Measurement of $CP$ violation in $B^0\to D^{*-}{\pi }^{+}$ and $B^0\to D^{-}{\pi }^{+}$ decays

We report measurements of time-dependent decay rates for $B^0\to D^{(*)-}{\pi }^{+}$ decays and extraction of $CP$ violation parameters that depend on ${\varphi }_3$. Using fully reconstructed $D^{(*)}\pi$ events and partially reconstructed $D^{*}\pi$ events from a data sample that contains $386\times {10}^6$ $B\overline{B}$ pairs that was collected near the ${\rm Y}(4S)$ resonance, with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider, we obtain the $CP$ violation parameters $S^{+}(D^{(*)}\pi )$ and $S^{-}(D^{(*)}\pi )$. We obtain $S^{+}(D^{*}\pi )=0.049\pm 0.020(\mathrm{stat})\pm 0.011(\mathrm{sys})$, $S^{-}(D^{*}\pi )=0.031\pm 0.019(\mathrm{stat})\pm 0.011(\mathrm{sys})$, and $S^{+}(D\pi )=0.031\pm 0.030(\mathrm{stat})\pm 0.012(\mathrm{sys})$, $S^{-}(D\pi )=0.068\pm 0.029(\mathrm{stat})\pm 0.012(\mathrm{sys})$. These results are an indication of $CP$ violation in $B^0\to D^{*-}{\pi }^{+}$ and $B^0\to D^{-}{\pi }^{+}$ decays at the $2.5\sigma$ and $2.2\sigma$ levels, respectively. If we use the values of $R_{D^{(*)}\pi }$ that are derived using assumptions of factorization and SU(3) symmetry, branching fraction measurements for the $B\to D_s^{(*)}\pi$ modes, and lattice QCD calculations, we can restrict the allowed region of $|\sin (2{\varphi }_1+{\varphi }_3)|$ to be above 0.44 and 0.52 at 68% confidence level from the $D^{*}\pi$ and $D\pi$ modes, respectively.

Figure 1

Diagrams for (a) $B^0\to D^{(*)-}{\pi }^{+}$ and (b) ${\overline{B}}^0\to D^{(*)-}{\pi }^{+}$. Those for ${\overline{B}}^0\to D^{(*)+}{\pi }^{-}$ and $B^0\to D^{(*)+}{\pi }^{-}$ can be obtained by charge conjugation.

Figure 2

$\Delta E$ and $M_{\mathrm{bc}}$ distributions for $B^0\to D^{*-}{\pi }^{+}$ candidates (a and b), and $B^0\to D^{-}{\pi }^{+}$ candidates (c and d). Curves are the fit results. Hatched regions indicate the background components of the fits.

Figure 3

(a) $\Delta t$ distribution for the signal candidates when all four signal categories are combined. (b) $(\mathrm{OF}-\mathrm{SF})/(\mathrm{OF}+\mathrm{SF})$ asymmetries. Curves are the fit results. The hatched region in (a) indicates the background.

Figure 4

$\Delta t$ distributions for the $D^{*}\pi$ events in the $0.875<r\le 1.0$ flavor-tagging quality bin. (a) $B^0\to D^{*+}{\pi }^{-}$, (b) $B^0\to D^{*-}{\pi }^{+}$, (c) ${\overline{B}}^0\to D^{*+}{\pi }^{-}$, (d) ${\overline{B}}^0\to D^{*-}{\pi }^{+}$. Curves show the results of fits to the entire event sample, and hatched regions indicate the backgrounds.

Figure 5

$\Delta t$ distributions for the $D\pi$ events in the $0.875<r\le 1.0$ flavor-tagging quality bin. (a) $B^0\to D^{+}{\pi }^{-}$, (b) $B^0\to D^{-}{\pi }^{+}$, (c) ${\overline{B}}^0\to D^{+}{\pi }^{-}$, (d) ${\overline{B}}^0\to D^{-}{\pi }^{+}$. Curves show the results of fits to the entire event sample, and hatched regions indicate the backgrounds.

Figure 6

Results of the kinematic fits to $D^{*}\pi$ candidates, projected onto (top) the $p_{{\pi }_f}$ axis, (middle) the $\cos {\delta }_{{\pi }_f{\pi }_s}$ axis and the (bottom) $\cos {\theta }_{\mathrm{hel}}$ axis, in both (left) selection region and (right) signal region. The arrows show the edges of the signal regions.

Figure 7

Result of the resolution parameter extraction procedure for $J/\psi \to {\mu }^{+}{\mu }^{-}$ candidates selected from (top) SVD1 and (bottom) SVD2 data, shown with both (left) linear and (right) logarithmic coordinate scales. The data points show the $\Delta z$ distribution for candidates in the signal region; the full line shows the result of the fit. The dashed line indicates the background.

Figure 8

Results of the fit to obtain $S^{+}$ and $S^{-}$. The fit result is superimposed on the data. The signal component is shown as the dashed line. The dotted line indicates the background contribution.

Figure 9

Results of the fit to obtain $S^{+}$ and $S^{-}$, shown as asymmetries in the (left) same flavor events and (right) opposite flavor events. The fit result is superimposed on the data.

Figure 10

Results of the $S^{\pm }$ measurements expressed in terms of $S^{-}$ vs $S^{+}$ for the $D^{*}\pi$ (left) and $D\pi$ (right) modes. Shaded regions indicate allowed regions with $1\sigma$, $2\sigma$ and $3\sigma$ uncertainties defined by $\sqrt{-2\ln \mathcal{L}}=1,4,9$, respectively

Figure 11

Excluded regions of ($2{\varphi }_1+{\varphi }_3$) vs $R$ space at 1, 2, $3\sigma$ level for the $D^{*}\pi$ (left) and $D\pi$ (right) decays. The range 0°–180° for $2{\varphi }_1+{\varphi }_3$ is shown; there are additional solutions at $2{\varphi }_1+{\varphi }_3⟶2{\varphi }_1+{\varphi }_3+180°$.

Figure 12

Lower limit on $|\sin (2{\varphi }_1+{\varphi }_3)|$ as a function of $R$ at $1\sigma$ (68% CL) (thin curves) and $2\sigma$ (95% CL) (thick curves) from (left) $D^{*}\pi$ and (right) $D\pi$. The estimated values for $R_{D^{(*)}\pi }$ are indicated as solid lines (central values). Coarse dotted lines and fine dotted lines indicate their $1\sigma$ and $2\sigma$ errors.