# Measurement of the $B^0 \to D^{*-} \tau^+ \nu_{\tau}$ branching fraction using three-prong $\tau$ decays

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## Abstract

The ratio of branching fractions ${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ 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 3fb$^{-1}$. 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 ${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-}\pi^+\pi^-\pi^+)$ 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 ${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm 0.054) \%$, where the third uncertainty is due to the limited knowledge of ${\cal{B}}(B^0\to D^{*-}\pi^+\pi^-\pi^+)$. A test of lepton flavor universality is performed using the well-measured branching fraction ${\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ to compute ${\cal{R}}(D^{*-}) = 0.291 \pm 0.019 \pm 0.026 \pm 0.013$, where the third uncertainty originates from the uncertainties on ${\cal{B}}(B^0 \to D^{*-}\pi^+\pi^-\pi^+)$ and ${\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$. This measurement is in agreement with the Standard Model prediction and with previous measurements.

## Figures and captions

 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. Fig1.pdf [228 KiB] HiDef png [367 KiB] Thumbnail [50 KiB] *.C file 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. Fig2.pdf [21 KiB] HiDef png [380 KiB] Thumbnail [81 KiB] *.C file Distribution of the $3\pi$ mass for candidates after the detached-vertex requirement. The $D ^+$ and $D ^+_ s$ mass peaks are indicated. Fig3.pdf [14 KiB] HiDef png [246 KiB] Thumbnail [59 KiB] *.C file Distribution of the $K ^- 3\pi$ mass for $D^0$ candidates where a charged kaon has been associated to the 3 $\pi$ vertex. Fig4.pdf [14 KiB] HiDef png [199 KiB] Thumbnail [55 KiB] *.C file Distribution of the $D ^{*-} {3\pi}$ mass (blue) before and (red) after a requirement of finding an energy of at least 8 $\mathrm{\,GeV}$ in the electromagnetic calorimeter around the 3 $\pi$ direction. Fig5.pdf [16 KiB] HiDef png [198 KiB] Thumbnail [66 KiB] *.C file 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. Fig6.pdf [14 KiB] HiDef png [160 KiB] Thumbnail [50 KiB] *.C file Distribution of the $D ^{*-} 3\pi$ mass for candidates passing the selection. Fig7.pdf [14 KiB] HiDef png [164 KiB] Thumbnail [59 KiB] *.C file Difference between the reconstructed and true $q^2$ variables divided by the true $q^2$ , observed in the $B ^0 \!\rightarrow D ^{*-} \tau ^+ \nu _\tau$ simulated signal sample after partial reconstruction. Fig8.pdf [14 KiB] HiDef png [131 KiB] Thumbnail [50 KiB] *.C file Distribution of the reconstructed $3\pi N$ mass observed in a data sample enriched by $B \rightarrow D ^{*-} D ^+_ s (X)$ candidates. Fig9.pdf [16 KiB] HiDef png [132 KiB] Thumbnail [56 KiB] *.C file 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. Fig10a.pdf [16 KiB] HiDef png [168 KiB] Thumbnail [61 KiB] *.C file Fig10b.pdf [15 KiB] HiDef png [189 KiB] Thumbnail [74 KiB] *.C file Fig10c.pdf [16 KiB] HiDef png [182 KiB] Thumbnail [65 KiB] *.C file Fig10d.pdf [17 KiB] HiDef png [236 KiB] Thumbnail [83 KiB] *.C file Distribution of the BDT response on the signal and background simulated samples. Fig11.pdf [16 KiB] HiDef png [173 KiB] Thumbnail [61 KiB] *.C file 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). Fig12.pdf [17 KiB] HiDef png [148 KiB] Thumbnail [55 KiB] *.C file Distributions of (a) ${\mathrm{min}}[m(\pi^+\pi^-)]$, (b) ${\mathrm{max}}[m(\pi^+\pi^-)]$, (c) $m(\pi^+\pi^+)$, (d) $m(\pi^+\pi^-\pi^+)$ for a sample enriched in $B \!\rightarrow D ^{*-} D ^+_ s (X)$ 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. Fig13.pdf [31 KiB] HiDef png [480 KiB] Thumbnail [112 KiB] *.C file Results from the fit to data for candidates containing a $D ^{*-}$ $D ^+_ s$ pair, where $D ^+_ s \rightarrow 3\pi$. 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. Fig14a.pdf [31 KiB] HiDef png [272 KiB] Thumbnail [90 KiB] *.C file Fig14b.pdf [30 KiB] HiDef png [232 KiB] Thumbnail [69 KiB] *.C file Fig14c.pdf [18 KiB] HiDef png [167 KiB] Thumbnail [67 KiB] *.C file Fig14d.pdf [19 KiB] HiDef png [168 KiB] Thumbnail [64 KiB] *.C file Distribution of $q^2$ for candidates in the $B\rightarrow D^{*-}D^0(X)$ control sample, after correcting for the disagreement between data and simulation. Fig15.pdf [17 KiB] HiDef png [239 KiB] Thumbnail [74 KiB] *.C file 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. Fig16a.pdf [16 KiB] HiDef png [155 KiB] Thumbnail [60 KiB] *.C file Fig16b.pdf [14 KiB] HiDef png [99 KiB] Thumbnail [39 KiB] *.C file Fig16c.pdf [14 KiB] HiDef png [90 KiB] Thumbnail [35 KiB] *.C file 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. Fig17.pdf [25 KiB] HiDef png [371 KiB] Thumbnail [126 KiB] *.C file Projection of the fit results on (a) ${\mathrm{min}}[m(\pi^+\pi^-)]$ and (b) $m(D^{*-}3\pi)$ distributions. The fit components are described in the legend. Fig18a.pdf [16 KiB] HiDef png [161 KiB] Thumbnail [62 KiB] *.C file Fig18b.pdf [18 KiB] HiDef png [211 KiB] Thumbnail [77 KiB] *.C file Fit to the $m(D^{*-}3\pi)$ distribution after the full selection in the (a) $\sqrt{s}=7$ TeV and (b) $8$ TeV data samples. Fig19a.pdf [29 KiB] HiDef png [254 KiB] Thumbnail [86 KiB] *.C file Fig19b.pdf [30 KiB] HiDef png [259 KiB] Thumbnail [84 KiB] *.C file (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 $D ^+_ s$ . Fig20a.pdf [18 KiB] HiDef png [162 KiB] Thumbnail [63 KiB] *.C file Fig20b.pdf [19 KiB] HiDef png [232 KiB] Thumbnail [79 KiB] *.C file Animated gif made out of all figures. PAPER-2017-027.gif Thumbnail

## Tables and captions

 List of the selection cuts. See text for further explanation. Table_1.pdf [66 KiB] HiDef png [99 KiB] Thumbnail [16 KiB] tex code Summary of the efficiencies (in %) measured at the various steps of the analysis for simulated samples of the $B ^0 \rightarrow D ^{*-} 3\pi$ channel and the $B ^0$ $\rightarrow$ $D ^{*-}$ $\tau ^+$ $\nu _\tau$ signal channel for both $\tau$ decays to 3 $\pi$ $\overline{\nu } _\tau$ and 3 $\pi$ $\pi ^0$ $\overline{\nu } _\tau$ modes. No requirement on the BDT output is applied for $D ^{*-} 3\pi$ candidates. The relative efficiency designates the individual efficiency of each requirement. Table_2.pdf [47 KiB] HiDef png [92 KiB] Thumbnail [13 KiB] tex code Results of the fit to the $D ^+_ s$ decay model. The relative contribution of each decay and the correction to be applied to the simulation are reported in the second and third columns, respectively. Table_3.pdf [55 KiB] HiDef png [178 KiB] Thumbnail [30 KiB] tex code Relative fractions of the various components obtained from the fit to the $B\rightarrow D^{*-}D_{s}^{+}(X)$ control sample. The values used in the simulation and the ratio of the two are also shown. Table_4.pdf [73 KiB] HiDef png [90 KiB] Thumbnail [15 KiB] tex code Summary of fit components and their corresponding normalization parameters. The first three components correspond to parameters related to the signal. Table_5.pdf [80 KiB] HiDef png [192 KiB] Thumbnail [30 KiB] tex code Fit results for the three-dimensional fit. The constraints on the parameters $f_{D_s^+}$, $f_{D_{s0}^{*+}}$, $f_{D_{s1}^+}$, $f_{D_s^+X}$ and $f_{(D_s^{+}X)_s}$ are applied taking into account their correlations. Table_6.pdf [77 KiB] HiDef png [203 KiB] Thumbnail [32 KiB] tex code List of the individual systematic uncertainties for the measurement of the ratio $\mathcal{B} ( B ^0 \rightarrow D^{*-}\tau^+\nu_{\tau})/\mathcal{B} ( B ^0 \rightarrow D^{*-}3\pi)$. Table_7.pdf [59 KiB] HiDef png [214 KiB] Thumbnail [32 KiB] tex code

Created on 16 February 2019.Citation count from INSPIRE on 21 February 2019.