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 protonproton collisions collected with the LHCb detector at centerofmass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3$ $fb$^{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 ${\cal{B}}(B^0 \to D^{*} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*}\pi^+\pi^\pi^+)$ 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 wellmeasured 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.
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. 
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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. 
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Distribution of the $3\pi$ mass for candidates after the detachedvertex requirement. The $ D ^+$ and $ D ^+_ s $ mass peaks are indicated. 
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Distribution of the $ K ^ 3\pi$ mass for $D^0$ candidates where a charged kaon has been associated to the 3 $\pi $ vertex. 
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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. 
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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. 
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Distribution of the $ D ^{*} 3\pi$ mass for candidates passing the selection. 
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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. 
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Distribution of the reconstructed $3\pi N$ mass observed in a data sample enriched by $ B \rightarrow D ^{*} D ^+_ s (X)$ candidates. 
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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. 
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Distribution of the BDT response on the signal and background simulated samples. 
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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). 
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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. 
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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. 
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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. 
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Projections of the threedimensional fit on the (a) $3\pi$ decay time, (b) $q^2$ and (c) BDT output distributions. The fit components are described in the legend. 
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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. 
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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. 
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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. 
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(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 $ . 
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Animated gif made out of all figures. 
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List of the selection cuts. See text for further explanation. 
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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. 
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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. 
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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. 
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Summary of fit components and their corresponding normalization parameters. The first three components correspond to parameters related to the signal. 
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Fit results for the threedimensional 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. 
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List of the individual systematic uncertainties for the measurement of the ratio $\mathcal{B} ( B ^0 \rightarrow D^{*}\tau^+\nu_{\tau})/\mathcal{B} ( B ^0 \rightarrow D^{*}3\pi)$. 
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Created on 09 December 2018.Citation count from INSPIRE on 09 December 2018.