Search for $b\to u$ transitions in $B^{-}\to D{K}^{-}$ and $D^{*}{K}^{-}$ decays

We report results from an updated study of the suppressed decays $B^{-}\to D{K}^{-}$ and $B^{-}\to D^{*}{K}^{-}$ followed by $D\to K^{+}{\pi }^{-}$, where $D^{(*)}$ indicates a $D^{(*)0}$ or a ${\overline{D}}^{(*)0}$ meson, and $D^{*}\to D{\pi }^0$ or $D^{*}\to D\gamma$. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity triangle angle $\gamma$ due to interference between the $b\to c$ transition $B^{-}\to D^{(*)0}{K}^{-}$ followed by the doubly Cabibbo-suppressed decay $D^0\to K^{+}{\pi }^{-}$, and the $b\to u$ transition $B^{-}\to {\overline{D}}^{(*)0}{K}^{-}$ followed by the Cabibbo-favored decay ${\overline{D}}^0\to K^{+}{\pi }^{-}$. We also report an analysis of the decay $B^{-}\to D^{(*)}{\pi }^{-}$ with the $D$ decaying into the doubly Cabibbo-suppressed mode $D\to K^{+}{\pi }^{-}$. Our results are based on $467\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at SLAC. We measure the ratios ${\mathcal{R}}^{(*)}$ of the suppressed ($[K^{+}{\pi }^{-}{]}_D{K}^{-}/{\pi }^{-}$) to favored ($[K^{-}{\pi }^{+}{]}_D{K}^{-}/{\pi }^{-}$) branching fractions as well as the $CP$ asymmetries ${\mathcal{A}}^{(*)}$ of those modes. We see indications of signals for the $B^{-}\to D{K}^{-}$ and $B^{-}\to D_{D{\pi }^0}^{*}{K}^{-}$ suppressed modes, with statistical significances of 2.1 and $2.2\sigma$, respectively, and we measure: ${\mathcal{R}}_{DK}=(1.1\pm 0.6\pm 0.2)\times {10}^{-2},{\mathcal{A}}_{DK}=-0.86\pm {0.47}_{-0.16}^{+0.12}$, ${\mathcal{R}}_{(D{\pi }^0)K}^{*}=(1.8\pm 0.9\pm 0.4)\times {10}^{-2},{\mathcal{A}}_{(D{\pi }^0)K}^{*}=+0.77\pm 0.35\pm 0.12,{\mathcal{R}}_{(D\gamma )K}^{*}=(1.3\pm 1.4\pm 0.8)\times {10}^{-2},{\mathcal{A}}_{(D\gamma )K}^{*}=+0.36\pm {0.94}_{-0.41}^{+0.25}$, where the first uncertainty is statistical and the second is systematic. We use a frequentist approach to obtain the magnitude of the ratio $r_B\equiv |A(B^{-}\to {\overline{D}}^0{K}^{-})/A(B^{-}\to D^0{K}^{-})|=({9.5}_{-4.1}^{+5.1})\%$, with $r_B<16.7\%$ at 90% confidence level. In the case of $B^{-}\to D^{*}{K}^{-}$ we find $r_B^{*}\equiv |A(B^{-}\to {\overline{D}}^{*0}{K}^{-})/A(B^{-}\to D^{*0}{K}^{-})|=({9.6}_{-5.1}^{+3.5})\%$, with $r_B^{*}<15.0\%$ at 90% confidence level.

Figure 1

Feynman diagrams for $B^{-}\to D^{(*)0}{K}^{(*)-}$ and ${\overline{D}}^{(*)0}{K}^{(*)-}$. The latter is CKM and color-suppressed with respect to the former.

Figure 2

Signal and background distributions of the neural network output, and results of the $NN$ verifications for $DK$ (a), $D^{(*)}K$ (b, c), $D\pi$ (d) and $D^{(*)}\pi$ (e, f) candidates. (a, d): $D{h}^{\pm }$ right-sign candidates, signal-enriched by a cut on the $\Delta E$, $m_{\mathrm{ES}}$ signal region. Shaded plain histograms are MC expectations for $q\overline{q}$ background (dark gray/blue), $b\overline{b}$ background (middle gray/green) and $B^{\pm }\to D{h}^{\pm }$ signal events (light gray/yellow). Points with error bars are on-peak data. (b, e): $D^{(*)}{h}^{\pm }$ wrong-sign background. (c, f): $D^{(*)}{h}^{\pm }$ right-sign background. Plots b, c, e, and f are normalized to unity. The dotted line histograms show the distribution of simulated continuum events. The off-peak data used to check the $NN$ are overlaid as data points. To increase the statistics, the $m_{\mathrm{ES}}$ and $\Delta E$ requirements on the off-peak and continuum MC events have been relaxed, and $D{h}^{\pm }$ and $D^{*}{h}^{\pm }$ contributions have been summed.

Figure 3

Projections on $m_{\mathrm{ES}}$ (a, b, c) and $NN$ (d, e, f) of the fit results for $D\pi$ (a, d), $D_{D{\pi }^0}^{*}\pi$ (b, e) and $D_{D\gamma }^{*}\pi$ (c, f) RS decays, for samples enriched in signal with the requirements $NN>0.94$ ($m_{\mathrm{ES}}$ projections) or $5.2725<m_{\mathrm{ES}}<5.2875\mathrm{GeV}/c^2$ ($NN$ projections). The points with error bars are data. The curves represent the fit projections for signal plus background (solid) and background (dashed).

Figure 4

Projections on $m_{\mathrm{ES}}$ (a, b, c) and $NN$ (d, e, f) of the fit results for $D\pi$ (a, d), $D_{D{\pi }^0}^{*}\pi$ (b, e) and $D_{D\gamma }^{*}\pi$ (c, f) WS decays, for samples enriched in signal with the requirements $NN>0.94$ ($m_{\mathrm{ES}}$ projections) or $5.2725<m_{\mathrm{ES}}<5.2875\mathrm{GeV}/c^2$ ($NN$ projections). The curves represent the fit projections for signal plus background (solid), the sum of all background components (dashed), and $q\overline{q}$ background only (dotted).

Figure 5

Projections on $m_{\mathrm{ES}}$ (a, b, c) and $NN$ (d, e, f) of the fit results for $DK$ (a, d), $D_{D{\pi }^0}^{*}K$ (b, e) and $D_{D\gamma }^{*}K$ (c, f) RS decays, for samples enriched in signal with the requirements $NN>0.94$ ($m_{\mathrm{ES}}$ projections) or $5.2725<m_{\mathrm{ES}}<5.2875\mathrm{GeV}/c^2$ ($NN$ projections). The points with error bars are data. The curves represent the fit projections for signal plus background (solid) and background (dashed).

Figure 6

Projections on $m_{\mathrm{ES}}$ (a, b, c) and $NN$ (d, e, f) of the fit results for $DK$ (a, d), $D_{D{\pi }^0}^{*}K$ (d, e) and $D_{D\gamma }^{*}K$ (c, f) WS decays, for samples enriched in signal with the requirements $NN>0.94$ ($m_{\mathrm{ES}}$ projections) or $5.2725<m_{\mathrm{ES}}<5.2875\mathrm{GeV}/c^2$ ($NN$ projections). The points with error bars are data. The curves represent the fit projections for signal plus background (solid), the sum of all background components (dashed), and $q\overline{q}$ background only (dotted).

Figure 7

Negative log-likelihood variation vs ${\mathcal{R}}_{DK}^{(*)}$ for $B^{\pm }\to D{K}^{\pm }$ (left), $B^{\pm }\to D_{D{\pi }^0}^{*}{K}^{\pm }$ (center) and $B^{\pm }\to D_{D\gamma }^{*}{K}^{\pm }$ (right). Systematic uncertainties are not included.

Figure 8

Projections on $m_{\mathrm{ES}}$ (a, b, c) and $NN$ (d, e, f) of the fit results for $D{K}^{+}$ (a, d), $D_{D{\pi }^0}^{*}{K}^{+}$ (b, e) and $D_{D\gamma }^{*}{K}^{+}$ (c, f) WS decays, for samples enriched in signal with the requirements $NN>0.94$ ($m_{\mathrm{ES}}$ projections) or $5.2725<m_{\mathrm{ES}}<5.2875\mathrm{GeV}/c^2$ ($NN$ projections). The points with error bars are data. The curves represent the fit projections for signal plus background (solid), the sum of all background components (dashed), and $q\overline{q}$ background only (dotted).

Figure 9

Projections on $m_{\mathrm{ES}}$ (a, b, c) and $NN$ (d, e, f) of the fit results for $D{K}^{-}$ (a, d), $D_{D{\pi }^0}^{*}{K}^{-}$ (b, e) and $D_{D\gamma }^{*}{K}^{-}$ (c, f) WS decays, for samples enriched in signal with the requirements $NN>0.94$ ($m_{\mathrm{ES}}$ projections) or $5.2725<m_{\mathrm{ES}}<5.2875\mathrm{GeV}/c^2$ ($NN$ projections). The points with error bars are data. The curves represent the fit projections for signal plus background (solid), the sum of all background components (dashed), and $q\overline{q}$ background only (dotted).

Figure 10

Constraints on $r_B^{(*)}$ from the combined $B^{-}\to [K\pi {]}_{D^{(*)}}{K}^{-}$ ADS measurements. The solid (dotted) curve shows the 1 minus the confidence level to exclude the abscissa value as a function of $r_B^{(*)}$. The horizontal lines show the exclusion limits at the 1 and 2 standard deviation levels.

Figure 11

One minus confidence level isocontours on $\gamma$ vs ${\delta }_B$ from the $B^{-}\to [K\pi {]}_D{K}^{-}$ ADS measurement.

Figure 12

One minus confidence level isocontours on $\gamma$ vs ${\delta }_B^{*}$ from the combined $B^{-}\to [K\pi {]}_{D^{*}}{K}^{-}$ ADS measurements.

Figure 13

Constraints on $\gamma$ from the combined $B^{-}\to D^{(*)}[K^{+}{\pi }^{-}]K^{-}$ ADS measurements. The solid curve shows the (1-C.L.) to exclude the abscissa value. The horizontal lines show the exclusion limits at the 1 and 2 standard deviation levels.