Measurement of the ration of the $B^0\rightarrow D^{*-} \tau^+ \nu_\tau$ and $B^0 \rightarrow D^{*-} \mu^+ \nu_\mu$ branching fractions using thee-prong $\tau$ decays.

Lepton universality, described in the Standard Model (SM), predicts equal coupling between gauge bosons and the three lepton families. SM extensions give additional interactions, implying in some cases a stronger coupling with the third generation of leptons. Semileptonic decays of b-hadrons provide a sensitive probe to such New Physics effects. The presence of additional particles, required by such SM extensions, can have significant effect on the semileptonic decay rate of the $B^0\rightarrow D^{*-} \tau^+ \nu_\tau$ decay. New physics effects can be revealed in measurements of the ratios: $R(D^{*-}) = \frac{\mathcal{B}(B^0 \rightarrow D^{*-} \tau^+ \nu_\tau)} {\mathcal{B}(B^0 \rightarrow D^{*-} \mu^+ \nu_\mu)}$ and $R(D^-) = \frac{\mathcal{B}(B^0 \rightarrow D^{-} \tau^+ \nu_\tau)}{\mathcal{B}(B^0 \rightarrow D^{-} \mu^+ \nu_\mu)}$, where experimental and theoretical uncertainties cancel at first order. The combination of experimental measurements performed by BaBar, Belle and LHCb in the channel where the $\tau$ decays in leptons, gives a deviation from the SM prediction of about 4 standard deviations. It is therefore important to perform additional measurements in this sector in order to improve the precision and confirm or disprove this deviation. This thesis reports a measurement performed on LHCb data using the channel where the semileptonic $\tau$ decays in 3 pions. A novel method is used which exploits the different vertex topologies of signal and backgrounds to isolate samples of semitauonic decays of \textit{b} hadrons with unprecedented purity. A measurement of $R(D^{*-})= 0.286 \pm 0.019 \pm 0.025 \pm 0.021$ is obtained, where the first uncertainty is statistical, the second systematic and the third originates from the uncertainty of the normalization modes. This measurement is in agreement with the SM prediction and with the previous measurements.