Testing lepton flavour universality with $B^0_s\to\phi\ell^+\ell^-$ decays and angular analysis of the $B^0_s\to\phi e^+e^-$ decay with the LHCb experiment

This thesis describes two measurements of properties of the decay process $B^0_s\to\phi\ell^+\ell^-$, where $\ell^{\pm}$ is either an electron or muon, using data collected by the LHCb experiment. The first is the first measurement of the branching fraction ratio $R_{\phi}=\mathcal{B}(B^0_s\to\phi\mu^+\mu^-)/\mathcal{B}(B^0_s\to\phi e^+e^-)$, in three bins of dilepton mass squared. Such a ratio tests an accidental symmetry of the Standard Model of particle physics, known as lepton flavour universality. This symmetry states that all lepton flavours have equal interaction strengths in the Standard Model, except for effects related to their different masses. The results of the analysis are found to be compatible with lepton flavour universality, which means that the $B^0_s\to\phi e^+e^-$ branching fractions are mostly below the Standard Model expectations, in the same way as those for $B^0_s\to\phi\mu^+\mu^-$. The second measurement is the first angular analysis of the $B^0_s\to\phi e^+e^-$ decay. Angular observables are measured by fitting the angular distribution, in the same three bins of dilepton mass squared as in the measurement of $R_{\phi}$. The measured observables are compared to previous LHCb measurements performed on the muon channel, to further test lepton flavour universality. The results are found to be compatible with the Standard Model as well as with previous measurements of the $B^0_s\to\phi\mu^+\mu^-$ decay. Furthermore, this thesis presents work done towards the commissioning of the upgraded LHCb detector, which was installed between 2018 and 2022. In particular, the thesis focuses on the upgraded vertex locator and muon detectors. Finally, the thesis includes work done as part of the LHCb Early Career, Gender and Diversity office, which aims at the improvement of the working environment of all LHCb members. The author filled the role of Early Career representative for two years, between 2023 and 2025, and has contributed to many activities both within the office and in collaboration with the other main LHC experiments.