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 $88\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ 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 $\sin 2\beta$, is derived from the decay-time distributions in such events. We measure $\sin 2\beta =0.741\pm 0.067\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\pm 0.034\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}$ and $|\lambda |=0.948\pm 0.051\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\pm 0.030\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}$. The magnitude of $\lambda$ is consistent with unity, in agreement with the standard model expectation of no direct $CP$ violation in these modes.