Test of Lepton Flavour Universality using the $B^0 \to D^{*-} \tau^+ \nu_\tau$ decays at LHCb

This thesis presents the measurement of the $R$($D$$^{*}$) $\equiv$ $\frac{B(B^0 \to D^{*-} \tau^{+}\nu_\tau}{B(B^0 \to D^{*-} \mu^{+}\nu_\mu}$ ratio with 2 fb$^{-1}$ of $pp$ collisions collected at $\sqrt s=13 \text{TeV}$ by LHCb during 2015-2016 using 3-prong tau decays. The study comprises a test of the Lepton Flavour Universality in $b$ $\to$ $c$$\ell$$\nu$$_{\ell}$ decays to help resolve the tension between the Standard Model $R(D^*)$ estimation and the experimental results from the B-factories and LHCb. The analysis builds upon a previous LHCb measurement with a new dataset and improved techniques. Most importantly, a novel fast simulation technique, ReDecay, is used to generate large simulated samples and Multivariate Analysis techniques are exploited in signal selection. Since the analysis has yet to undergo an internal LHCb review, and several systematic uncertainties must be computed, the $R(D^*)$ value is blinded. Nonetheless, nearly complete documentation of the analysis is presented in this thesis. The current relative statistical uncertainty on the $R(D^*)$ is 5.56 %.