Test of Lepton Flavor Universality by the measurement of the $B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau }$ branching fraction using three-prong $\tau$ decays

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 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 $B^0 \to D^{-}\pi^+\pi^-\pi^+$decayasthenormalizationchannel,theratio${\cal{B}}(B^0 \to D^{-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{-}\pi^+\pi^-\pi^+)$ismeasuredtobe$1.97 \pm 0.13 \pm 0.18$, where the first uncertainty is statistical and the second systematic. An average of branching fraction measurements for the normalization channel is used to derive ${\cal{B}}(B^0 \to D^{-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm 0.054) %$,wherethethirduncertaintyisduetothelimitedknowledgeof${\cal{B}}(B^0\to D^{-}\pi^+\pi^-\pi^+)$. A test of lepton flavor universality is performed using the well-measured branching fraction ${\cal{B}}(B^0 \to D^{-} \mu^+\nu_{\mu})$tocompute${\cal{R}}(D^{-}) = 0.291 \pm 0.019 \pm 0.026 \pm 0.013$, where the third uncertainty originates from the uncertainties on $\mathcal{B}(B^0\to D^{\ast -}{\pi }^{+}{\pi }^{-}{\pi }^{+})$ and ${\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$. This measurement is in agreement with the Standard Model prediction and with previous measurements.