Measurement of the $CP$ Asymmetry Amplitude $\sin 2\beta$ with $B^0$ Mesons

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.

Figure 1

Distributions for $B_{CP}$ candidates satisfying the tagging and vertexing requirements: (a) $m_{\mathrm{E}\mathrm{S}}$ for the final states $J/\psi K_S^0$, $\psi (2S)K_S^0$, ${\chi }_{c1}{K}_S^0$, ${\eta }_c{K}_S^0$, and $J/\psi K^{*0}(K^{*0}\to K_S^0{\pi }^0)$, and (b) $\Delta E$ for the final state $J/\psi K_L^0$.

Figure 2

(a) Number of ${\eta }_f=-1$ candidates ($J/\psi K_S^0$, $\psi (2S)K_S^0$, ${\chi }_{c1}{K}_S^0$, and ${\eta }_c{K}_S^0$) in the signal region with a $B^0$ tag $N_{B^0}$ and with a ${\overline{B}}^0$ tag $N_{{\overline{B}}^0}$, and (b) the raw asymmetry $(N_{B^0}-N_{{\overline{B}}^0})/(N_{B^0}+N_{{\overline{B}}^0})$ as functions of $\mathrm{\Delta }t$. The solid (dashed) curves represent the fit projection in $\mathrm{\Delta }t$ for $B^0$ (${\overline{B}}^0$) tags. The shaded regions represent the background contributions. (c) and (d) contain the corresponding information for the ${\eta }_f=+1$ mode $J/\psi K_L^0$.