Searching for new physics in $b\rightarrow sl^+l^-$ transitions at the LHCb experiment

Flavour Changing Neutral Currents are transitions between different quarks with the same charge such as b $\rightarrow$ s processes. These are forbidden at tree level in the Standard Model (SM) but can happen through loop diagrams, which causes the branching ratio of this type of decays to be small, typically $\sim10^{-6}$ or less. Particles beyond the SM can contribute in the loops enhancing the branching fractions of these decays, which are therefore very sensitive new physics. In this work two analysis of semileptonic $b\rightarrow sl^+l^-$ decays are presented. In the first, $\Lambda^0_b\rightarrow \Lambda \mu^+mu^-$ decays are analysed to measure their branching fraction as a function of the square of the dimuon invariant mass, \q$^2$. An angular analysis of these decays is also performed for the first time. Secondly, $B^0 \rightarrow K^{\star 0} l^+l^-$ decays are analysed measuring the $R_{K\star 0}$ ratio between the muon, $B^0 \rightarrow K^{\star 0} e^+e^-$, channels, which is interesting as it is largely free from uncertainties due to the knowledge of the hadronic matrix elements. This thesis is organised in the following way. Chapter 1 introduces the Standard Model and the concept of flavour and explains how rare decays can help us in the quest to find physics beyond the SM. Chapter 2 describes the LHCb detector, which was used to collect the data analysed in this thesis. This chapter also includes studies performed to validate the hadronic physics in LHCb simulation software. Chapter 3 presents the measurement of the differential branching fraction of the $\Lambda^0_b\rightarrow \Lambda\mu^+\mu^-$ decay, while Chapter 4 describes its angular analysis. Finally, Chapter 5 reports themeasurement of the $R_{K\star0}$ ratio. Concluding remarks are given in Chapter 6.