Bound on the Ratio of Decay Amplitudes for ${\overline{B}}^0\to J/\psi K^{*0}$ and $B^0\to J/\psi K^{*0}$

We have measured the time-dependent decay rate for the process $B\to J/\psi K^{*0}(892)$ in a sample of about $88\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC. In this sample we study flavor-tagged events in which one neutral $B$ meson is reconstructed in the $J/\psi K^{*0}$ or $J/\psi {\overline{K}}^{*0}$ final state. We measure the coefficients of the cosine and sine terms in the time-dependent asymmetries for $J/\psi K^{*0}$ and $J/\psi {\overline{K}}^{*0}$, find them to be consistent with the standard model expectations, and set upper limits at 90% confidence level (C.L.) on the decay amplitude ratios $|A({\overline{B}}^0\to J/\psi K^{*0})|/|A(B^0\to J/\psi K^{*0})|<0.26$ and $|A(B^0\to J/\psi {\overline{K}}^{*0})|/|A({\overline{B}}^0\to J/\psi {\overline{K}}^{*0})|<0.32$. For a single ratio of wrong-flavor to favored amplitudes for $B^0$ and ${\overline{B}}^0$ combined, we obtain an upper limit of 0.25 at 90% C.L.

Figure 1

Distributions of $m_{\mathrm{E}\mathrm{S}}$ (a) for $J/\psi K^{+}{\pi }^{-}$ candidates and (b) for $J/\psi K^{-}{\pi }^{+}$ candidates satisfying the tagging and vertexing requirements. The fit is described in the text.

Figure 2

Number of $J/\psi K^{+}{\pi }^{-}$ and $J/\psi K^{-}{\pi }^{+}$ candidates in the signal region (a) with an opposite-flavor $B$ tag, $N_{\mathrm{O}\mathrm{F}}$, (b) with a same-flavor $B$ tag, $N_{\mathrm{S}\mathrm{F}}$, and (c) the observed asymmetry $(N_{\mathrm{O}\mathrm{F}}-N_{\mathrm{S}\mathrm{F}})/(N_{\mathrm{O}\mathrm{F}}+N_{\mathrm{S}\mathrm{F}})$ as functions of $\mathrm{\Delta }t$. In each figure the solid (dashed) curve represents the fit projection in $\mathrm{\Delta }t$ for $J/\psi K^{+}{\pi }^{-}$ $(J/\psi K^{-}{\pi }^{+})$ candidates. The shaded regions in (a) and (b) represent the background contributions.