Measurement ofϕ3with a Dalitz plot analysis ofB+→D(*)K(*)+decay

We present a measurement of the unitarity triangle angle ${\varphi }_3$ using a Dalitz plot analysis of the $K_S^0{\pi }^{+}{\pi }^{-}$ decay of the neutral $D$ meson from the $B^{\pm }\to D^{(*)}{K}^{(*)\pm }$ process. The method exploits the interference between $D^0$ and ${\overline{D}}^0$ to extract the angle ${\varphi }_3$, strong phase $\delta$ and the ratio $r$ of suppressed and allowed amplitudes. We apply this method to a $357{\mathrm{fb}}^{-1}$ data sample collected by the Belle experiment. The analysis uses three modes: $B^{+}\to D{K}^{+}$, $B^{+}\to D^{*}{K}^{+}$ with $D^{*}\to D{\pi }^0$, and $B^{+}\to D{K}^{*+}$ with $K^{*+}\to K_S^0{\pi }^{+}$, as well as the corresponding charge-conjugate modes. From a combined maximum likelihood fit to the three modes, we obtain ${\varphi }_3=53°\genfrac{}{}{0ex}{}{+15°}{-18°}(\mathrm{stat})\pm 3°(\mathrm{syst})\pm 9°(\mathrm{\text{model}})$. The corresponding 2 standard deviation interval is $8°<{\varphi }_3<111°$.