Search for $b\to u$ transitions in $B^{-}\to D^0{K}^{-}$ and $B^{-}\to D^{*0}{K}^{-}$

We search for $B^{-}\to {\tilde{D}}^0{K}^{-}$ and $B^{-}\to {\tilde{D}}^{*0}{K}^{-}$ and charge conjugates. Here the symbol ${\tilde{D}}^0$ indicates decay of a $D^0$ or ${\overline{D}}^0$ into $K^{+}{\pi }^{-}$, while the symbol ${\tilde{D}}^{*0}$ indicates decay of a $D^{*0}$ or ${\overline{D}}^{*0}$ to ${\tilde{D}}^0{\pi }^0$ or ${\tilde{D}}^0\gamma$. These final states can be reached through the $b\to c$ transition $B^{-}\to D^{(*)0}{K}^{-}$ followed by the doubly Cabibbo-Kobayashi-Maskawa (CKM)-suppressed $D^0\to K^{+}{\pi }^{-}$, or the $b\to u$ transition $B^{-}\to {\overline{D}}^{(*)0}{K}^{-}$ followed by the CKM-favored ${\overline{D}}^0\to K^{+}{\pi }^{-}$. The interference of these two amplitudes is sensitive to the angle $\gamma$ of the unitarity triangle. Our results are based on $232\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at SLAC. We find no significant evidence for these decays. We set a limit $r_B\equiv |A(B^{-}\to {\overline{D}}^0{K}^{-})/A(B^{-}\to D^0{K}^{-})|<0.23$ at 90% C.L. using the most conservative assumptions on the values of the CKM angle $\gamma$ and the strong phases in the $B$ and $D$ decay amplitudes. In the case of the $D^{*}$ we set a 90% C.L. limit $r_B^{*2}\equiv |A(B^{-}\to {\overline{D}}^{*0}{K}^{-})/A(B^{-}\to D^{*0}{K}^{-}){|}^2<(0.16{)}^2$ which is independent of assumptions on $\gamma$ and strong phases.

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. The CKM-suppression factor is $|V_{ub}{V}_{cs}^{*}/V_{cb}{V}_{us}^{*}|\approx 0.4$. The naive color-suppression factor is $\frac{1}{3}$.

Figure 2

Distributions of the continuum suppression neural network ($NN$ and $N{N}^{\prime }$) outputs for the three modes. (a), (b), and (c) show the expected distribution from signal events. The dashed line histogram shows the distribution of simulated signal events and the histogram with error bars shows the distribution of $D^{(*)0}\pi$ control sample events with background subtracted using the $m_{\mathrm{ES}}$ sideband ($5.20\mathrm{GeV}<m_{\mathrm{ES}}<5.27\mathrm{GeV}$). (d), (e), and (f) show the expected distribution for continuum background events. The dashed line histogram shows the distribution of simulated continuum events and the histogram with errors shows the distribution of off-resonance events. The $m_{\mathrm{ES}}$ and $\Delta E$ requirements on the off-resonance and continuum Monte Carlo events have been kept loose to increase the statistics. Each Monte Carlo histogram is normalized to the area of the corresponding data histogram.

Figure 3

$\Delta E$ distributions for normalization events ($DK$ and $D^{*}K$) with $m_{\mathrm{ES}}$ within $3\sigma$ of $m_B$ with the fit model overlaid. (a) $DK$ events. (b) $D^{*}K$ events with $D^{*}\to D{\pi }^0$. (c) $D^{*}K$ events with $D^{*}\to D\gamma$. The dashed (dot-dashed) lines are the contributions from $D\pi$ or $D^{*}\pi$ ($DK$ or $D^{*}K$) events. The dotted lines are the contributions from other backgrounds, and the solid line is the total.

Figure 4

$m_{\mathrm{ES}}$ distributions for normalization events ($DK$ and $D^{*}K$) with $\Delta E$ in the signal region with the fit model overlaid. (a) $DK$ events. (b) $D^{*}K$ events with $D^{*}\to D{\pi }^0$. (c) $D^{*}K$ events with $D^{*}\to D\gamma$. The dashed lines represent the backgrounds; these are mostly from $D\pi$ or $D^{*}\pi$, and also peak at the $B$ mass. As explained in the text, the size of the $D\pi$ and $D^{*}\pi$ backgrounds is constrained by the simultaneous fits to the distributions of Fig. 3.

Figure 5

$m_{\mathrm{ES}}$ distributions for $\overline{D}K$ and ${\overline{D}}^{*}K$ events with $K\pi$ mass in a sideband of the reconstructed $D$ mass and with $\Delta E$ in the signal region. These events are used to constrain the size of possible peaking backgrounds from charmless $B$-meson decays, i.e., decays without a $D$ in the final state. The fit model is overlaid. (a) $\overline{D}K$ events. (b) ${\overline{D}}^{*}K$ events with $D^{*}\to D{\pi }^0$. (c) ${\overline{D}}^{*}K$ events with $D^{*}\to D\gamma$. Note that the $K\pi$ mass range in the sideband selection is a factor of 2.7 larger than in the signal selection.

Figure 6

$m_{\mathrm{ES}}$ distributions for candidate signal events with the fit model overlaid. (a) $\overline{D}K$ events. (b) ${\overline{D}}^{*}K$ events with $D^{*}\to D{\pi }^0$. (c) ${\overline{D}}^{*}K$ events with $D^{*}\to D\gamma$.

Figure 7

Likelihood functions as obtained from the fit described in the text for ${\mathcal{R}}_{K\pi ,D{\pi }^0}^{*}$ (solid line) and ${\mathcal{R}}_{K\pi ,D\gamma }^{*}$ (dashed line).

Figure 8

Probability distribution function (arbitrary units) for $r_B^{*2}$ obtained as described in the text. The integral of the function for $0<r_B^{*2}<(0.16{)}^2$ is nine-tenths of the integral for $r_B^{*2}>0$. The vertical dashed line is drawn at $r_B^{*2}=(0.16{)}^2$.

Figure 9

Likelihood function (arbitrary units) for ${\mathcal{R}}_{K\pi }$ as extracted from the fit described in the text. The integral of the likelihood function for $0<{\mathcal{R}}_{K\pi }<0.029$ is nine-tenths of the integral for ${\mathcal{R}}_{K\pi }>0$. The vertical dashed line is drawn at ${\mathcal{R}}_{K\pi }=0.029$.

Figure 10

Expectations for ${\mathcal{R}}_{K\pi }$ and the number of signal events vs $r_B$. Dark filled-in area: allowed region for any value of $\delta$, with a $\pm 1\sigma$ variation on $r_D$, and $51°<\gamma <66°$. Hatched area: additional allowed region with no constraint on $\gamma$. Note that the uncertainty on $r_D$ has a very small effect on the size of the allowed regions. The horizontal line represents the 90% C.L. limit ${\mathcal{R}}_{K\pi }<0.029$. The vertical dashed lines are drawn at $r_B=0.203$ and $r_B=0.233$. They represent the 90% C.L. upper limits on $r_B$ with and without the constraint on $\gamma$. The light filled-in area represents the 68% C.L. region corresponding to ${\mathcal{R}}_{K\pi }=0.013{\pm }_{0.009}^{0.011}$.