Probing Lepton Flavour Universality through semitauonic $\Lambda_b^0$ decays using three-pions $\tau$-lepton decays with the LHCb experiment at CERN

Probing Lepton Flavour Universality has been recently a very promising topic to test for the presence of New Physics contributions in Standard Model processes. Measurements involving semitauonic decays are interesting as potential New Physics couplings to the $\tau$-lepton could be enhanced with respect to the two other leptons due to its mass. Experimental measurements of $B\rightarrow D^*\tau\nu$ and $B\rightarrow D\tau\nu$ branching fractions are currently in tension with theoretical predictions at the 3.78$\sigma$ level. Both precise measurements and analyses of new channels are thus required to understand the source of this disagreement. The work presented in this thesis describes the use of a new technique to reconstruct $\tau$-lepton using its decay into three pions and its use to measure ratios of branching fractions for two decays $B\rightarrow D^*\tau\nu$ and $\Lambda_b^0\rightarrow \Lambda_c\tau\nu$ with respect to the same decays involving a muon, these ratios are referred to as $\mathcal{R}(D^*)$ and $\mathcal{R}(\Lambda_c)$. Using the 3 fb$^{-1}$ of proton-proton collisions recorded by the LHCb detector during the LHC Run1 at a centre-of-mass energy of 7 and 8 TeV, $\mathcal{R}(D^*)$ was measured using the three-pions reconstruction for the $\tau$ to be $R(D^{*-}) = 0.291 \pm 0.019(stat) \pm 0.026(syst) \pm 0.013(ext)$ This result is compatible with the Standard Model expectation at the 1$\sigma$ level and is consistent with previous measurements. Its precision is able to slightly enforce the disagreement between the combination of the measurements with the theoretical prediction. The same dataset is also analysed in this thesis to study the $\Lambda_b^0\rightarrow \Lambda_c\tau\nu$ decay which is observed for the first time with a significance of 5.7$\sigma$. Both statistical and systematic uncertainties were estimated and $\mathcal{R}(\Lambda_c)$ can then be expressed as $\mathcal{R}(\Lambda_c) = X\times(1 \pm 0.105(stat) \pm 0.162(syst) \pm 0.12(ext))$ with its central value remaining blind at the moment.