Measurement of $\mathit{CP}$-Violating Asymmetries in ${\mathit{B}}^0$ Decays to $\mathit{CP}$ Eigenstates

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 $23\times {10}^6$ $\Upsilon \left(4S\right)\to B\overline{B}$ 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 $\sin 2\beta$, is derived from the decay time distributions in such events. The result is $\sin 2\beta =0.34\mathrm{}\pm 0.20\left(\mathrm{stat}\right)\pm 0.05\left(\mathrm{syst}\right)$.