Branching fraction measurement of $\Lambda_{b}^{0} \rightarrow J/\psi \Lambda$

In this thesis, the first measurement of the branching fraction $\mathcal{B}(\Lambda_{b}^{0}\rightarrow J/\psi\Lambda)$ at the LHC is presented. The measurement uses the full Run 2 proton-proton data collected with the LHCb detector at $\sqrt{s}$ = 13 TeV. Using the decay $B^0\rightarrow J/\psi K^{0}_{S}$ as a normalisation channel, the measurement is reported to be $\mathcal{B}(\Lambda_{b}^{0}\rightarrow J/\psi\Lambda) = (2.67 \pm 0.03 \text{ (stat.)} \pm 0.20\text{ (external syst.)})\times 10^{-4}$, excluding experimental systematic uncertainties. This is the most precise measurement to date with an uncertainty improved by more than a factor three compared to previous estimations. The improved precision on $\mathcal{B}(\Lambda_{b}^{0}\rightarrow J/\psi\Lambda)$ will significantly reduce the uncertainties for the measurement of the branching fraction $\mathcal{B}(\Lambda_b^0\rightarrow\Lambda \mu^+ \mu^-)$ and search for the Lepton Flavour Violating decay $\mathcal{B}(\Lambda^0_b\rightarrow\Lambda e^{\pm}\mu^{\mp})$, for both of which $\Lambda_{b}^{0}\rightarrow J/\psi\Lambda$ is used as a normalisation channel.