Measurement of the Quark Mixing Parameter $\cos 2{\varphi }_1$ Using Time-Dependent Dalitz Analysis of ${\overline{B}}^0\to D[K_S^0{\pi }^{+}{\pi }^{-}]h^0$

We present a measurement of the angle ${\varphi }_1$ of the Cabibbo-Kobayashi-Maskawa unitarity triangle using a time-dependent Dalitz analysis of $D\to K_S^0{\pi }^{+}{\pi }^{-}$ decays produced in neutral $B$ meson decay to a neutral $D$ meson and a light meson (${\overline{B}}^0\to D^{(*)}{h}^0$). The method allows a direct extraction of $2{\varphi }_1$ and, therefore, helps to resolve the ambiguity between $2{\varphi }_1$ and $\pi -2{\varphi }_1$ in the measurement of $\sin 2{\varphi }_1$. We obtain $\sin 2{\varphi }_1=0.78\pm 0.44\pm 0.22$ and $\cos 2{\varphi }_1={1.87}_{-0.53-0.32}^{+0.40+0.22}$. The sign of $\cos 2{\varphi }_1$ is determined to be positive at 98.3% C.L.

Figure 1

Diagram for the dominant color-suppressed amplitude for ${\overline{B}}^0\to D{\pi }^0$.

Figure 2

$\Delta E$ distributions for the ${\overline{B}}^0$ decays to (a) $D{\pi }^0$, (b) $D\omega$, (c) $D\eta$, and (d) $D^{*}{\pi }^0$, $D^{*}\eta$. Points with error bars represent the data and curves show the results of the fit.

Figure 3

Dalitz plot distribution for the $D{h}^0$ candidates from $B$ signal region (left) and $M_{\mathrm{bc}}$ sideband.

Figure 4

Raw asymmetry distribution for the $D^{(*)}[K_S^0{\rho }^0]h^0$ candidates. The smooth curve is the result of the fit to the full Dalitz plot.