Measurements of branching fractions and time-dependent $CP$ violating asymmetries in $B^0\to D^{(*)\pm }{D}^{\mp }$ decays

We report measurements of branching fractions and time-dependent $CP$ asymmetries in $B^0\to D^{+}{D}^{-}$ and $B^0\to D^{*\pm }{D}^{\mp }$ decays using a data sample that contains $(772\pm 11)\times {10}^{6}B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We determine the branching fractions to be $\mathcal{B}(B^0\to D^{+}{D}^{-})=(2.12\pm 0.16\pm 0.18)\times {10}^{-4}$ and $\mathcal{B}(B^0\to D^{*\pm }{D}^{\mp })=(6.14\pm 0.29\pm 0.50)\times {10}^{-4}$. We measure $CP$ asymmetry parameters ${\mathcal{S}}_{D^{+}{D}^{-}}=-{1.06}_{-0.14}^{+0.21}\pm 0.08$ and ${\mathcal{C}}_{D^{+}{D}^{-}}=-0.43\pm 0.16\pm 0.05$ in $B^0\to D^{+}{D}^{-}$ and ${\mathcal{A}}_{D^{*}D}=+0.06\pm 0.05\pm 0.02$, ${\mathcal{S}}_{D^{*}D}=-0.78\pm 0.15\pm 0.05$, ${\mathcal{C}}_{D^{*}D}=-0.01\pm 0.11\pm 0.04$, $\Delta {\mathcal{S}}_{D^{*}D}=-0.13\pm 0.15\pm 0.04$ and $\Delta {\mathcal{C}}_{D^{*}D}=+0.12\pm 0.11\pm 0.03$ in $B^0\to D^{*\pm }{D}^{\mp }$, where the first uncertainty is statistical and the second is systematic. We exclude the conservation of $CP$ symmetry in both decays at equal to or greater than $4\sigma$ significance.

Figure 1

$M_{\mathrm{bc}}$ and $\Delta E$ distributions (data points with error bars) and fit projections (solid lines) for (a)–(b) $B^0\to D^{+}{D}^{-}$ and (c)–(d) $B^0\to D^{*\pm }{D}^{\mp }$ decays. The dotted (dashed) lines represent projections of signal (background) fit components. A $|\Delta E|<30\mathrm{MeV}$ ($M_{\mathrm{bc}}>5.27\mathrm{GeV}/c^2$) requirement is applied in plotting the $M_{\mathrm{bc}}(\Delta E)$ distributions.

Figure 2

Top: $\Delta t$ distributions (data points with error bars) of (a) $B^0\to D^{+}{D}^{-}$ and (b) $B^0\to D^{*+}{D}^{-}+B^0\to D^{*-}{D}^{+}$ candidates associated with high quality flavor tags ($r>0.5$). The lines show projections of the sum of signal and background components in the fit. The signal purity for $r>0.5$ is 69% (66%) for $B^0\to D^{+}{D}^{-}(B^0\to D^{*\pm }{D}^{\mp })$. Bottom: The $CP$ asymmetry obtained from the above distributions and projections.