Measurement of the branching ratio of $\overline{B}\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }$ relative to $\overline{B}\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays with hadronic tagging at Belle

We report a measurement of the branching fraction ratios $R(D^{(*)})$ of $\overline{B}\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }$ relative to $\overline{B}\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$ (where $\ell =e$ or $\mu$) using the full Belle data sample of $772\times {10}^{6}B\overline{B}$ pairs collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The measured values are $R(D)=0.375\pm 0.064(\text{stat})\pm 0.026(\text{syst})$ and $R(D^{*})=0.293\pm 0.038(\text{stat})\pm 0.015(\text{syst})$. The analysis uses hadronic reconstruction of the tag-side $B$ meson and purely leptonic $\tau$ decays. The results are consistent with earlier measurements and do not show a significant deviation from the standard model prediction.

Figure 1

Fit projections and data points with statistical uncertainties in the $D^{+}{\ell }^{-}$ (top) and $D^0{\ell }^{-}$ (bottom) data samples. Left: $M_{\text{miss}}^2$ distribution for $M_{\text{miss}}^2<0.85{\mathrm{GeV}}^2/c^4$; right: $o_{\mathrm{NB}}^{\prime }$ distribution for $M_{\text{miss}}^2>0.85{\mathrm{GeV}}^2/c^4$.

Figure 2

Fit projections and data points with statistical uncertainties in the $D^{*+}{\ell }^{-}$ (top) and $D^{*0}{\ell }^{-}$ (bottom) data samples. Left: $M_{\text{miss}}^2$ distribution for $M_{\text{miss}}^2<0.85{\mathrm{GeV}}^2/c^4$; right: $o_{\mathrm{NB}}^{\prime }$ distribution for $M_{\text{miss}}^2>0.85{\mathrm{GeV}}^2/c^4$.

Figure 3

Projections of the fit results and data points with statistical uncertainties for the high $M_{\text{miss}}^2$ region. Top left: $D^{+}{\ell }^{-}$; top right: $D^{*+}{\ell }^{-}$; bottom left: $D^0{\ell }^{-}$; bottom right: $D^{*0}{\ell }^{-}$.

Figure 4

Projections of the fit results and data points with statistical uncertainties in a signal-enhanced region of $M_{\text{miss}}^2>2.0{\mathrm{GeV}}^2/c^4$ in the $E_{\mathrm{ECL}}$ dimension. Top left: $D^{+}{\ell }^{-}$; top right: $D^{*+}{\ell }^{-}$; bottom left: $D^0{\ell }^{-}$; bottom right: $D^{*0}{\ell }^{-}$.

Figure 5

Projections of the fit results and data points with statistical uncertainties in a signal-enhanced region of $M_{\text{miss}}^2>2.0{\mathrm{GeV}}^2/c^4$ in the $p_{\ell }^{*}$ dimension. Top left: $D^{+}{\ell }^{-}$; top right: $D^{*+}{\ell }^{-}$; bottom left: $D^0{\ell }^{-}$; bottom right: $D^{*0}{\ell }^{-}$.

Figure 6

Exclusion level of $R(D)-R(D^{*})$ value assumptions in standard deviations, systematic uncertainties included.

Figure 7

Theoretical predictions with $1\sigma$ error ranges for $R(D)$ (red) and $R(D^{*})$ (blue) for different values of $\tan \beta /m_{H^{+}}$ in the 2HDM of type II. The fit results for $\tan \beta /m_{H^{+}}=0.5c^2/\mathrm{GeV}$ and SM are shown with their $1\sigma$ ranges as red and blue bars with arbitrary width for better visibility.

Figure 8

Background-subtracted $q^2$ distributions of the $\tau$ signal in the region of $M_{\text{miss}}^2>0.85{\mathrm{GeV}}^2/c^4$. The distributions are efficiency corrected and normalized to the fitted yield. The error bars show the statistical uncertainties. The histogram is the respective expected distribution from signal MC. Left: Standard Model result, right: Type-II 2HDM result with $\tan \beta /m_{H^{+}}=0.5c^2/\mathrm{GeV}$, top: $\overline{B}\to D{\tau }^{-}{\overline{\nu }}_{\tau }$, bottom: $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$