Measurement of the time-dependent $CP$ asymmetry of partially reconstructed $B^0\to D^{*+}{D}^{*-}$ decays

We present a new measurement of the time-dependent $CP$ asymmetry of $B^0\to D^{*+}{D}^{*-}$ decays using ($471\pm 5$) million $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II $B$ Factory at the SLAC National Accelerator Laboratory. Using the technique of partial reconstruction, we measure the time-dependent $CP$ asymmetry parameters $S=-0.34\pm 0.12\pm 0.05$ and $C=+0.15\pm 0.09\pm 0.04$. Using the value for the $CP$-odd fraction $R_{\perp }=0.158\pm 0.028\pm 0.006$, previously measured by BABAR with fully reconstructed $B^0\to D^{*+}{D}^{*-}$ events, we extract the $CP$-even components $S_{+}=-0.49\pm 0.18\pm 0.07\pm 0.04$ and $C_{+}=+0.15\pm 0.09\pm 0.04$. In each case, the first uncertainty is statistical and the second is systematic; the third uncertainty on $S_{+}$ is the contribution from the uncertainty on $R_{\perp }$. The measured value of the $CP$-even component $S_{+}$ is consistent with the value of $\sin 2\beta$ measured in $b\to (c\overline{c})s$ transitions, and with the Standard Model expectation of small penguin contributions.

Figure 1

Leading and subleading order Feynman graphs for the ${\overline{B}}^0\to D^{(*)+}{D}^{(*)-}$ decays.

Figure 2

Momenta and angles in the ${\rm Y}(4S)$ center of mass frame used in partial reconstruction. The orthogonal axes $u$ and $v$ are normal to the momentum ${\overrightarrow{p}}_{D^{*}}$ of the reconstructed $D^{*}$, and $u$ lies in the plane defined by the momenta of the $D^{*}$ and slow pion, ${\overrightarrow{p}}_{D^{*}}$ and ${\overrightarrow{p}}_s$. The angle $\varphi$ is measured in the $u-v$ plane.

Figure 3

Result of the kinematical fit of kaon (top) and lepton tagged (bottom) data events, with PDF’s overlaid: total PDF (solid line), total background ($B\overline{B}+\mathrm{\text{continuum}}$, short dashed line), $B\overline{B}$ combinatorial background (dashed line), continuum $u$, $d$, $s$, $c$ background (dot-dashed line) and signal (red, dotted line).

Figure 4

Result of the kinematical fit of kaon- (top) and lepton tagged (bottom) events for the Fisher function, with PDF’s overlaid: total $B\overline{B}$ (solid line), $B\overline{B}$ (dashed line) and continuum $u$, $d$, $s$, $c$ background (dash-dotted line).

Figure 5

Top: $\Delta t$ distribution for $B^0$ (dashed) and ${\overline{B}}^0$ (solid) kaon tags; the lower curves are the corresponding signal PDF’ s. Bottom: raw time-dependent $CP$ asymmetry. Only data in the restricted signal region $m_{\mathrm{rec}}>1.860\mathrm{GeV}/c^2$ are shown.

Figure 6

Top: $\Delta t$ distribution for $B^0$ (dashed) and ${\overline{B}}^0$ (solid) lepton tags; the lower curves are the corresponding signal PDF’ s. Bottom: raw time-dependent $CP$ asymmetry. Only data in the restricted signal region $m_{\mathrm{rec}}>1.860\mathrm{GeV}/c^2$ are shown.