Angular analysis $B_s^0\to\phi\mu^+\mu^-$ decays with the LHCb Experiment

This thesis presents an angular analysis of the rare decay $B_s^0\to(\phi\to K^+K^-)\mu^+\mu^-$. The full data set taken at the LHCb experiment during Runs~1 and 2 of the LHC is used to perform this analysis. The angular observables, consisting of four $C\!P$-averages and four $C\!P$-asymmetries, are extracted in four-dimensional maximum likelihood fits to the three decay angles and the reconstructed mass of the $B_s^0$ candidate in regions of the squared invariant dimuon mass ($q^2$). The angular observables are locally consistent with the Standard Model (SM) prediction at the level of $2$ standard deviations ($\sigma$) in each of the $q^2$ regions. This measurement constitutes the most precise determination of the angular observables to date and supersedes the previous measurement performed by the LHCb experiment. The consistency of the measured $C\!P$-averages with the theory prediction is tested by determining a shift in the muonic vector coupling strength $({\Delta \cal R}e ({\cal C}_9))$ from its SM value with a global fit. The data are found to be globally consistent with the SM prediction at the level of $1.9\,\sigma$ but prefer a shift of the muonic vector coupling strength of ${\Delta \cal R}e ({\cal C}_9)=-1.3\,^{+0.7}_{-0.6}$. This deviation is consistent with shifts in other $b\to s\ell^+\ell^-$ transitions.