Analysis of $\Lambda^0_b\rightarrow\Lambda\mu^+\mu^-$ and $\Lambda^0_b\rightarrow J/\psi \Lambda$ decays with the LHCb detector

In this thesis the angular analysis of $\Lambda^0_b\rightarrow\Lambda\mu^+\mu^-$ and $\Lambda^0_b\rightarrow J/\psi\Lambda$ decays is presented, using data from $pp$ collisions recorded by the LHCb experiment between 2011 and 2016, corresponding to an integrated luminosity of approximately 5 fb$^{-1}$. For the $\Lambda^0_b\rightarrow\Lambda\mu^+\mu^-$ decay, the angular observables are extracted at low hadronic-recoil using the method of moments. This is the first time that the complete set of the angular observables has been measured; the results are published in Ref. [1]. A measurement of the angular observables of the $\Lambda^0_b\rightarrow J/\psi\Lambda$ decays is also performed. The angular observables are extracted using a moment analysis; an interpretation of the results in terms of the production polarisation of $\Lambda^0_b$ and the decay amplitudes is also performed. This is the first time that the complete set of the angular observables of the $\Lambda^0_b\rightarrow J/\psi\Lambda$ has been measured; the results are preliminary and correspond to the current status of the analysis.