Lepton Universality measurements in semileptonic decays of $B$-quark hadrons in the LHCb experiment at CERN

Lepton Flavour Universality (LFU) is an assumed symmetry within the Standard Model (SM) that implies that the coupling between gauge bosons and the different leptons does not depend on the flavour (family) of the lepton. In particular, the so-called LFU ratios such as $R(D^{(*)})\equiv\frac{{B}\to D^{(*)}\tau^-\bar{\nu}_\tau}{B\to D^{(*)}\mu^-\bar{\nu}_\mu}$ are being thoroughly measured by different experiments, finding tensions with the SM predictions up to the 3$\sigma$ range. In this thesis, a preliminary simultaneous measurement of the $B^-\to D^{(*)0}\tau^-\bar{\nu}_\tau$ branching fractions and the $R(D^{(*)0})$ LFU ratios is reported, with the decay channels \begin{equation*}\begin{aligned} D^{*0}&\to D^0 \{\pi^0,\gamma\},\\ D^0&\to K^-\pi^+,\\ \tau^-&\to\pi^-\pi^+\pi^-(\pi^0)\nu_\tau. \end{aligned}\end{equation*} This work is done with LHCb Run 2 data corresponding to $pp$ collisions at a centre-of-mass energy of 13 TeV from the years 2016–2018, with an integrated luminosity of $5.4 \text{ fb}^{-1}$. The obtained results, with blinded values, are \begin{equation*}\begin{aligned} \mathcal{B}(B^-\to D^{0}\tau^-\bar{\nu}_\tau) &= (\text{xxx} \pm 0.13 \text{ (stat.)} \pm 0.22 \text{ (syst.)} \pm 0.07 \text{ (ext.)}) \times 10^{-2}~, \\ \mathcal{B}(B^-\to D^{*0}\tau^-\bar{\nu}_\tau) &= (\text{xxx} \pm 0.11 \text{ (stat.)}\ {}_{-0.14}^{+0.15} \text{ (syst.)} \pm 0.15 \text{ (ext.)}) \times 10^{-2}~, \end{aligned}\end{equation*} for the branching fractions, and \begin{equation*}\begin{aligned} R(D^0) &= \text{xxx} \pm 0.056 \text{ (stat.)} \pm 0.096 \text{ (syst.)} \pm 0.034 \text{ (ext.)}~,\\ R(D^{*0}) &= \text{xxx} \pm 0.020 \text{ (stat.)}\pm 0.026 \text{ (syst.)} \pm 0.029 \text{ (ext.)}~, \end{aligned}\end{equation*} for the LFU ratios. In addition, the base work for a complementary and analogous measurement of the $R(D^{(*)-})$ ratios and $B^0\to D^{(*)-}\tau^+\nu_\tau$ branching fractions, with $\tau^-\to\pi^-\pi^+\pi^-(\pi^0)\nu_\tau$ and $D^-\to K^-\pi^+\pi^+$, is laid out, including the production of simulation samples, the selection of events, and the study of the relevant control samples.