# 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

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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$^{-1}$. For the first time ${\cal{R}}(D^{*-})$ 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 ${\cal{B}}(B^0\to D^{*-}\tau^+\nu_{\tau})/{\cal{B}}(B^0\to D^{*-}\pi^+\pi^-\pi^+) = 1.97 \pm 0.13 \pm 0.18$, where the first uncertainty is statistical and the second systematic. The value of ${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm 0.054)\%$ 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 ${\cal{R}}(D^{*-}) = 0.291 \pm 0.019 \pm 0.026 \pm 0.013$ 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.

## 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. For $B \rightarrow D ^* 3\pi (X)$ decays, the 3 $\pi$ vertex coincides with the $B$ vertex. Fig1.pdf [228 KiB] HiDef png [367 KiB] Thumbnail [151 KiB] *.C file % {Results from the fit to the invariant mass of the $D ^{*-}$ $D ^+_ s$ pair for the $D ^{*-} D ^+_ s (X)$ data control sample, with $D ^+_ s \rightarrow 3\pi$. The components contributing to the fit model are indicated in the legend. } Fig2.pdf [30 KiB] HiDef png [263 KiB] Thumbnail [227 KiB] *.C file Distribution of ${\mathrm{min}}[m(\pi^+\pi^-)]$ for a sample enriched in $B \rightarrow D ^{*-} D ^+_ s (X)$ decays, obtained by requiring the BDT output below a threshold. The different fit components are indicated in the legend. Fig3.pdf [16 KiB] HiDef png [199 KiB] Thumbnail [161 KiB] *.C file % 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. Fig4.pdf [25 KiB] HiDef png [392 KiB] Thumbnail [338 KiB] *.C file Animated gif made out of all figures. PAPER-2017-017.gif Thumbnail

## Tables and captions

 Relative systematic uncertainties on ${\cal{R}}( D ^{*-} )$. Table_1.pdf [56 KiB] HiDef png [85 KiB] Thumbnail [39 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [538 KiB] This ZIP file contains supplemetary material for the publication LHCb-PAPER-2017-017. The files are: supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in variuous formats Fig1a.pdf [228 KiB] HiDef png [367 KiB] Thumbnail [151 KiB] *C file Fig1b.pdf [190 KiB] HiDef png [307 KiB] Thumbnail [127 KiB] *C file Fig2a.pdf [29 KiB] HiDef png [254 KiB] Thumbnail [215 KiB] *C file Fig2b.pdf [30 KiB] HiDef png [258 KiB] Thumbnail [213 KiB] *C file Fig3.pdf [18 KiB] HiDef png [609 KiB] Thumbnail [322 KiB] *C file

Created on 17 August 2019.Citation count from INSPIRE on 23 August 2019.