Measurement of ratios of branching fractions and $CP$-violating asymmetries of $B^{\pm }\to D^{*}{K}^{\pm }$ decays

We report a study of $B^{\pm }\to D^{*}{K}^{\pm }$ decays with $D^{*}$ decaying to $D{\pi }^0$ or $D\gamma$, using $383\times {10}^6$ $B\overline{B}$ pairs collected at the $\mathit{{\rm Y}}(4S)$ resonance with the BABAR detector at the SLAC PEP-II $B$ Factory. The $D$ meson decays under study include a non-$CP$ mode $(K^{\pm }{\pi }^{\mp })$, $CP$-even modes $(K^{\pm }{K}^{\mp },{\pi }^{\pm }{\pi }^{\mp })$, and $CP$-odd modes $(K_S^0{\pi }^0,K_S^0\varphi ,K_S^0\omega )$. We measure ratios ($R_{CP\pm }^{*}$) of branching fractions of decays to $CP$ eigenmode states and to flavor-specific states as well as $CP$ asymmetries ($A_{CP\pm }^{*}$). These measurements are sensitive to the unitarity triangle angle $\gamma$. We obtain $A_{CP+}^{*}=-0.11\pm 0.09\pm 0.01$, $R_{CP+}^{*}=1.31\pm 0.13\pm 0.04$, and $A_{CP-}^{*}=0.06\pm 0.10\pm 0.02$, $R_{CP-}^{*}=1.10\pm 0.12\pm 0.04$, where the first error is statistical and the second error is systematic. Translating our results into an alternative parametrization, widely used for related measurements, we obtain $x_{+}^{*}=0.11\pm 0.06\pm 0.02$ and $x_{-}^{*}=0.00\pm 0.06\pm 0.02$. No significant $CP$-violating charge asymmetry is found in either the flavor-specific mode $D\to K^{\pm }{\pi }^{\mp }$ or in $B^{\pm }\to D^{*}{\pi }^{\pm }$ decays.

Figure 1

Distributions of $\Delta E_K$ (upper plots) and the PID variable ${\mathcal{T}}_{\mathcal{R}}$ (lower plots) from MC simulations of the categories (from left to right) $D^{*}K$, $D^{*}\pi$, $B_K$, and $B_{\pi }$ (the latter two from $B^{+}{B}^{-}$, $B^0{\overline{B}}^0$, and $q\overline{q}$ MC samples), for the mode $D^{*}\to D{\pi }^0$, $D\to K^{\pm }{\pi }^{\mp }$. In the upper plots, the dots represent the MC sample spectrum, and the curves show the PDFs. Note the vertical log scale in the lower plots.

Figure 2

$\Delta E_K$ distributions, with a cut on the PID variable ${\mathcal{T}}_{\mathcal{R}}>0$ to enhance the kaon part of the sample. Distributions are shown for each of the decays modes: (left panels) $D^{*}\to D{\pi }^0$ and (right panels) $D^{*}\to D\gamma$, with the $D$ decay modes indicated on the left of the figure. Dots denote the distribution of the data. Curves denote the PDFs for the various categories: signal $K$ (long-dashed curve), signal $\pi$ (dotted curve), and background $K$ (short-dashed curve); background $\pi$ does not appear because the ${\mathcal{T}}_{\mathcal{R}}>0$ cut completely removes this category. The thick curve denotes the total PDF.