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The ratio of branching fractions ${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \toD^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ is measuredusing a data sample of proton-proton collisions collected with the LHCbdetector at center-of-mass energies of 7 and 8 Tev, corresponding to anintegrated luminosity of 3$~$fb$^{-1}$. For the first time ${\cal{R}}(D^{*-})$is determined using the $\tau$ lepton decays with three charged pions in thefinal state. The $B^0 \to D^{*-} \tau^+\nu_{\tau}$ yield is normalized to thatof the $B^0\to D^{*-} \pi^+\pi^-\pi^+$ mode, providing a measurement of${\cal{B}}(B^0\to D^{*-}\tau^+\nu_{\tau})/{\cal{B}}(B^0\toD^{*-}\pi^+\pi^-\pi^+) = 1.97 \pm 0.13 \pm 0.18$, where the first uncertaintyis statistical and the second systematic. The value of ${\cal{B}}(B^0 \toD^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm 0.054)\% $ isobtained, where the third uncertainty is due to the limited knowledge of thebranching fraction of the normalization mode. Using the well-measured branchingfraction 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, wherethe third uncertainty is due to the limited knowledge of the branchingfractions of the normalization and $B^0\to D^{*-}\mu^+\nu_{\mu}$ modes. Thismeasurement is in agreement with the Standard Model prediction and withprevious results.

physical review letters

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