Measurement of an excess of $\overline{B}\to D^{\mathbf{(}*\mathbf{)}}{\tau }^{\mathbf{-}}{\overline{\nu }}_{\tau }$ decays and implications for charged Higgs bosons

Based on the full BABAR data sample, we report improved measurements of the ratios $\mathcal{R}(D)=\mathcal{B}(\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}(\overline{B}\to D{\ell }^{-}{\overline{\nu }}_{\ell })$ and $\mathcal{R}(D^{*})=\mathcal{B}(\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}(\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })$, where $\ell$ refers to either an electron or muon. These ratios are sensitive to new physics contributions in the form of a charged Higgs boson. We measure $\mathcal{R}(D)=0.440\pm 0.058\pm 0.042$ and $\mathcal{R}(D^{*})=0.332\pm 0.024\pm 0.018$, which exceed the standard model expectations by $2.0\sigma$ and $2.7\sigma$, respectively. Taken together, the results disagree with these expectations at the $3.4\sigma$ level. This excess cannot be explained by a charged Higgs boson in the type II two-Higgs-doublet model. Kinematic distributions presented here exclude large portions of the more general type III two-Higgs-doublet model, but there are solutions within this model compatible with the results.

Figure 1

Parton level diagram for $\overline{B}\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }$ decays. The gluon lines illustrate the QCD interactions that affect the hadronic part of the amplitude.

Figure 2

Predicted $q^2$ spectra for (a) $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$ and $\overline{B}\to D{\ell }^{-}{\overline{\nu }}_{\ell }$ decays for $V_1(1)V_{cb}=0.0427$ and (b) $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ and $\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays for $h_{A_1}(1)V_{cb}=0.0359$ [4].

Figure 3

Predicted $q^2$ distributions for (a) $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$ and (b) $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ decays for different values of $\tan \beta /m_{H^{\pm }}$. All curves are normalized to unit area.

Figure 4

Input variables for the BDT selector trained on the $D^{*0}\ell$ sample. Histograms are normalized to 1000 entries.

Figure 5

Comparison of data control samples (data points) with MC simulated samples (histograms) of the $|{\mathit{p}}_{\ell }^{*}|$ distributions for (a) off-peak data prior to $|{\mathit{p}}_{\ell }^{*}|$ reweighting, (b) the intermediate $E_{\mathrm{extra}}$ sample prior to $|{\mathit{p}}_{\ell }^{*}|$ reweighting, and (c) the intermediate $E_{\mathrm{extra}}$ sample after $|{\mathit{p}}_{\ell }^{*}|$ reweighting; (d) the $E_{\mathrm{extra}}$ distribution for the combinatorial background; and the $m_{\mathrm{ES}}$ distributions for (e) the intermediate $E_{\mathrm{extra}}$ sample, and (f) the low $E_{\mathrm{extra}}$ sample. The results are shown for the four $D^{(*)}\ell$ samples combined.

Figure 6

Projections of the simulated $m_{\mathrm{miss}}^2$ and $|{\mathit{p}}_{\ell }^{*}|$ distributions and the PDFs for the following contributions to the $D^0\ell$ sample: (a), (b) $D^0\tau \nu$; (c), (d) $D^0\ell \nu$; (e), (f) $D^{*0}\ell \nu$; (g), (h) $D^{**}(\ell /\tau )\nu$, and (i), (j) $B\overline{B}$ background. The light and dark blue (gray) bands mark the $1\sigma$ and $2\sigma$ envelopes of the variations of the PDF projections due to their statistical uncertainty.

Figure 7

Comparison of the $m_{\mathrm{miss}}^2$ and $|{\mathit{p}}_{\ell }^{*}|$ distributions of the $D^{(*)}\ell$ samples (data points) with the projections of the results of the isospin-unconstrained fit (stacked colored distributions). The $|{\mathit{p}}_{\ell }^{*}|$ distributions show the normalization-enriched region with $m_{\mathrm{miss}}^2<1{\mathrm{GeV}}^2$, thus excluding most of the signal events in these samples.

Figure 8

Comparison of the $m_{\mathrm{miss}}^2$ and $|{\mathit{p}}_{\ell }^{*}|$ distributions of the $D^{(*)}\ell$ samples (data points) with the projections of the results of the isospin-unconstrained fit (stacked colored distributions). The region above the dashed line of the background component corresponds to $B\overline{B}$ background and the region below corresponds to continuum. The peak at $m_{\mathrm{miss}}^2=0$ in the background component is due to charge cross-feed events. The $|{\mathit{p}}_{\ell }^{*}|$ distributions show the signal-enriched region with $m_{\mathrm{miss}}^2\ge 1{\mathrm{GeV}}^2$, thus excluding most of the normalization events in these samples.

Figure 9

Comparison of the $m_{\mathrm{miss}}^2$ and $|{\mathit{p}}_{\ell }^{*}|$ distributions of the $D^{(*)}{\pi }^0\ell$ samples (data points) with the projections of the results of the isospin-unconstrained fit (stacked colored distributions). The region above the dashed line of the background component corresponds to $B\overline{B}$ background and the region below corresponds to continuum.

Figure 10

Pion momentum in the laboratory from $B\to D^{*+}\ell \nu$ and $B\to D^{*+}\tau \nu$ decays: (a) $D^{*+}\to D^0{\pi }^{+}$, and (b) $D^{*+}\to D^{+}{\pi }^0$ decays. Histograms are normalized to 1000 entries.

Figure 11

Measurements of $\mathcal{R}(D)$ and $\mathcal{R}(D^{*})$ for different data subsamples. Top: for four run periods with statistical uncertainties only. Bottom: for electrons and muons with statistical and uncorrelated systematic uncertainties. The vertical bands labeled “SM” and “All data” mark the SM predictions and the results of the fits to the whole data sample, respectively.

Figure 12

Measurements of $\mathcal{R}(D)$ and $\mathcal{R}(D^{*})$ for different BDT requirements, impacting the signal/background ratio. The horizontal bands mark the $\mathcal{R}(D)$ and $\mathcal{R}(D^{*})$ results for the isospin-constrained fit to the nominal (100%) sample. The data points represent the results of the fits for $B^{+}$ and $B^0$ mesons with their statistical uncertainties.

Figure 13

Likelihood scan for the two signal yields compared to a parabola. The dashed lines indicate the number of standard deviations ($n_{\sigma }$) away from the fit result.

Figure 14

Histograms: $\mathcal{R}(D^{(*)})$ distributions resulting from 1000 variations of $f_{D^{**}}$. Solid curves: Gaussian fits to the $\mathcal{R}(D^{(*)})$ distributions.

Figure 15

$E_{\mathrm{extra}}$ distributions for events with $m_{\mathrm{miss}}^2>1.5{\mathrm{GeV}}^2$ scaled to the results of the isospin-unconstrained (first two columns) and isospin-constrained (last column) fits. The region above the dashed line of the background component corresponds to $B\overline{B}$ background and the region below corresponds to continuum. In the third column, the $B^0$ and $B^{+}$ samples are combined, and the normalization and background events are subtracted.

Figure 16

$m_{\mathrm{ES}}$ distributions before (left) and after (center) subtraction of normalization of background events, and lepton momentum distributions after this subtraction (right) for events with $m_{\mathrm{miss}}^2>1.5{\mathrm{GeV}}^2$ scaled to the results of the isospin-constrained fit. The $B^0$ and $B^{+}$ samples are combined. See Fig. 15 for a legend.

Figure 17

Representation of ${\chi }^2$ [Eq. (33)] in the $\mathcal{R}(D)\mathrm{\text{−}}\mathcal{R}(D^{*})$ plane. The white cross corresponds to the measured $\mathcal{R}(D^{(*)})$, and the black cross to the SM predictions. The shaded bands represent one standard deviation each.

Figure 18

$m_{\mathrm{miss}}^2$ and $|{\mathit{p}}_{\ell }^{*}|$ projections of the $D^0\tau \nu \Rightarrow D^0\ell$ PDF for various values of $\tan \beta /m_{H^{\pm }}$.

Figure 19

Left: Variation of the $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$ (top) and $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ (bottom) efficiency in the 2HDM with respect to the SM efficiency. The band indicates the increase on statistical uncertainty with respect to the SM value. Right: Variation of the fitted $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$ (top) and $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ (bottom) yields as a function of $\tan \beta /m_{H^{\pm }}$. The band indicates the statistical uncertainty of the fit.

Figure 20

Comparison of the results of this analysis (light band, blue) with predictions that include a charged Higgs boson of type II 2HDM (dark band, red). The widths of the two bands represent the uncertainties. The SM corresponds to $\tan \beta /m_{H^{\pm }}=0$.

Figure 21

Level of disagreement between this measurement of $\mathcal{R}(D^{(*)})$ and the type II 2HDM predictions for all values in the $\tan \beta \mathrm{\text{−}}{m}_{H^{\pm }}$ parameter space.

Figure 22

Favored regions for real values of the type III 2HDM parameters $S_R$ and $S_L$ given by the measured values of $\mathcal{R}(D^{(*)})$. The bottom two solutions are excluded by the measured $q^2$ spectra.

Figure 23

Efficiency corrected $q^2$ distributions for $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$ (top) and $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ (bottom) events with $m_{\mathrm{miss}}^2>1.5{\mathrm{GeV}}^2$ scaled to the results of the isospin-constrained fit. Left: SM. Center: $\tan \beta /m_{H^{\pm }}=0.30{\mathrm{GeV}}^{-1}$. Right: $\tan \beta /m_{H^{\pm }}=0.45{\mathrm{GeV}}^{-1}$. The points and the shaded histograms correspond to the measured and expected distributions, respectively. The $B^0$ and $B^{+}$ samples are combined and the normalization and background events are subtracted. The distributions are normalized to the number of detected events. The uncertainty on the data points includes the statistical uncertainties of data and simulation. The values of ${\chi }^2$ are based on this uncertainty.

Figure 24

Comparison of the previous measurements of $\mathcal{R}(D^{(*)})$ with statistical and total uncertainties (Table 10) with this measurement (BABAR 2012). The vertical bands represent the average of the previous measurements (light shading) and SM predictions (dark shading), separately for $\mathcal{R}(D)$ and $\mathcal{R}(D^{*})$. The widths of the bands represents the uncertainties.

Figure 25

Assessment of the uncertainties on the $q^2$ distributions of background events with $m_{\mathrm{miss}}^2>1.5{\mathrm{GeV}}^2$. Left: results of the isospin-constrained fit for the SM. Center: sample with $0.5<E_{\mathrm{extra}}<1.2\mathrm{GeV}$ and $5.27<m_{\mathrm{ES}}<5.29\mathrm{GeV}$. Right: sample satisfying the BDT requirements in the $5.20<m_{\mathrm{ES}}<5.26\mathrm{GeV}$ region. The data/MC plots show a fourth order polynomial fit and the total systematic uncertainty considered. The simulation in the control samples is normalized to the number of events in data. See Fig. 15 for a legend.

Figure 26

Left: $q^2$ distributions for the different $\overline{B}\to D^{**}({\tau }^{-}/{\ell }^{-})\overline{\nu }$ contributions, all normalized to 100 events. Center: $q^2$ distributions for events with $m_{\mathrm{miss}}^2<1.5{\mathrm{GeV}}^2$ scaled to the results of the isospin-constrained fit for the SM. See Fig. 15 for a legend. Right: $q^2$ dependence of the efficiency. The scale for the efficiency of the normalization decays is chosen so that the maximum value is 1. The efficiency data for the signal are adjusted so that they overlap with the data for normalization decays in the central part of the $q^2$ range. The signal efficiencies with and without the $m_{\mathrm{miss}}^2$ selection have the same scale.