Measurement of the semileptonic decays $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$ and $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$

We present measurements of the semileptonic decays $B^{-}\to D^0{\tau }^{-}{\overline{\nu }}_{\tau }$, $B^{-}\to D^{*0}{\tau }^{-}{\overline{\nu }}_{\tau }$, ${\overline{B}}^0\to D^{+}{\tau }^{-}{\overline{\nu }}_{\tau }$, and ${\overline{B}}^0\to D^{*+}{\tau }^{-}{\overline{\nu }}_{\tau }$, which are sensitive to non-standard model amplitudes in certain scenarios. The data sample consists of $232\times {10}^6{\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ collider. We select events with a $D$ or $D^{*}$ meson and a light lepton ($\ell =e$ or $\mu$) recoiling against a fully reconstructed $B$ meson. We perform a fit to the joint distribution of lepton momentum and missing mass squared to distinguish signal $\overline{B}\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }({\tau }^{-}\to {\ell }^{-}{\overline{\nu }}_{\ell }{\nu }_{\tau })$ events from the backgrounds, predominantly $\overline{B}\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$. We measure the branching-fraction ratios $R(D)\equiv \mathcal{B}(\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}(\overline{B}\to D{\ell }^{-}{\overline{\nu }}_{\ell })$ and $R(D^{*})\equiv \mathcal{B}(\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}(\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })$ and, from a combined fit to $B^{-}$ and ${\overline{B}}^0$ channels, obtain the results $R(D)=(41.6\pm 11.7\pm 5.2)\%$ and $R(D^{*})=(29.7\pm 5.6\pm 1.8)\%$, where the uncertainties are statistical and systematic. Normalizing to measured $B^{-}\to D^{(*)0}{\ell }^{-}{\overline{\nu }}_{\ell }$ branching fractions, we obtain $\mathcal{B}(\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau })=(0.86\pm 0.24\pm 0.11\pm 0.06)\%$ and $\mathcal{B}(\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau })=(1.62\pm 0.31\pm 0.10\pm 0.05)\%$, where the additional third uncertainty is from the normalization mode. We also present, for the first time, distributions of the lepton momentum, $|{\mathbf{p}}_{\ell }^{*}|$, and the squared momentum transfer, $q^2$.

Figure 1

Generated $q^2$ distributions for (a) $\overline{B}\to D{\ell }^{-}{\overline{\nu }}_{\ell }$ and $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$; (b) $\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell }$ and $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$. The two curves in each plot show $q^2$ for the light lepton (dashed line) and for the $\tau$ (solid line). All distributions use the CLN form factor model with experimentally measured shape parameters. The distributions are normalized to equal areas.

Figure 2

Generated lepton energy distributions for (a) $\overline{B}\to D{\ell }^{-}{\overline{\nu }}_{\ell }$ and $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$; (b) $\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell }$ and $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$. The three curves in each plot show the ${\ell }^{-}$ energy in $\overline{B}\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$ (dashed line), the ${\tau }^{-}$ energy in $\overline{B}\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }$ (solid line), and the secondary lepton energy in $\overline{B}\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }$ (dotted line), all defined in the $B$ meson rest frame. All distributions use the CLN form factor model with experimentally measured shape parameters. The distributions are normalized to equal areas.

Figure 3

Generated $m_{\mathrm{miss}}^2$ distributions for (a) $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$ and (b) $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$. Both distributions use the CLN form factor model with experimentally measured shape parameters.

Figure 4

Distributions of $m_{\mathrm{ES}}$ in selected events. (a) shows all $B_{\mathrm{tag}}$ candidates reconstructed in $20{\mathrm{fb}}^{-1}$ of data, and the purity of this plot has been increased by requiring $|\Delta \mathrm{E}|<50\mathrm{MeV}$. (b) shows the distribution for the complete data sample after the signal $B$ and total-event selection requirements. Note the substantial improvement in purity due to the complete reconstruction.

Figure 5

Distributions of $E_{\mathrm{extra}}$ in simulated events, shown after all event selection except the cut on $E_{\mathrm{extra}}$ itself. Signal $\overline{B}\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }$ events are shown as points, while $\overline{B}\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$ normalization events are shown as the histogram. The gap between the $E_{\mathrm{extra}}=0$ bin and the remainder of the distribution corresponds to the minimum allowed photon energy, 50 MeV, while the bump at 100 MeV is due to events with two minimum-energy photons. The normalization is arbitrary. The agreement between the two distributions indicates that the efficiency of a cut on $E_{\mathrm{extra}}$ will cancel when we measure the branching-fraction ratio.

Figure 6

Distributions of $|{\mathbf{p}}_{\ell }^{*}|$ versus $m_{\mathrm{miss}}^2$ for selected data events in the four signal channels. The structures seen here can be compared to the distributions from simulation seen in Fig. 7 and described in the text.

Figure 7

Distributions of $|{\mathbf{p}}_{\ell }^{*}|$ versus $m_{\mathrm{miss}}^2$ for several MC samples after all event selection. Red (light grey) regions indicate relatively high density of reconstructed events, while blue (dark grey) indicate relatively low density. Shown are (a) $D^0{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^0{\ell }^{-}$, (b) $D^{*0}{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^0{\ell }^{-}$, (c) $D^0{\tau }^{-}{\overline{\nu }}_{\tau }\Rightarrow D^0{\ell }^{-}$, (d) $D^{*0}{\tau }^{-}{\overline{\nu }}_{\tau }\Rightarrow D^0{\ell }^{-}$, (e) $D^{**}{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^0{\ell }^{-}$, (f) $D^0{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^{*0}{\ell }^{-}$, (g) $D^{*0}{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^{*0}{\ell }^{-}$, (h) $D^{*0}{\tau }^{-}{\overline{\nu }}_{\tau }\Rightarrow D^{*0}{\ell }^{-}$, (i) $D^{**}{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^{*0}{\ell }^{-}$, (j) charge-cross feed reconstructed in the $D^0{\ell }^{-}$ and $D^{+}{\ell }^{-}$ channels, (k) charge-cross feed reconstructed in the $D^{*0}{\ell }^{-}$ and $D^{*+}{\ell }^{-}$ channels, and (l) combinatorial background in the four $D^{(*)}{\ell }^{-}$ channels. The reconstruction channel notation $\Rightarrow$ and the features of these distributions are discussed in the text.

Figure 8

Kinematic control sample plots: (a) $|{\mathbf{p}}_{\ell }^{*}|$; (b) $q^2$; (c) $|{\mathbf{p}}_{\mathrm{miss}}|$; (d) $m_{\mathrm{miss}}^2$; (e) $E_{\mathrm{extra}}$; (f) $m_{\mathrm{miss}}^2$ in the $D^{*}$ channels, assuming that the soft $\pi /\gamma$ had been lost; multiplicity of (g) charged tracks and (h) neutral clusters used to reconstruct the $B_{\mathrm{tag}}$. In all plots, the points with error bars are the data and the solid histogram is the simulation, scaled to the data luminosity. Good agreement is seen between data and simulation in a variety of variables corresponding to reconstruction, kinematics, and hermeticity requirements. Small differences between data and simulation cancel in the relative measurement and have no detrimental effect on the analysis. The large steps in (a) and (b) are due to the combination of two control samples, as described in the text. The structure in (g) is caused by the larger efficiency to reconstruct charged $B_{\mathrm{tag}}$ candidates—with an odd number of charged tracks—than neutral candidates, while the prominent even-odd structure in (h) is due to the fact that most neutral clusters correspond to the process ${\pi }^0\to \gamma \gamma$ and so appear in pairs.

Figure 9

Projections of the PDF from fits to MC samples. The left plots show projections onto $m_{\mathrm{miss}}^2$, while the right plots show projections onto $|{\mathbf{p}}_{\ell }^{*}|$. Shown are projections for four of the PDFs used in the fit: (a) $D^{*0}{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^{*0}{\ell }^{-}$, (b) $D^{*0}{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^0{\ell }^{-}$, (c) $D^{*0}{\tau }^{-}{\overline{\nu }}_{\tau }\Rightarrow D^{*0}{\ell }^{-}$, and (d) $D^{**}{\ell }^{-}{\overline{\nu }}_{\ell }\Rightarrow D^{*0}{\ell }^{-}$. The MC sample is shown as points, and the projection of the fit is shown as a curve. Note the sharp peak at $m_{\mathrm{miss}}^2=0$ in (a), while the peak in (b) is somewhat spread out and shifted to larger values of $m_{\mathrm{miss}}^2$ because of the lost ${\pi }^0$ or $\gamma$ from $D^{*0}$ decay.

Figure 10

Distributions of events and fit projections in $m_{\mathrm{miss}}^2$ for the four final states: $D^{*0}{\ell }^{-}$, $D^0{\ell }^{-}$, $D^{*+}{\ell }^{-}$, and $D^{+}{\ell }^{-}$. The normalization region $m_{\mathrm{miss}}^2\approx 0$ is shown with finer binning in the insets. The fit components are combinatorial background (white, below dashed line), charge-cross feed background (white, above dashed line), the $\overline{B}\to D{\ell }^{-}{\overline{\nu }}_{\ell }$ normalization mode (forward slanted hatching, yellow), the $\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell }$ normalization mode (backward slanted hatching, light blue), $\overline{B}\to D^{**}{\ell }^{-}{\overline{\nu }}_{\ell }$ background (dark, or blue), the $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$ signal (light grey, green), and the $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ signal (medium grey, magenta). The fit shown incorporates the $B^{-}-{\overline{B}}^0$ constraints.

Figure 11

Distributions of events and fit projections in $|{\mathbf{p}}_{\ell }^{*}|$ for the four final states $D^{*0}{\ell }^{-}$, $D^0{\ell }^{-}$, $D^{*+}{\ell }^{-}$, and $D^{+}{\ell }^{-}$, shown in the normalization region, $m_{\mathrm{miss}}^2<1(\mathrm{GeV}/c^2{)}^2$. The fit components are shaded as in Fig. 10.

Figure 12

Distributions of events and fit projections in $|{\mathbf{p}}_{\ell }^{*}|$ for the four final states $D^{*0}{\ell }^{-}$, $D^0{\ell }^{-}$, $D^{*+}{\ell }^{-}$, and $D^{+}{\ell }^{-}$, shown in the signal region, $m_{\mathrm{miss}}^2>1(\mathrm{GeV}/c^2{)}^2$. The fit components are shaded as in Fig. 10.

Figure 13

Distributions of events and fit projections in $m_{\mathrm{miss}}^2$ for the four $D^{**}$ control samples $D^{*0}{\pi }^0{\ell }^{-}$, $D^0{\pi }^0{\ell }^{-}$, $D^{*+}{\pi }^0{\ell }^{-}$, and $D^{+}{\pi }^0{\ell }^{-}$. The fit components are shaded as in Fig. 10.

Figure 14

Distributions of events and fit projections in $|{\mathbf{p}}_{\ell }^{*}|$ for the four $D^{**}$ control samples $D^{*0}{\pi }^0{\ell }^{-}$, $D^0{\pi }^0{\ell }^{-}$, $D^{*+}{\pi }^0{\ell }^{-}$, and $D^{+}{\pi }^0{\ell }^{-}$. The fit components are shaded as in Fig. 10.

Figure 15

Distributions of fit results for systematic uncertainties due to Monte Carlo statistics, shown for (a) $B^{-}\to D^0{\tau }^{-}{\overline{\nu }}_{\tau }$, (b) $B^{-}\to D^{*0}{\tau }^{-}{\overline{\nu }}_{\tau }$, (c) ${\overline{B}}^0\to D^{+}{\tau }^{-}{\overline{\nu }}_{\tau }$, (d) ${\overline{B}}^0\to D^{*+}{\tau }^{-}{\overline{\nu }}_{\tau }$, (e) $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$, and (f) $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$. In all figures, the branching-fraction ratio $R$ is shown.

Figure 16

Combinatorial background modeling variation for the four signal channels, showing the projections onto (a) $m_{\mathrm{miss}}^2$, and (b) $|{\mathbf{p}}_{\ell }^{*}|$. In both figures, the MC sample without reweighting is shown as data points, while the light and dark shaded regions show the $1\sigma$ and $2\sigma$ envelopes of the ensemble of reweighted PDF shapes.

Figure 17

$q^2$ distributions of events in the four final states $D^{*0}{\ell }^{-}$, $D^0{\ell }^{-}$, $D^{*+}{\ell }^{-}$, and $D^{+}{\ell }^{-}$, shown in the normalization region, $m_{\mathrm{miss}}^2<1(\mathrm{GeV}/c^2{)}^2$. The data are shown as points with error bars. The shaded histograms are taken from MC samples with normalizations from the fit to data. The components are shaded as in Fig. 10.

Figure 18

$q^2$ distributions of events in the four final states $D^{*0}{\ell }^{-}$, $D^0{\ell }^{-}$, $D^{*+}{\ell }^{-}$, and $D^{+}{\ell }^{-}$, shown in the signal region, $m_{\mathrm{miss}}^2>1(\mathrm{GeV}/c^2{)}^2$. The data are shown as points with error bars. The shaded histograms are taken from MC samples with normalizations from the fit to data. The components are shaded as in Fig. 10.

Figure 19

Distribution of $-\log \mathcal{L}$ from simulated experiments, showing (a) the unconstrained fit and (b) the $B^{-}-{\overline{B}}^0$ constrained fit. The observed values of $-\log \mathcal{L}$ in the fit to data are indicated with arrows. The fraction of experiments with $-\log \mathcal{L}$ larger than the observed value is used to estimate the goodness of fit.