Measurement of cos2β in B0→D(*)h0 Decays with a Time-Dependent Dalitz Plot Analysis of D→Ks0π+π−

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We study the time-dependent Dalitz plot of $D\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ in ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)}{h}^{0}$ decays, where ${h}^{0}$ is a ${\ensuremath{\pi}}^{0}$, $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}$, or $\ensuremath{\omega}$ meson and ${D}^{*}\ensuremath{\rightarrow}D{\ensuremath{\pi}}^{0}$, using a data sample of $383\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ decays collected with the BABAR detector. We determine $\mathrm{cos}2\ensuremath{\beta}=0.42\ifmmode\pm\else\textpm\fi{}0.49\ifmmode\pm\else\textpm\fi{}0.09\ifmmode\pm\else\textpm\fi{}0.13$, $\mathrm{sin}2\ensuremath{\beta}=0.29\ifmmode\pm\else\textpm\fi{}0.34\ifmmode\pm\else\textpm\fi{}0.03\ifmmode\pm\else\textpm\fi{}0.05$, and $|\ensuremath{\lambda}|=1.01\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.02$, where the first error is statistical, the second is the experimental systematic uncertainty, and the third, where given, is the Dalitz model uncertainty. Assuming the world average value for $\mathrm{sin}2\ensuremath{\beta}$ and $|\ensuremath{\lambda}|=1$, $\mathrm{cos}2\ensuremath{\beta}>0$ is preferred over $\mathrm{cos}2\ensuremath{\beta}<0$ at 86% confidence level.

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