Lepton Flavor Universality test using 'B \to D^{*} \tau \nu_\tau' with '\tau \to 3\pi^{\pm}(\piz)\nu_\tau' decays at LHCb

The Standard Model of Particle Physics predicts that the three charged leptons \Pe, \Pmu, and \Ptau, should have identical electroweak couplings. The only distinction between them arises from their masses, due to their interactions with the Higgs field. However, experiments such as BaBar, Belle, Belle~II and LHCb, have observed deviations from these predictions, particularly in the \btoclnu transitions, known as \textit{charged-current flavor anomalies}. This thesis investigates the \decay{\Bd}{\Dstar \tau \nu} decays, with the \tau lepton being reconstructed from its hadronic decays \decay{\tau}{3\pi \nu (\piz)}. The study aims to measure \rdstar, which is a ratio of the former's decay branching fraction to the \decay{\Bd}{\Dstar \mu \nu} branching fraction. This observable is used for Lepton Flavor Universality test in \btoclnu transitions. By utilizing techniques such as ReDecay for fast simulation, and Multivariate Analyses for signal selection, this analysis builds upon and improves the methods used in previous LHCb measurements: the first analysis~\cite{lhcbcollaborationMeasurementRatioBranching2015a,lhcbcollaborationMeasurementRatioEnsuremath2018} was performed on data collected during the \runone (2011--2012), the second one~\cite{lhcbcollaborationErratumTestLepton2024} on initial stages of data collection during \runtwo (2015--2016). This thesis present for the first time a measurement using the full \runtwo dataset (2015--2018). The precision of the \rdstar measurement is refined, currently achieving approximately \staterr statistical uncertainty. Although the final value is currently \textit{blinded}, pending the estimation of systematical uncertainties and an internal LHCb collaboration review, this thesis presents a comprehensive documentation of the analysis.