Tests of Lepton Flavour Universality with semileptonic $D$ and $B$ decays at the LHCb experiment

In The Standard Model of particle physics (SM), the coupling between the leptons and the gauge bosons is independent of the lepton generation. This SM feature is called Lepton Flavour Universality (LFU) and finding processes that violate it could be a sign of new physics (NP). Recent experimental results on LFU tests with $b \to c\ell\nu_\ell$ and $b \to s\ell\ell$ transitions show a tension from the theoretical predictions. This thesis aims to test LFU by studying two different processes involving D and B meson decays and using data recorded by the LHCb experiment. The LHCb experiment is dedicated to perform heavy flavour physics measurements and it is an excellent place to search for indirect evidences of NP. The LHCb experiment collected data from proton-proton collisions in two runs, Run 1 (2010-2012) and Run 2 (2015-2018). The combination of the two data samples corresponds to an integrated luminosity of 9 fb$^{−1}$. The LHCb Upgrade I detector started to take data in 2022, aiming to record an integrated luminosity of 50 fb$^{−1}$ (300 fb$^{−1}$) by the end of 2030 (2040). It is programmed to run at an instantaneous luminosity of $2 × 10^{33} \textrm{cm}^{2} \textrm{s}^{−1}$, implying a higher multiplicity of inelastic pp collisions. The LHCb Upgrade I features a fully software-based trigger system, making software development and trigger line migration crucial. In this thesis, aiming to optimise LFU studies in $H_b \to H_c\tau^+ \nu_\tau$ decays, where the $\tau$ lepton is reconstructed by its $\tau^+ \to \pi^+\pi^- \pi^+ \overline{\nu}_\tau$ decay and $H_b (H_c)$ is a $b-(c-)$ hadron, trigger lines for these processes are implemented. The goal of the first LFU test is to measure the branching fraction ratio$R_{\mu/e}$ , defined as $R_{\mu/e} = \mathcal{B} (D^0 \to K^- ,\mu^+ \nu_{\mu}) / \mathcal{B} (D^0 \to K^- ,e^+ \nu_{e})$ . $D^0$ candidates are selected from $D^{∗+} \to D^0 \mu^+$ decays and the undetected neutrino is accounted for using two reconstruction methods. The value of $R_{\mu/e}$ is obtained as the ratio of the signal $ D^0 \to K^−\ell^+ \nu_{\ell}$ decays multiplied by their respective efficiencies. The value of $R_{\mu/e}$ is blinded, resultingin $x.xxx \pm 0.003 \pm 0.013$, where the first uncertainty is due to statistics and the second contribution is an estimation of the systematic uncertainty. The second study aims to test LFU considering $B^- \to D^{(*)0}\tau^- \overline{\nu}_\tau$ decays, where the $\tau$ is reconstructed using $\tau^+ \to \pi^+\pi^- \pi^+ \overline{\nu}_\tau$. The observables sensitive to LFU $R(D^0)$ and $R(D^{∗0})$, defined as $R(D^{(∗)0}) = \mathcal{B}(B^− \to D^{(∗)0}\tau^- \overline{\nu}_\tau)/ \mathcal{B} (B^− \to D^{(∗)0}\ell^- \overline{\nu}_\tau)$, are measured simultaneously. To select signal candidates, it is of paramount importance to model the main background contributions. These are due to doubly-charmed decays, $B \to DDX$, where a $D^+_s$, a $D^+$ or a $D^0$ meson decays inclusively into 3 pions. In this thesis, a model to control inclusive $D^+_s \to \pi^+\pi^- \pi^+ (X)$ decays is implemented. This is a reweighting procedure to correct the simulation accounting for the main $D^+_s \to \pi^+\pi^- \pi^+ (X)$ decay modes. The relative branching fractions obtained from the model agree with the PDG [1] within uncertainties. Finally, the blinded results for $R(D^0)$ and $R(D^{∗0})$ respectively $x.xx \pm 0.093\pm 0.034$ % and $x.xx\pm0.024\pm0.029$%, where the first contribution to the uncertainty is due to statistics and the second is the systematic uncertainty. This thesis is structured as follows. The introduction is reported in Ch. 1. The hypotheses are reported in detail in Ch. 2, which reports the theoretical principles, and in Ch. 3, which reports the current experimental status. The objectives, methodology and results of the thesis are addressed in the specific sections of the analyses chapters, Ch. 5 and 6. For the $D^0 \to K^- \ell^+ \tau_\ell$ analysis the objectives and methodology are reported in Sec. 5.1 and the results are reported in Sec. 5.9, while for the $R(D^{(∗)0})$ the objectives and methodology are in Sec. 6.1 and the results in Sec. 6.11. Besides, the description of the LHCb detector and how its data are recorded is reported in Ch. 4. The LHCb Upgrade I detector description and the trigger selection for the upgrade are reported in Ch. 7. Finally, the thesis conclusions are reported in Ch. 8 and the the- sis summary in Galician in Appendix C. All the abbreviations and acronyms used throughout this thesis are listed after the lists of figures and tables. Finally, at the end of the document the bibliography is reported.