetric $B$ Factory at SLAC. In this sample, we find events in which one neutral $B$ meson is fully reconstructed in a $\mathrm{CP}$ eigenstate 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 is $\mathrm{sin}2\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.34\ifmmode\pm\else\textpm\fi{}0.20(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.05(\mathrm{syst})$.