Measurement of the Ratio of the $B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau }$ and $B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu }$ Branching Fractions Using Three-Prong $\tau$-Lepton Decays

The ratio of branching fractions $\mathcal{R}(D^{*-})\equiv \mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu })$ is measured using a data sample of proton-proton collisions collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$. For the first time, $\mathcal{R}(D^{*-})$ is determined using the $\tau$-lepton decays with three charged pions in the final state. The $B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau }$ yield is normalized to that of the $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ mode, providing a measurement of $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})=1.97\pm 0.13\pm 0.18$, where the first uncertainty is statistical and the second systematic. The value of $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })=(1.42\pm 0.094\pm 0.129\pm 0.054)\%$ is obtained, where the third uncertainty is due to the limited knowledge of the branching fraction of the normalization mode. Using the well-measured branching fraction of the $B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu }$ decay, a value of $\mathcal{R}(D^{*-})=0.291\pm 0.019\pm 0.026\pm 0.013$ is established, where the third uncertainty is due to the limited knowledge of the branching fractions of the normalization and $B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu }$ modes. This measurement is in agreement with the standard model prediction and with previous results.

Figure 1

Topology of the signal decay. A requirement on the distance between the $3\pi$ and the $B^0$ vertices along the beam direction to be greater than 4 times its uncertainty is applied. For $B\to D^{*}3\pi (X)$ decays, the $3\pi$ vertex coincides with the $B$ vertex.

Figure 2

Results from the fit to the invariant mass of the $D^{*-}{D}_s^{+}$ pair for the $D^{*-}{D}_s^{+}(X)$ data control sample, with $D_s^{+}\to 3\pi$. The components contributing to the fit model are indicated in the legend.

Figure 3

Distribution of $\min [m({\pi }^{+}{\pi }^{-})]$ for a sample enriched in $B\to D^{*-}{D}_s^{+}(X)$ decays, obtained by requiring the BDT output below a threshold. The different fit components are indicated in the legend.

Figure 4

Distributions of (left) $t_{\tau }$ and (right) $q^2$ in four different BDT bins, with increasing values of the BDT response from top to bottom. The various fit components are described in the legend.