Measurement of theCPAsymmetry Amplitudesin2βwithB0Mesons

We present results on time-dependent $CP$ asymmetries in neutral $B$ decays to several $CP$ eigenstates. The measurements use a data sample of about $88\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ decays collected between 1999 and 2002 with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC. We study events in which one neutral $B$ meson is fully reconstructed in a final state containing a charmonium meson and the other $B$ meson is determined to be either a ${B}^{0}$ or ${\overline{B}}^{0}$ from its decay products. The amplitude of the $CP$ asymmetry, which in the standard model is proportional to $\mathrm{sin}2\ensuremath{\beta}$, is derived from the decay-time distributions in such events. We measure $\mathrm{sin}2\ensuremath{\beta}=0.741\ifmmode\pm\else\textpm\fi{}0.067\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\ifmmode\pm\else\textpm\fi{}0.034\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}$ and $|\ensuremath{\lambda}|=0.948\ifmmode\pm\else\textpm\fi{}0.051\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\ifmmode\pm\else\textpm\fi{}0.030\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}$. The magnitude of $\ensuremath{\lambda}$ is consistent with unity, in agreement with the standard model expectation of no direct $CP$ violation in these modes.