On the measurement of the unitarity triangle angle $\gamma$ from $B^0\to D{K}^{*0}$ decays

The decay $B^0\to D{K}^{*0}$ is well known to provide excellent potential for a precise measurement of the unitarity triangle angle $\gamma$ in future experiments. It is noted that the sensitivity can be significantly enhanced by studying the amplitudes relative to those of the flavor-specific decay $B^0\to D_2^{*-}{K}^{+}$, which can be achieved by analyzing the $B^0\to D{\pi }^{-}{K}^{+}$ Dalitz plot.

Figure 1

Feynman diagrams for $B^0\to D{K}^{*0}$, via (left) a $\overline{b}\to \overline{c}u\overline{s}$ transition and (right) a $\overline{b}\to c\overline{u}\overline{s}$ transition.

Figure 2

Feynman diagram for the flavor-specific $B^0\to D_2^{*-}{K}^{+}$ decay.

Figure 3

Argand diagrams illustrating the measurements of relative amplitudes and phases from analysis of the Dalitz plots of (left) ${\overline{D}}^0{\pi }^{-}{K}^{+}$ and (right) $D_{CP}{\pi }^{-}{K}^{+}$. In these illustrative examples the following values are used: $|A(B^0\to {\overline{D}}^0{K}^{*0})/A(B^0\to D_2^{*-}{K}^{+})|=1.5$, $\Delta =\arg (A(B^0\to {\overline{D}}^0{K}^{*0})/A(B^0\to D_2^{*-}{K}^{+}))=20°$, $\gamma =75°$, ${\delta }_B=45.0°$ and $r_B=0.4$. These are in line with expectation and current measurements, though $\Delta$ and ${\delta }_B$ are unconstrained at present.