Test of lepton flavor universality by the measurement of the $B^0\to {D^{*}}^{-}{\tau }^{+}{\nu }_{\tau }$ branching fraction using three-prong $\tau$ 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 $3{\mathrm{fb}}^{-1}$. The $\tau$ lepton is reconstructed with three charged pions in the final state. A novel method is used that exploits the different vertex topologies of signal and backgrounds to isolate samples of semitauonic decays of $b$ hadrons with high purity. Using the $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ decay as the normalization channel, the ratio $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})$ is measured to be $1.97\pm 0.13\pm 0.18$, where the first uncertainty is statistical and the second systematic. An average of branching fraction measurements for the normalization channel is used to derive $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })=(1.42\pm 0.094\pm 0.129\pm 0.054)\%$, where the third uncertainty is due to the limited knowledge of $\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})$. A test of lepton flavor universality is performed using the well-measured branching fraction $\mathcal{B}(B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu })$ to compute $\mathcal{R}(D^{*-})=0.291\pm 0.019\pm 0.026\pm 0.013$, where the third uncertainty originates from the uncertainties on $\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})$ and $\mathcal{B}(B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu })$. This measurement is in agreement with the Standard Model prediction and with previous measurements.

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 four times its uncertainty is applied.

Figure 2

Distribution of the distance between the $B^0$ vertex and the $3\pi$ vertex along the beam direction, divided by its uncertainty, obtained using simulation. The vertical line shows the $4\sigma$ requirement used in the analysis to reject the prompt background component.

Figure 3

Distribution of the $3\pi$ mass for candidates after the detached-vertex requirement. The $D^{+}$ and $D_s^{+}$ mass peaks are indicated.

Figure 4

Distribution of the $K^{-}3\pi$ mass for $D^0$ candidates where a charged kaon has been associated to the $3\pi$ vertex.

Figure 5

Distribution of the $D^{*-}3\pi$ mass (blue) before and (red) after a requirement of finding an energy of at least 8 GeV in the electromagnetic calorimeter around the $3\pi$ direction.

Figure 6

Distribution of the $K^{-}$ ${\pi }^{+}$ ${\pi }^{+}$ mass for $D^{+}$ candidates passing the signal selection, where the negative pion has been identified as a kaon and assigned the kaon mass.

Figure 7

Distribution of the $D^{*-}3\pi$ mass for candidates passing the selection.

Figure 8

Difference between the reconstructed and true $q^2$ variables divided by the true $q^2$, observed in the $B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau }$ simulated signal sample after partial reconstruction.

Figure 9

Distribution of the reconstructed $3\pi N$ mass observed in a data sample enriched by $B\to D^{*-}{D}_s^{+}(X)$ candidates.

Figure 10

Normalized distributions of (a) $\min [m({\pi }^{+}{\pi }^{-})]$, (b) $\max [m({\pi }^{+}{\pi }^{-})]$, (c) approximated neutrino momentum reconstructed in the signal hypothesis, and (d) the $D^{*-}3\pi$ mass in simulated samples.

Figure 11

Distribution of the BDT response on the signal and background simulated samples.

Figure 12

Composition of an inclusive simulated sample where a $D^{*-}$ and a $3\pi$ system have been produced in the decay chain of a $b$ $\overline{b}$ pair from a $pp$ collision. Each bin shows the fractional contribution of the different possible parents of the $3\pi$ system (blue from a $B^0$, yellow for other $b$ hadrons): from signal; directly from the $b$ hadron (prompt); from a charm parent $D_s^{+}$, $D^0$, or $D^{+}$ meson; $3\pi$ from a $B$ and the $D^0$ from the other $B$ ($B1B2$); from $\tau$ lepton following a $D_s^{+}$ decay; from a $\tau$ lepton following a $D^{**}{\tau }^{+}{\nu }_{\tau }$ decay ($D^{**}$ denotes here any higher excitation of $D$ mesons). (Top) After the initial selection and the removal of spurious $3\pi$ candidates. (Middle) For candidates entering the signal fit. (Bottom) For candidates populating the last 3 bins of the BDT distribution (cf. Fig. 16).

Figure 13

Distributions of (a) $\min [m({\pi }^{+}{\pi }^{-})]$, (b) $\max [m({\pi }^{+}{\pi }^{-})]$, (c) $m({\pi }^{+}{\pi }^{+})$, (d) $m({\pi }^{+}{\pi }^{-}{\pi }^{+})$ for a sample enriched in $B\to D^{*-}{D}_s^{+}(X)$ decays, obtained by requiring the BDT output below a certain threshold. The different fit components correspond to $D_s^{+}$ decays with (red) $\eta$ or (green) ${\eta }^{\prime }$ in the final state, (yellow) all the other considered $D_s^{+}$ decays, and (blue) backgrounds originating from decays not involving the $D_s^{+}$ meson.

Figure 14

Results from the fit to data for candidates containing a $D^{*-}$ $D_s^{+}$ pair, where $D_s^{+}\to 3\pi$. The fit components are described in the legend. The figures correspond to the fit projection on (a) $m(D^{*-}3\pi )$, (b) $q^2$, (c) $3\pi$ decay time $t_{\tau }$ and (d) BDT output distributions.

Figure 15

Distribution of $q^2$ for candidates in the $B\to D^{*-}{D}^0(X)$ control sample, after correcting for the disagreement between data and simulation.

Figure 16

Projections of the three-dimensional fit on the (a) $3\pi$ decay time, (b) $q^2$ and (c) BDT output distributions. The fit components are described in the legend.

Figure 17

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

Figure 18

Projection of the fit results on (a) $\min [m({\pi }^{+}{\pi }^{-})]$ and (b) $m(D^{*-}3\pi )$ distributions. The fit components are described in the legend.

Figure 19

Fit to the $m(D^{*-}3\pi )$ distribution after the full selection in the (a) $\sqrt{s}=7\mathrm{TeV}$ and (b) 8 TeV data samples.

Figure 20

(a) Distribution of $m(3\pi )$ after selection, requiring $m(D^{*-}3\pi )$ to be between 5200 and $5350\mathrm{MeV}/c^2$; (b) fit in the mass region around the $D_s^{+}$.